TR-4423-99-C
June 1999
IR Open-Path Monitoring
Guidance Document
Third Edition
O)
C
1000
2000
3000
-i
Wavenumber (cm )
ManTech Environmental Technology, Inc.
P.O. Box 12313
Research Triangle Park, NC 27709
A ManTech International Company
4000
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Submitted to:
TR-4423-99-03
June 1999
FT-IR Open-Path Monitoring
Guidance Document
Third Edition
by
George M. Russwurm and Jeffrey W. Childers
ManTech Environmental Technology, Inc.
Research Triangle Park, North Carolina 27709
William A. McClenny
Work Assignment Manager
Human Exposure and Atmospheric Sciences Division
National Exposure Research Laboratory
Research Triangle Park, North Carolina 27711
Contract 68-D5-0049
Reviewed and Approved by:
eorge M. Russwurm, Principal Investigator E. Hunter Daughtrey,^., Area Supervisor
ManTech Environmental Technology, Inc.
P.O. Box 12313
Research Triangle Park, NC 27709
A ManTech International Company
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TR-4423-99-03
Foreword
This report presents the results of work performed'by ManTech Environmental
Technology, Inc., under Contract 68-D5-0049 for the Atmospheric Methods and Monitoring
Branch, National Exposure Research Laboratory, U.S. Environmental Protection Agency,
Research Triangle Park, NC. This report has been reviewed by ManTech Environmental
Technology, Inc., and approved for publication. Mention of trade names or commercial
products does not constitute endorsement or recommendation for use.
in
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Preface to the Third Edition
The Fourier transform infrared remote sensing technique for measuring gas
concentrations in the atmosphere has undergone a vigorous growth and development period
over the last 10 years. There seems to be an expanding awareness of the capabilities of this
technique and therefore a continuing demand for a guidance document that is useful to the
people entering the field for the first time. It is our hope that this document will fulfill that
need. The intent of this document is to provide information about the FT-IR technique that will
assist the user in understanding how the system functions.
While there is some difficulty in producing a document that addresses all the questions
operators may have about the FT-IR remote sensing technique, we have tried to include as
much pertinent information as is available at this time. Some of the topics included here are
more rigorous than would at first be deemed necessary. But both authors have come to
understand that the operator should have an in-depth understanding of the instrumentation in
order to make appropriate choices about the data acquisition and processing.
The data that has been used to compile the information in this document was acquired
over a several year period and with several different instruments. We have tried to present
guidance that would be common to all instruments, but in some instances that is not possible.
The judgements included in this document are based on our study of spectra acquired with
high (0.1 25 cm'1) resolution and with low (1.0 cm'1) resolution instruments and with both the
monostatic and the bistatic systems. During the data acquisition phase of this project we also
acquired the ancillary data of relative humidity, temperature, and atmospheric pressure. This
provided us with much of the information necessary to understand the effects of water vapor
on the data and the manufacture of a background spectrum and a water vapor reference.
The document contains 1 2 chapters that we believe address the most important
aspects of atmospheric monitoring with the FT-IR remote sensing technique. As we have
defined this technique, we mean the use of an open-air path up to 1 km long. Chapter 1 2 is
a bibliography that contains more than 330 citations of papers and presentations that describe
the technique. While this is not an exhaustive compilation, it shows that there is a wealth of
information about the use and efficacy of the technique.
The authors wish to emphasize that this document is meant to be a primer for the new
users of the FT-IR remote sensing technique and to give them some guidance in the overall
operation of the instrument. It is not meant to be a standard operating procedure. For that,
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there is an EPA-approved method (compendium method TO-1 6) and also two ASTM methods
that are available. These are cited in the text and in the bibliography.
GMR
JWC
June 1999
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Contents
Foreword iii
Preface to the Third Edition '. . . . v
Figures xi
Tables xv
Acknowledgement xvii
1 Introduction 1-1
1.1 Overview of Document 1-1
1.2 References 1-2
2 The Fourier Transform Spectrometer . . 2-1
2.1 Introduction and Overview 2-1
2.2 The Michelson Interferometer 2-3
2.2.1 Interference 2-3
2.2.2 Resolution 2-7
2.2.3 Throughput 2-8
2.2.4 The Detector 2-8
2.2.5 The IR Source 2-10
2.3 Transfer Optics, Telescopes, and Beam-Return Optics 2-10
2.3.1 Bistatic System 2-13
2.3.2 Monostatic System 2-14
2.4 The Electronics 2-15
2.5 The Computer 2-16
2.6 The Data Output 2-17
2.6.1 Beer's Law 2-17
2.6.2 The Interferogram ., 2-19
2.6.2.1 Truncation 2-19
2.6.2.2 Phase Shift 2-19
2.6.3 The Transform : 2-20
2.6.4 The Single-Beam Spectrum 2-20
2.6.5 Data Analysis 2-21
2.6.5.1 Generation of the Absorption Spectrum 2-21
2.6.5.2 Generation of the Reference Spectrum 2-21
2.6.5.3 Analytical Methods 2-22
2.6.5.3.1 Comparison Technique 2-23
2.6.5.3.2 Scaled Subtraction Technique 2-23
2.6.5.3.3 Multicomponent Analysis Techniques .... 2-24
2.7 References 2-24
3 Initial Instrument Operation 3-1
3.1 Introduction and Overview 3-1
3.2 The Single-Beam Spectrum 3-2
3.2.1 Wave Number Shift 3-4
3.2.2 Change in Resolution 3-4
3.3 Distance to Saturation 3-5
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3.4 Return Intensity as a Function of Distance 3-5
3.5 Determination of the Stray Light Signal 3-6
3.6 Determination of the Random Noise of the System 3-7
3.7- Return Intensity as a Function of Water Vapor 3-10
3.8 References 3-10
4 Background Spectra 4-1
4.1 Introduction and Overview 4-1
4.2 Synthetic Background Spectra 4-3
4.3 Upwind Background Spectra 4-3
4.4 Short-Path Background Spectra 4-4
4.5 Averaged Background Spectra 4-6
4.6 Why Use a Background 4-7
4.7 General Advice About Background Spectra 4-8
5 Water Vapor Spectra 5-1
5.1 Introduction and Overview 5-1
5.2 Water Vapor Spectra Considerations 5-2
5.3 General Process for the Production of a Water Vapor Spectrum 5-2
5.3.1 Selection of Spectra 5-3
5.3.2 Creation of Synthetic Background . 5-3
5.3.3 Creation of the Absorption Spectrum 5-3
5.3.4 Subtraction of the Target Gas 5-4
5.4 Calculated Water Spectra 5-4
5.5 Methane and Ozone Examples 5-5
6 Siting 6-1
6.1 Introduction and Overview 6-1
6.2 Selecting the Path 6-3
6.2.1 The Longest Path 6-5
6.2.2 Shortest Path Requirements 6-5
6.2.3 Short Path Versus Long Path 6-6
6.2.4 Prevailing Winds 6-8
6.2.5 Slant Path Versus Horizontal Path 6-8
6.3 Changing the Path 6-8
6.4 Ancillary Measurements 6-9
6.5 A Specific Case 6-9
6.6 References 6-12
7 Resolution Considerations in Long-Path, Open-Path FT-IR Spectrometry 7-1
7.1 Introduction and Overview 7-1
7.2 Definition of Resolution 7-3
7.3 Trading Rules in FT-IR Spectrometry 7-4
7.4 Example Spectra of CO2 and Water Vapor 7-6
7.4.1 Resolution Effects 7-8
7.4.1.1 Laboratory Measurements 7-8
7.4.1.2 Long-Path Measurements 7-10
7.4.2 Zero-Filling Effects ' . 7-11
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7.4.3 Apodization Effects 7-12
7.5 Effect of Resolution on Quantitative Analyses 7-14
7.5.1 Studies from the Literature 7-15
7.5.2 Case Study: The Effect of Resolution and Related
Parameters on the CIS Analysis of Multicomponent
Mixtures 7-17
7.5.2.1 Mixtures of CO and 13CO 7-18
7.5.2.2 Mixtures of Acetone, Methylene Chloride,
and Ethanol 7-19
7.5.2.2.1 Effect of the Number of Data Points
on the CIS Analysis 7-20
7.5.2.2.2 Effect of S/N Ratio on the CIS Analysis . . 7-22
7.5.2.3 Mixtures of Methylene Chloride and Nitrous Oxide . . 7-22
7.5.2.4 Conclusions and Recommendations Based
on Case Study 7-23
7.6 General Conclusions and Recommendations 7-24
7.7 Guidance for Selecting Resolution and Related Parameters 7-25
7.8 References 7-28
8 Nonlinear Response Caused by Apodization Functions and Its
Effect on FTIR Data 8-1
8.1 Introduction and Overview 8-1
8.2 Procedure and Theoretical Basis 8-4
8.3 Results of Calculations 8-7
8.4 Analysis 8-13
8.5 Discussion 8-17
8.6 Conclusions and Recommendations 8-19
8.7 References 8-20
9 The Technique of Classical Least Squares 9-1
9.1 Introduction and Overview 9-1
9.2 Least Squares Analysis for One Gas 9-1
9.3 Matrices 9-5
9.3.1 Matrix Types 9-5
9.3.2 Some Matrix Properties 9-6
9.3.3 Multiplication of Matrices 9-7
9.3.4 The Identity Matrix 9-8
9.3.5 The Transpose of a Matrix 9-9
9.3.6 The Determinant of a Matrix 9-9
9.3.7 Cofactors of Matrices 9-11
9.3.8 The Inverse of a Matrix 9-11
9.4 Matrices and Algebraic Equations 9-13
9.5 Least Squares and Matrices 9-14
9.6 Expansion to Many Gases 9-18
9.7 Least Squares Errors 9-20
9.8 References 9-21
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10 Quality Assurance and Quality Control 10-1
10.1 Introduction and Overview 10-1
10.2 Project Plan Categories 10-2
10.2.1 Category Definitions 10-3
10.2.2 Category I Points to be Addressed 10-3
10.2.2.1 Project Description 10-4
10.2.2.2 Project Organization and Responsibilities 10-4
10.2.2.3 QA Objectives 10-5
10.2.2.4 Site Selection and Sampling Procedures 10-5
10.2.2.5 Sample Custody 10-6
10.2.2.6 Calibration Procedures and Frequency 10-6
10.2.2.7 Analytical Procedures 10-7
10.2.2.8 Data Reduction, Validation, and Reporting 10-7
10.2.2.9 Internal Quality Control Checks 10-8
10.2.2.10 Performance and System Audits 10-8
10.2.2.11 Preventive Maintenance 10-8
10.2.2.12 Calculation of Data Quality Indicators 10-9
10.2.2.13 Corrective Action 10-9
10.2.2.14 Quality Control Reports to Management 10-9
10.2.2.15 References 10-9
10.2.2.16 Other Items 10-9
10.3 Case Study: QA Data Collected Over Two and One-Half Months
at a Semipermanent Field Site 10-10
10.4 Recommendations of Tests to Be Included in a QA Program
for FT-IR Long-Path Monitors 10-14
10.4.1 Noise Measurements 10-15
10.4.2 Stability of Instrument 10-15
10.4.3 Accuracy and Precision 10-16
10.4.4 Completeness and Representativeness of Data 10-18
10.4.5 Comparability of the Data 10-18
10.4.6 Ancillary Measurements 10-19
10.4.7 Documentation 10-19
10.5 References 10-19
11 Glossary of Terms for FT-IR Open-Path Remote Sensing 11-1
11.1 Introduction and Overview 11-1
11.2 Terms 11-1
11.3 References 11-7
12 Bibliography 12-1
1 2.1 Introduction and Overview 1 2-1
12.2 Publications 12-1
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Figures
Number Page
2-1 A Schematic of the Simplest Form of a Michelson Interferometer 2-4
2-2 Schematic of Interference Created by Division of Amplitude 2-5
2-3 Center Burst Increasing as the Wave Number Range Expands 2-6
2-4 Interferograms for a Range of 3500 cm"1 2-6
2-5 Interferogram of Two Cosine Waves as a Function of AT1 2-7
2-6 The Bistatic Configuration 2-11
2-7 The Monostatic Configuration 2-12
2-8 Data Reduction Flow Chart 2-22
3-1 Single-Beam Spectrum Along a 414-m Path 3-2
3-2 Single-Beam Spectrum Recorded at a 20-m Total Path Length
Indicating Nonlinear Operation 3-3
3-3 Region Between 1000 and 1025 cm"1 3-4
3-4 Subtraction of Spectra for the Determination of Line Shifts and
Resolution Changes 3-5
3-5 Effect of Stray Light 3-7
3-6 The RMS Baseline Noise Measured Between 980 and 1020 cm'1,
2480 and 2520 cm'1, and 4380 and 4420 cm'1 3-9
4-1 Synthetic 70 Spectrum 4-3
4-2 A Possible Configuration for I0 Spectrum Acquisition • 4-4
4-3 Procedure for Acquiring a Short-Path Background Spectrum 4-5
5-1 The Portion of a Single-Beam Spectrum over Which Methane Absorbs 5-5
5-2 Methane Region with Synthetic Background Spectrum Superimposed 5-5
5-3 Methane Reference Spectrum and the Calculated Absorption Spectrum .... 5-6
5-4 Water Vapor Spectrum Made for the Methane Absorption Region 5-6
5-5 Atmospheric Ozone Absorption Spectrum and Ozone
Reference Spectrum ; 5-6
5-6 Ozone Measured at Research Triangle Park During June 5-7
6-1 Sulfur Hexafluoride Reference Spectrum 6-7
6-2 Aerial Photograph of a Superfund Site 6-11
7-1 Single-Beam IR Spectra of CO2 Measured at 0.25-, 0.50-, 1.0-, and
2.0-cm"1 Resolution with No Apodization and No Additional Zero Filling .... 7-7
7-2 Single-Beam IR Spectra of Water Vapor Measured at 0.25-, 0.50-, 1.0-,
and 2.0-cm"1 Resolution with No Apodization and No Additional
Zero Filling 7-7
7-3 Single-Beam IR Spectra of Water Vapor Measured at 2-, 1-, and 0.5-cm'1
Resolution over a 1 50-m Path 7-7
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7-4 IR Spectra of Water ....................................... 7-11
7-5 Absorption Spectra of C02 Measured at 0.25-cm'1 Resolution with a
Zero-Filling Factor of 1, 0.5-cm"1 Resolution with No Zero-Filling, and
0.5-cm"1 with a Zero-Filling Factor of 2 .......................... 7-1 1
7-6 Absorption Spectra of Water Vapor Measured at 0.25-cm"1 Resolution
with a Zero-Filling Factor of 1, 0.5-cm"1 Resolution with a Zero-Filling
Factor of 2, and 1-cm"1 Resolution with a Zero-Filling Factor of 4 ........ 7-12
7-7 Absorption Spectra of CO Measured at a Nominal 0.125-cm"1 Resolution
with No, Triangular, Happ-Genzel, and Norton-Beer-Medium
Apodization Functions ...................................... 7-13
7-8 Absorption Spectra of Water Vapor Measured at 0.5-cm"1 Resolution
with a Zero-Filling Factor of 2 and with No, Triangular, Happ-Genzel,
and Norton-Beer-Medium Apodization Functions .................... 7-13
7-9 Reference 0.25-cm'1 Spectra of 13CO and CO and Spectra of Synthetic
Mixtures of 150 ppm CO and 100 ppm 13CO Measured at 0.25-, 0.5-,
1 .0-, and 2.0-cm"1 Resolution .............. . .................. 7-19
7-10 Concentration Calculated from CLS Analysis vs. Known
Concentration for 13CO/CO Mixtures Measured at 2-cm"1 Resolution ...... 7-19
7-1 1 Reference 0.25-cm"1 Spectra of Acetone, Methylene Chloride, and
Ethanol and Spectra of Synthetic Mixtures of 100 ppm Acetone,
100 ppm Methylene Chloride, and 500 ppm Ethanol Measured at
1 .0-, 2.0-, and 4.0-cm"1 Resolution ............................. 7-20
7-12 Spectra of Synthetic Mixtures of 100 ppm Acetone, 100 ppm
Methylene Chloride, and 500 ppm Ethanol Measured at 1-cm"1
Resolution with 0, 1, 5, 10, and 25% Noise Added ................. 7-22
7-13 Reference 0.25-cm"1 Spectra of N2O and Methylene Chloride and
Spectra of Synthetic Mixtures of 50 ppm N20 and 100 ppm Methylene
Chloride Measured at 0.25-, 0.5-, and 1 .0-cm"1 Resolution ............ 7-23
7-14 Concentration Calculated from CLS Analysis vs. Known Concentration for
N2O/Methylene Chloride Mixtures Measured at 0.25-cm"1 Resolution ..... 7-23
8-1 A Portion of a Water Spectrum Using Boxcar Apodization and
Triangular Apodization ....................................... 8-2
8-2 Schematic of Actual and Assumed FT-IR Responses ................. 8-3
8-3 Measured Concentration of Methane vs. the Experimental Response
of the FT-IR .............................................. 8-7
8-4 Methane Absorbance at 2927 cm"1 ............................. 8-9
8-5 Ammonia Absorbance at 967 cm"1 .............................. 8-9
8-6 Water Absorbance at 1014.5 cm"1 ............................. 8-10
8-7 Methane Absorbance vs. CL at 2927 cm"1 ....................... 8-10
8-8 Ammonia Absorbance at 2927 cm"1 ............................ 8-11
8-9 Water Absorbance vs. P at 1 01 4.5 cm"1 ......................... 8-11
8-10 Water Absorbance for 0.5 torr at 1014.5 cm"1 .................... 8-12
8-1 1 Water Absorbance for 35 torr at 1014.5 cm"1 ..................... 8-12
8-12 Match of Water Absorbance at 1014.5 cm"1 ...................... 8-14
8-1 3 Analysis Results for Methane from 291 5 to 2929 cm"1 .............. 8-16
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8-14 Analysis Results for Methane from 2900 to 3000 cm"1 .............. 8-16
8-1 5 Methane Analysis Allowing the Water Reference Concentration to
Vary .................................................. 8-17
8-16 Plot of Regression Slopes vs. Temperature ....................... 8-18
8-17 Difference After Regression Coefficients Have Been Applied ........ '. . . 8-19
9-1 Least Squares Fit of a Data Set ................................ 9-3
10-1 Return Signal Magnitude of the FT-IR Monitor Measured Daily at
0700 and 1 200 .......................................... 10-11
10-2 The RMS Baseline Noise Measured Between 980 and 1020 cm'1,
2480 and 2520 cm'1, and 4380 and 4420 cm'1 .................... 10-11
10-3 Repeatability of the Position of the Water Vapor Singlet at 1014.2 cm"1
Measured on November 10, 1993, December 22, 1993, and
January 4, 1 994 ......................................... 10-12
10-4 Measurement of Ambient Methane Concentration and Single Beam
Intensity at 987 cm'1 on November 17 and 18, 1993 ................ 10-13
10-5 Peak Area of 2998. 8-cm'1 Absorption Band of CH4 and the 1014.2-cm"1
Absorption Band of Water Vapor Measured on November 17-18, 1993 ... 10-14
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Tables
Number Page
6-1 Estimated Method Detection Limits for Selected Gases 6-4
6-2 Minimum Usable Path Lengths 6-7
7-1 Resolution Test Data 7-6
7-2 Optimal Wave Number Region and Minimum Resolution 7-16
7-3 Effect of the Number of Data Points on the CLS Analysis 7-21
7-4 The Effect of Zero Filling on the CLS Analysis 7-21
7-5 Effect of Noise on the CLS Analysis 7-22
8-1 Maximum Values Over Which Response Can be Considered Linear and
Associate Errors 8-13
9-1 Partial Listing of Spectral Absorbance Data 9-2
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Acknowledgement
There have been many helpful comments and reviews of this document that the
authors have received from many people since the first edition was published. In particular,
we would like to thank the following people. Dr. William Herget (now deceased) reviewed the
original document and the contents of Chapter 8 in this version. Dr. Steven Levine of the
University of Michigan provided much support and an excellent review of an earlier version.
Dr. Peter Griffiths of the University of Idaho provided an excellent and comprehensive review
of the second edition of this document.
Professor Konradin Weber of the Fachhochschule in Dusseldorf, Germany, and a
doctoral candidate, Mr. Alexander Ropertz, provided us with the experimental verification of
the nonlinear response discussed in Chapter 8. Professor Weber was also the first person to
provide us with the information that the detection limits when measured from the actual data
do not seem to change with path length.
Dr. William Phillips of SpectraSoft Technology in Tullahoma, Tennessee, provided us
with much of the mathematical development and some of the software that allowed us to
perform the calculations in Chapter 8.
The authors wish to thank two companies for their support in this endeavor. The
MIDAC Corporation in Irvine, California, provided us with a bistatic system capable of
acquiring data at 0.5-cm"1 resolution. Kayser-Threde Gmbh in Munich, Germany, provided us
with a high-resolution instrument which gave us a great deal of insight about the need for
higher resolution spectra.
We must also express our gratitude to Ms. Janet Parsons for editing this entire
document again. We are convinced that Ms. Parsons has made this document a more readable
document.
Finally, we wish to thank Dr. William McClenny for his support in the preparation of this
work.
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Chapter 1
Introduction
The Michelson interferometer has had
a remarkable history in that new uses for the
deyice have been found for more than
100 years. One use of the interferometer
that has experienced rapid growth since the
mid-1960s is as the main optical component
of Fourier transform infrared (FT-IR)
spectrometers. Although there have been
several applications of FT-IR spectrometers
to unique and difficult problems, the majority
of FT-IR systems have been used to make
qualitative measurements under controlled
conditions in the laboratory. More than
20 years ago, some efforts were made to
use the instrument for making quantitative
measurements of atmospheric gaseous
pollutants over extended open paths (Hanst
1970; Herget and Brasher 1979). Although
these efforts were largely successful, they
were overlooked by the great majority of
people engaged in environmental monitoring.
During the 1 980s there was steady but slow
progress in development of the technique. In
the late 1980s, a revival of the technique
occurred, initiated in part during a meeting of
the Chemical Manufacturer's Association in
Houston (Russwurm and McClenny 1990;
Levine et al. 1991; McClenny et al. 1991),
and today there is a large amount of
developmental activity taking place. (See the
bibliography in Chapter 10.)
This document describes the
components of FT-IR monitors and is
intended to provide guidance for the FT-IR
operator in field monitoring applications. It is
a point of reference for further development
and evaluation of FT-IR open-path monitors
as field instruments.
1.1 Overview of Document
A brief discussion of the FT-IR open-
path monitor and its function is given in
Chapter 2, along with a more in-depth
description of the various components of the
sensor. Chapter 3 includes the preliminary
procedures for setting up the FT-IR
instrumentation for monitoring. Chapter 4 is
a discussion of background spectra, and
Chapter 5 is a discussion of water vapor
spectra. Chapter 6 presents guidance on
how to set up the monitoring instruments
within the physical constraints of a site.
Chapter 7 presents experimental data that
illustrate the effect of resolution and related
parameters on the spectral data. Chapter 8
contains a discussion of the effects of the
apodization function on the FTIR data using
classical least squares analysis. It also
discusses some of the effects due to ambient
temperature. Chapter 9 describes the
classical least squares analysis technique
itself. It starts with a description of a linear
regression for a dependent and one
independent variable and proceeds to the
multiple regression case using matrix
notation. Chapter 10 contains quality control
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TR-4423-99-03
and quality assurance guidelines,
incorporating portions of an approved quality
assurance plan, and includes selected QA
data we collected over a recent one-year
period. Chapter 11 is a glossary of terms,
and Chapter 1 2 is a general bibliography of
work that addresses FT-IR monitoring and
the principles of FT-IR spectrometry.
Each chapter begins with a summary
highlighting the primary contents of the
chapter. This is followed by an introduction
and overview of the chapter.
1.2 References
Hanst, P.L. 1970. Infrared Spectroscopy
and Infrared Lasers in Air Pollution Research
and Monitoring. Appl. Spectrosc. 24:161-
174.
Herget, W.F., and J.D. Brasher. 1979.
Remote Measurement of Gaseous Pollutant
Concentrations Using a Mobile Fourier
Transform Interferometer System.
Opt. 18(20):3404-3420.
Appl.
Levine, S., H. Xiao, W. Herget, R. Spear, and
T. Pritchett. 1 991. Remote Sensing (ROSE)
FTIR. In Proceedings of the 1991 U.S.
EPA/A&WMA International Symposium on
the Measurement of Toxic and Related Air
Pollutants, Air & Waste Management
Association, Pittsburgh, PA, pp. 707-711.
McClenny, W.A., G.M. Russwurm,
M.W. Holdren, A.J. Pollack, J.D. Pleil,
J.L. Varns, J.D. Mulik, K.D. Oliver, R.E.
Berkley, D.D. Williams, K.J. Krost, and
W.T. McLeod. 1991. Superfund Innovative
Technology Evaluation. The Delaware SITE
Study, 1989. U.S. Environmental Protection
Agency, Research Triangle Park, NC.
Russwurm, G.M., and W.A. McClenny.
1990. A Comparison of FTIR Open Path
Ambient Data with Method TO-14 Canister
Data. In Proceedings of the 1990 U.S.
EPA/A&WMA International Symposium on
the Measurement of Toxic and Related Air
Pollutants, Air & Waste Management
Association, Pittsburgh, PA, pp. 248-253.
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Chapter 2
The Fourier Transform Spectrometer
SUMMARY
The major topics discussed in this chapter are the following.
• The basic principles of FT-IR spectrometers
• Resolution and throughput
• Detectors and sources
• Electronics and computer requirements
• The fundamental aspects of the interferogram, the Fourier
transform, and single-beam spectra
• The optics used in long-path, open-path FT-IR monitors
• Transfer optics, telescopes, and beam return optics
• Monostatic and bistatic configurations
• Beer's law and data analysis procedures
2.1 Introduction and Overview
This chapter describes the
components of a complete FT-IR monitoring
system, which include the following: the
FT-IR spectrometer, the transmitting and
receiving optics, the electronics, the
computer, and the data output. The
. discussions in this chapter are based on the
general configurations of instruments that are
commercially available at the time of this
writing. There are currently other
manufacturers with instruments in the design
or developmental stages.
It is not necessary to have a thorough
understanding of the underlying physics
describing how an FT-IR spectrometer
functions to obtain reliable data with a long-
path, open-path FT-IR monitoring system.
However, familiarity with the basic principles
of FT-IR spectrometry is required if proper
operational choices are to be made under
varying field conditions. And, the better the
operator understands the functions of the
instrument, the more likely it is that reliable
data will be produced. This chapter includes
a description of long-path, open-path FT-IR
monitors and an in-depth discussion of the
various components of FT-IR spectrometers.
The integral components of an FT-IR
monitoring system, which include the
interferometer, detector, IR source, transfer
and beam-return optics, electronics, and
computers, are described. The fundamental
processes of FT-IR spectrometry, including
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TR-4423-99-03
the interference phenomenon, generation of
the interferogram, optical throughput,
resolution, and the-Fourier transform, are
explained. A brief discussion of Beer's law
and its application to the data analysis is
provided. In addition to providing quantitative
results, the relationships that are explained
by Beer's law are important when estimating
detection limits and determining optimum
path lengths.
The heart of an FT-IR system is the
interferometer. Most, but not all, commercial
instruments use the Michelson
interferometer. A detailed description of the
Michelson interferometer is provided in
Section 2.2. The trace of the output of the
interferometer is referred to as an
interferogram. The interferogram is the actual
data produced by an FT-IR spectrometer and
contains all of the information about the
spectrum. However, the information
contained in the interferogram is not in a
form that is readily recognizable to most
spectroscopists. To change the data into a
form that is more easily interpretable, the
raw data are converted into a spectrum (a
plot of intensity versus wave number) by
performing a Fourier transform on the
interferogram. A computer system with the
appropriate software packages is used to
apply this and all other necessary
mathematical functions to the data. Although
the execution of these calculations is virtually
invisible to the operator, a basic
understanding of the principles involved is
necessary to ensure that the optimum
parameters are used to collect and process
the FT-IR data.
All quantitative data analysis in long-
path, open-path FT-IR spectrometry is based
on Beer's law. Beer's law states that for a
constant path length, the IR energy
traversing an absorbing medium diminishes
exponentially with concentration.
Mathematically, this is written as
where /0(v) is the intensity of the incident
beam, a(v) is the optical absorption
coefficient of the absorbing material (e.g.,
target gas) as a function of wave number (v),
C is the concentration of the target gas, and
L is the path length.
Two primary configurations, mono-
static and bistatic, are used to transmit the
IR beam along the path, as described in
Section 2.3. The monostatic system has
both the IR source and the detector at one
end of the path and a retroreflector at the
other. The retroreflector returns the beam
either along or collinear to the original path,
which doubles the effective path length and
thus the measured absorbance of the target
gas. The bistatic system has the detector at
one end of the path and the source at the
other. This configuration minimizes the
optical components that are required for
open-path monitoring. However, in the
bistatic system, the IR beam is limited to a
single pass along the path. Both types of
configurations are currently in use for
environmental monitoring.
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2.2 The Michelson Interferometer
The primary optical.component in an
FT-IR instrument is a Michelson
interferometer. It is not generally necessary
to have a fundamental understanding of how
the interferometer functions to obtain reliable
data with an FT-IR instrument. However,
familiarity with some of the aspects of the
interferometer is required if proper
operational choices are to be made under
varying field conditions. To that purpose, a
brief discussion of the optics of the FT-IR
instrument is included in this subsection. The
following major topics are discussed:
interference (Section 2.2.1), resolution
(Section 2.2.2), throughput (Section 2.2.3),
the detector (Section 2.2.4), and the IR
source (Section 2.2.5).
A variety of devices have been used
over the last 200 years to study interference
phenomena. These devices are conveniently
classified by the amount of four primary
attributes that they exhibit: monochrom-
atism, fringe localization, fringe production by
division of wave front or by division of
amplitude, and double or multiple beams. The
interferometric device that today bears his
name was first introduced by A. A.
Michelson in 1881 (Michelson 1881). It is
the most famous of a group of
interferometers that produce interference
fringes by the division of amplitude. 'Four
years after Michelson introduced the
interferometer, it was shown that the Fourier
transform of the interferogram was the
original spectrum or intensity as a function of
wavelength. The Michelson interferometer
has been used to define and measure the
standard meter, to measure the angular
separation of binary stars, and to provide the
experimental data for one of the four
cornerstones of relativity theory. During
recent times, the Michelson interferometer
has been used successfully to measure the
concentrations of various chemicals that
absorb energy in the IR portion of the
electromagnetic spectrum. (See Chapter 10,
Bibliography.) It is currently being developed
as an instrument to make similar
measurements over extended open paths,
and it is in this context that the
interferometer is discussed here.
A schematic of the simplest form of a
Michelson interferometer is shown in
Figure 2-1. It consists of a beam splitter and
two mirrors, one of them movable. The
figure also shows an arrangement for the
light source and the detector. For the most
accurate use, the two mirrors must be kept
perpendicular to one another. One of the two
mirrors moves along the optic axis. During
this motion the perpendicularity cannot
change. This requirement can represent a
stringent limitation for the mechanisms
involved with the motion. The light incident
on the beam splitter should be collimated,
because uncollimated light gives rise to poor
resolution.
2.2.1 Interference
This section is presented for
completeness and because there seems to
be some confusion as to how the
interferogram arises. It is somewhat
2-3
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Moving
Mirror
•a
01
X
Detector
Infrared
Source
Figure 2-1. A Schematic of the Simplest
Form of a Michelson Interferometer.
mathematically rigorous and can be omitted
without jeopardizing the ability of the
operator to obtain reliable FT-IR data.
Interference is the underlying physical
phenomenon that allows a Fourier transform
instrument to obtain spectrometric data. The
interference phenomenon cannot be
physically explained by the simple addition of
the intensities of two or more optical beams.
The amplitudes of the individual interfering
beams must, be added according to the
principle of superposition, and the total
intensity must be calculated from that result.
Interference phenomena are linear in
amplitude. The principle of linear
superposition, which is operating here,
follows directly from Maxwell's equations
and the fact that these equations are linear
differential equations. To arrive at the basic
equation that describes how the Michelson
works, consider the arrangement of
Figure 2-2. A monochromatic electromag-
netic plane wave is incident on a device at A
that divides its amplitude into two
components. After the division, the individual
beams traverse a medium along different
paths and are somehow recombined at a
point P in space. On arrival at point P, the
two beams, which need not be collinear,
have the following amplitudes.
^ _ ^ gi(u/-27M7yA.)
The two A0 terms are the amplitudes
of the individual beams, the co is the angular
frequency of the radiation, n is the index of
refraction of the medium, and the two T
terms are the physical path lengths that each
beam has traversed. The product nT is called
the optical path length that the beam has
traveled. At point P, where the two beams
are recombined, the total amplitude is the
sum of these terms. The intensity is then
given by the product of this sum and its
complex conjugate. Thus the intensity at
point P is given by Equation 2-1 .
(2-1)
The first two terms are the intensities of the
original two beams, and the last two terms
are called the interference terms. When the
amplitudes AQ and A0' are equal, they can be
combined.
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Source
Plane
Wave
Amplitude
Divider
Figure 2-2. Schematic of Interference Created by Division of Amplitude.
Path 1 has physical length 7,, and Path 2 has physical length 72.
By using the relation 2cosx = e" + e*, the
intensity at point P is given by Equation 2-2.
cos
(2-2)
Here 70 is the intensity of either beam.
Thus as the difference of the path length,
T2 - 7,, changes, the intensity at point P can
vary from 0 to 4/0. The fact that/can be 4/0
does not violate the conservation of energy
law. There is no physical requirement that
the intensity at every point in space be 2/0.
The requirement is that the interference term
averaged over space must be zero (Rossi
1957).
When a plane monochromatic wave is
incident on the beam splitter of the
Michelson interferometer, the amplitude
ideally is evenly divided along each leg. At
any position of . the moving mirror, the
detector output is.proportional to the integral
of the intensities over wavelength, and this
recording is called the interferogram. From
Equation 2-2, it is seen that at zero path
(T2 - r, = 0) difference, the cosine term is 1
for all wavelengths. Thus for all
wavelengths, the intensity is 4/0, and the
output of the detector is large compared to
any other mirror position. This is quite
noticeable in the interferogram and is
commonly called the center burst.
This center burst does not appear
when the radiation is monochromatic.
Figure 2-3 shows how the center burst builds
as the wave number range is expanded to
include more wavelengths. The
interferograms in this figure were calculated
from Equation 2-1 in the following way. All
the wave numbers have the same intensity
and add incoherently. The wave number
value was stepped in increments.of 0.1 cm"1.
The retardation (actually, the term T2 - 7,)
was taken in increments of the wavelength
of a He-Ne laser. At each position of the
mirror the proper phase for each wave
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B
D
T
Figure 2-3. Center Burst Increasing as the
Wave Number Range Expands.
number was used to calculate the intensity,
and then the intensities were added. The
interferograms were actually calculated for
6000 incremental movements of the mirror;
however, only a portion of the data is shown
for clarity. The interferograms in Figure 2-3
are for (A) a 2-cm"1range, (B)a 50-cm"1 range,
(C)a 500-cm'1 range, and (D) a 3500-cm"1
range. The two. interferograms shown in
Figure 2-4 are for a range of 3500 cm'1, but
curve B has a 1500.K blackbody radiation
curve superimposed on it, and it appears quite
similar to the interferogram actually recorded
by the FT-IR spectrometers.
Equation 2-2 shows that as the mirror
moves, the path difference causes a
modulation of the intensity at each
wavelength. The modulation can be used to
advantage in open-path FT-IR monitors. For
example, if the IR beam traverses the
interferometer before it is sent along the
open path, any background radiation entering
Figure 2-4. Interferograms for a Range of
3500 cm'1. Interferogram B has a 1500 K
blackbody radiation spectrum
superimposed on it.
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TR-4423-99-03
the system from the surroundings is not
modulated and will not be processed by the
electronics. However, a portion of this
unmodulated light will still be incident on the
detector and in extreme situations could
cause the detector to become saturated.
Therefore, it is prudent to avoid setting the
instrument up along a path that includes
bright (hot) IR sources.
2.2.2 Resolution
The resolution of an instrument
determines how close two absorption
features can be and still be separated enough
for analysis. There are several criteria for this
instrument parameter, but the one most
often used for the FT-IR instrument is
described below. Equation 2-2 shows that all
wavelengths have a maximum and are in
phase with one another at zero, path
difference. The most common definition of
resolution for the FT-IR spectrometer states
that two absorbing features centered at
wavelengths A, and A2 will be resolved if the
mirror moves at least to the point where
these two wavelengths are again in phase.
To determine when this occurs, the following
example may be considered. If only two
spectral features situated at A, and A2 make
up the spectrum, then the interferogram is
made up of two spectra, each described by
Equation 2-2. The result of adding these two
spectra is shown in Figure 2-5 and is given
by Equation 2-3.
Figure 2-5. Interferogram of Two Cosine
Waves vs. AT. The wavelengths differ by
10 cm"1. The minimum occurs when the
two waves are 180° out of phase.
The second cosine term produces a
high-frequency signal that is modulated by a
low-frequency signal described by the first
cosine term. It is the first term that is of
interest when determining the resolution of
the system. The signal is a maximum when
the argument of this cosine term is 2Mi,
where N = 0, 1, 2, ... . Thus, setting n the
index of refraction equal to 1, the first time
that the two wavelengths are in phase after
the center burst is when N - 1, so that
7tA7T.l/A2- I/A,) = 2n
This implies that
A7 = 2/(l/A2-l/A,)
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However, the term in the denominator is the
difference in the wave numbers of the
absorption peaks,.so that AT" = 2/Av. Thus, if
the operator desires a resolution of 0.5 cm"1,
the optical path difference must be 4 cm.
Because the beam traverses the path in the
interferometer twice, the actual motion of the
mirror must be only 2 cm. It should be noted
here that this is an idealized result. The fact
that the interferogram is first truncated and
then apodized changes this result somewhat
(Marshall and Verdun 1990; Beer 1992).
The question of what resolution
should be used for a specific data collection
task is not addressed in this section. It is
discussed in more depth in Chapter 7 and
Chapter 8. The answers to the resolution
questions are specific to the gases to be
monitored and the effects of water vapor in
their regions of absorbance. At the present
time, each monitoring situation must be
considered separately.
2.2.3 Throughput
The throughput of an optical system is
defined as the product of the area of an
aperture A and the solid angle Q of the light
beam at that aperture. This quantity is
theoretically a constant throughout the
system, so that once it is defined for an
aperture it is known for all apertures. For
small angles, the solid angle of the beam can
be shown to be equivalent to the product
ir62, where 6 is the half angle of the field of
view of the instrument. It can be shown that
the throughput is related to the f# of the
system by recognizing that 9 = 1/(2/#), so
that the throughput is equal to An[M(4f#)]2.
With FT-IR instruments, the selection of the
system 1# is generally a compromise. An
important consideration is the solid angle of
the beam as it traverses the interferometer.
A portion of the beam traversing the
interferometer at a large angle will travel
over a longer path through the
interferometer, and a beam traversing at a
smaller angle will travel over a shorter path.
This angular dispersion tends to degrade the
resolution of the instrument, because energy
at the same wavelength appears to the
interferometer as though it covers a range of
wavelengths. Smaller f#s are at first
attractive because they indicate that a
smaller aperture can be used. However,
small f#s imply large solid angles and
therefore a loss in resolution. The
manufacturers of these instruments have
taken this into account in the instrument
design, but nevertheless the aperture size is
fixed, and once a specific instrument is
purchased, there is little, if anything, the
operator can do to change the throughput.
2.2.4 The Detector
The detector in most FT-IR
instruments used for monitoring atmospheric
pollutant gases is a semiconductor device
made of mercury, cadmium, and telluride,
commonly called an MCT detector. There are
three modes of operation for this device, as
a photovoltaic device, as a photoelectro-
magnetic device, and as a photoconductive
device. The MCT photoconductive detector
is the one most often used in the FT-IR
instrument. This device converts a beam of
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TR-4423-99-03
photons to an electrical current that can be
measured. In addition to the spectral region
that the detector responds to, the two most
important parameters of the detector are the
noise equivalent power (NEP) and the
sensitivity of the detector in terms of a
quantity called D* (pronounced "Dee Star").
For an MCT photoconductive device, the
spectral response ranges from 2 to 20 fjm, or
from 500 to 5000 cm'1. The NEP is given in
terms of W/(Hz)'/1. For the detectors used in
FT-IR instruments, this parameter has a value
of about 5 x 10~12 . The user should be
aware that this parameter represents a
measure of the inherent noise in the detector
and that small numbers are better than large
numbers. The D* is a measure of the
sensitivity of the detector and has units of
cm(Hz)'/1/W. This number is actually defined
as the ratio of the square root of the detector
area to the NEP, or D* = JA/NEP. For the
MCT photoconductive detectors, this number
is about 5 x 1010 at 10 /urn. Here, larger
numbers are better. However, there is little
that the operator can do about the magnitude
of these parameters once the instrument is
purchased. But if the detector has to be
replaced, some acceptance criteria for the
NEP and the D* should be specified.
There are, in general, two types of
MCT detectors available, wide band and
narrow band. Each has somewhat different
characteristics. Wide band MCT detectors
cut off at around 500 cm"1, whereas the
narrow band MCT detectors cut off near
600 cm"1. For long-path measurements the
region below 722 cm'1 is nearly opaque
because . of absorption by CO2 in the
atmosphere, so a wide band detector does
not offer any real advantages. Also, the D*
for the narrow band detector is 5 to 10 times
higher than that for the wide band detector.
There is also an indium antinomide (In-Sb)
detector that can be used in the higher wave
number region with advantage. One
particular application for using this type of
detector is the measurement of HF.
An important requirement for the
detectors in FT-IR monitoring systems is that
they must be cooled to operate properly.
Liquid nitrogen temperatures (77 K) allow
optimum operation of these detectors.
Currently, two techniques are used to cool
the detector. The first is to place the
detector in a Dewar that uses liquid nitrogen
as a refrigerant. For this mode, a supply of
liquid nitrogen must be available for use in
the field, and the operator must fill the
Dewar periodically. This has not been a
major problem in the past, as the liquid
nitrogen requirement is only a few pints per
day of operation. The second technique to
achieve cold temperatures is with a
cryogenic cooler, such as a Stirling engine, a
Joule-Thompson cooler, or a closed-cycle
helium refrigeration system. In the Stirling
engine, the heat is exchanged through a wall
from the enclosure to cool the gas. Currently,
the major problems with this cooling device
is the mean time between failures is too
short, and these coolers seem to add noise
to the spectra. One-half year of continuous
operation is about the maximum that can be
expected. If unattended operation is a
necessity, the Stirling engine is one choice.
The Joule-Thompson cooler forces dry
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TR-4423-99-03
nitrogen through an orifice, after which it
expands and cools. This device uses
nitrogen, which has to be of high purity, at
the rate of about one 300 size cylinder in
40 h of operation. Other options for
unattended operation are the use of larger
detector Dewars with longer hold times or
devices that automatically refill the detector
Dewar.
2.2.5 The IR Source
All IR sources that are available today
for use with the FT-IR monitor are heated
elements that are open to the atmosphere.
They are resistive devices that radiate
approximately as black body radiators. These
devices operate at a color temperature from
1 200 to 1 500 K. The Wien displacement law
states that the product of the wavelength of
maximum power output and the temperature
of the source, Amaxr, is a constant equal to
0.2987 cm K"1. This indicates that there is an
inverse relation between peak wavelength
and source temperature. Planck's radiation
law shows that there is more energy at all
wavelengths for hotter sources. The ideal
would be a source that is at about 3000 K,
so it would have a peak at about 1.1 //m.
The materials that are necessary to make
such a source have not been available until
now.
Perhaps the most detrimental
characteristic of the available sources is that
they are large compared to the focal length
of the collimating optics. From geometrical
optics, it is clearly seen that the beam can
never be. better, collimated than the angle
that the source subtends at the collimating
optics (lens or mirror). Thus, all available
FT-IR spectrometers have beam divergences
that are too large for the rest of the optics.
This means that retroreflectors or receiving
optics are overfilled, and much of the initially
available energy is lost. Ultimately, this
divergence restricts the path length that can
be used to advantage. Perhaps as further
developments occur, a small hot source will
be developed that will minimize this
difficulty.
2.3 Transfer Optics, Telescopes, and
Beam-Return Optics
There are two primary geometrical
configurations available for transmitting the
IR beam along the path. One is a bistatic
system (Figure 2-6); the other a monostatic
system (Figure 2-7). The monostatic system
has both the IR source and the detector at
the same end of the path, whereas the
bistatic system has the detector at one end
of the path and the source at the other. In
the bistatic system, the optical path length is
equal to the physical path length, whereas in
the monostatic configuration, the optical
path length is twice the physical path length.
In this document, we always refer to the
optical path length. The reflecting optics for
a bistatic FT-IR monitoring system are
relatively straightforward (see Section
2.3.1), whereas the optics in a monostatic
system may include one or more telescopes,
an additional beam splitter, and return-beam
optics. The possible configurations for a
monostatic system are described in
Section 2.3.2.
2-10
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MAP/:
TR-4423-99-03
A)
Detector
Receiving
Optics
» i
i i
IR Path \
-^--v « \
\ * «
* * *
Transmitting
Optics
Interferometer
"*---.
-^"•""" IR
Sou re
B)
Detector
t
Absorbing Medium
X
.-*
IR
Source
....'••••"
Figure 2-6. The Bistatic Configuration.
2-11
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TR-4423-99-03
A)
/
• 1
f f
\
Translating
Retroref lector
*"•"*"»
/ Transmitting IR Pattf
« »
*• \ W.
7 Return IR Path i--**
Transmitting
Optics
Receiving
Optics
Interferomet*
*-&
Detector
;t
^
..-*
-*•*" IR
Source
Absorbing Medium
B)
Retroreflector *
....
4
/
*
*
.—
.'•••""••
4
* **•»*«.*...
** *
IR Path
« .
'-.t
«
•
— A1*-.-
«
*,
..^^
«
t
•
^^"
4
rransmitting/Recetvtng
Optics
^
\
• i
Additional
Beam Splitter
/•
r
Interferometer
-^"- .
**
.-•*
•^•-*" IR
Source
Detector
Figure 2-7. The Monostatic Configuration.
2-12
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There are several types of telescopes
that could be used to transmit and collect the
IR beam. Those in current use are the
Cassegrain and the Newtonian telescopes.
They are optically equivalent, and the only
difference is the placement of the diagonal
mirror that removes the beam from the
telescope. In the Cassegrain, the beam exits
from the end of the telescope, and for the
Newtonian it exits from the side. Optically,
the number of reflections is the same, and
otherthings being equal, the reflection losses
are also essentially the same. The
geometrical configuration for the whole
instrument is slightly different for these two
designs. In one, the overall package enlarges
vertically, whereas in the other it grows
longitudinally. These are minor points as far
as instrument operation is concerned.
In most cases, the beam is expanded
before it is sent along the path, and in
principle there are essentially no size limits.
The physical quantity that is of interest to
the operator is how much of the IR beam is
absorbed by the gases of interest. This is, in
general, very small (about 1 part in a 1000).
This fact is not changed by expanding the
beam. In general, beam expansion allows
more energy to be transmitted along the
path, thereby increasing the overall signal-to-
noise ratio (S/N). There are, of course,
practical limitations to the size of the optics
that can be accommodated.
must reduce the size of the beam so that it
can pass through the system to the detector
without vignetting and also to set the solid
angle of the beam so that the resolution
remains acceptable.
2.3.1 Bistatic System
The bistatic configuration minimizes
the optical components that are required for
open-path monitoring. At the source end of
the path there must be some method for
collimating the beam. This can easily be done
with a mirror shaped as a parabola or one of
the other conic sections. At the receiving end
of the path, a collector, similar in design to
the collimator, may be used to transfer the
beam to the interferometer and the detector.
In commercially available instruments, the
diameter of the collector generally is the
same as that of the transmitter, although
there is no optical necessity for this choice.
There are two configurations that can
be used for bistatic systems. One
configuration places the IR source,
interferometer, and transmitting optics at one
end of the path and the receiving optics and
detector at the other end (Figure 2-6A). The
advantage of this configuration is that the IR
beam is modulated along the path, which
enables the unmodulated background
radiation to be rejected by the system's
electronics.
As a rule, the optics in either system
are reflecting optics rather than refracting
optics to avoid transmission losses. Once the
IR energy has been collected, the optics
The other configuration places the IR
source and transmitting optics at one end of
the path and the receiving optics,
interferometer, and detector at the other end
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TR-4423-99-03
of the path (Figure 2-6B). This is the more
common configuration of bistatic systems in
current use. The -main drawback to. this
configuration is that the IR source is not
modulated before it is transmitted along the
path. Therefore, the system has no way to
distinguish between the active IR source and
the background IR radiation.
Still another version is being tested at
the present time. In this bistatic system the
light source is modulated by some
mechanical means. This configuration
requires a feedback loop to the
interferometer (via radio link or optical cable)
so that proper phasing can be obtained.
Because the IR radiation makes only a
single pass through the optics, less of the
radiation is lost in bistatic systems. Also, this
makes the systems more amenable to
passive measurements, such as emission
measurements or absorption measurements
with a natural background hot source. For
various reasons, this single pass through the
absorbing medium is not seen as a severe
drawback.
Ambient monitoring in confined areas
or rough terrain may pose certain logistics
problems with a bistatic system. One is that
this mode of operation requires two power
sources, one at each end of the path.
Another is that there is only one pass
through the absorbers. The absorbance for
most gases of interest is very small, and for
short paths, as those encountered with
plumes, a single pass through the gas may
be insufficient.
2.3.2 Monostatic System
There are currently two techniques in
use for returning the beam along the optical
path when the monostatic mode is used. One
is to set up an arrangement of mirrors that
translates the beam slightly for its return
path, and another is to place a retroreflector
array at the end of the path. These two
configurations are optically equivalent.
In the first configuration, an optical
system is placed at the end of the path that
/
translates the IR beam slightly so that it does
not fold back on itself (Figure 2-7A). The
receiving end then has a second telescope
slightly removed from the transmitter with
the detector at the primary focus. This
technique circumvents a possible objection to
the second monostatic configuration.
The second configuration for the
monostatic monitoring mode uses the same
telescope for the transmitting and the
receiving optics and uses a retroreflector
array at the end of the beam (Figure 2-7B). A
retroreflector is an arrangement of mirrors
that reflects the beam so that the incident
and reflected directions of propagation are
collinear but opposite to one another. It is
made of three reflecting surfaces that are
mutually orthogonal, such as the floor and
two adjacent walls of a room. It is often
assumed that after reflection the beam
returns along the same path over which it
was transmitted. That is true only in a gross
sense because if the beam is small compared
to the reflecting surfaces, a measurable
translation takes place, and there is always
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TR-4423-99-03
an inversion and a reversion of the beam. In
order to transmit and receive with the same
optics, a beam splitter must be placed in the
optical path. An objection to this
configuration is that the IR energy must
traverse this beam splitter twice, once on the
transmitting end and once on the receiving
end. The most effective beam splitter
transmits 50% of the light and rejects the
other 50%. Thus,, in two passes, the
transmission is only 25% of the original
beam. Because this loss affects the S/N, it
may be a significant drawback of this
configuration of the monostatic mode.
Because of the design of the
orthogonal mirror retroreflector, it is quite
insensitive to small motions such as those
caused by a wind. Retroreflector arrays are
also very easy to align with the
transmitting-receiving telescope, and a few
degrees of misalignment will pose no
problem to the operator. This does not seem
to be the case with the spherical mirror
configuration. Although this arrangement is
also easy to align, it seems somewhat more
sensitive to a small error.
2.4 The Electronics
Ah in-depth discussion of the
electronics of the FT-IR system is beyond the
scope of this document. However, some
points that are of interest to the operator are
covered. The interferogram is in the form of
intensity versus position of the moving
mirror. As the mirror moves, the detector
measures a varying intensity, and this signal
is first amplified and then sent to an analog-
to-digital (A/D) converter for digitization.
There are two important features that pertain
to this digitization process.
The first concerns the dynamic range
of the signal, which can actually be too
large. There must be enough resolution in the
A/D converter so that the least significant bit
can always be reserved for recording the
noise in the system. If this not the case, the
spectrum derived by performing the Fourier
transform on the interferogram will be
distorted. For this reason, most commercially
available instruments today use a 1 6-bit A/D
converter. Higher range converters exist but
the trade-off comes in the noise and the
speed of the device. So a 20-bit converter
may not offer much of an advantage over a
16-bit converter. This means that if the noise
is recorded on the least significant bit, the
highest signal that can be recorded is a
factor of 215 above the noise. This is not
really as high as it seems. For example, if the
noise is about 1 /nV, the largest signal that
can be recorded is about 0.5 V.
The second feature concerns the
amount of data that has to be recorded in
digital form so that the original waveform
can be reproduced. There is some relation
between the rate at which a signal varies and
the number of sampling pulses that are
needed to reproduce it exactly. The sampling
theorem from modern communication theory,
sometimes called the Nyquist theorem,
states that at least 2/m equally spaced
samples are needed each second to
reproduce the waveform without distortion.
Here fm is the maximum frequency
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component that is contained in the original
waveform.
As the mirror of the Michelson
interferometer moves, each wavelength is
modulated at a frequency that is related to
the velocity of the mirror and the particular
wavelength. Since the light must traverse the
distance from the beam splitter to the mirror
twice (down and back) in any one cycle, 2
times the actual velocity can be used for the
determination of the frequency range to
which the electronics must respond. If the
mirror moves at a speed of 1 cm/s and the
wavelength range is from 2.5 /xm to 20 /*m,
then the frequency range is from 8000 Hz to
1000 Hz. Thus, according to the Nyquist
theorem, the digital sampling rate must be at
least 16000 equally spaced samples per
second.
There is also a need for measuring the
position of the mirror and for signaling to the
electronics when to record data. This is done
by using an He-Ne laser. The laser beam is
sent through the interferometer and
modulated in the same way as all other
wavelengths are. The amplifier output is
capacitively coupled to the rest of the
electronics so that the He-Ne interferogram
is an ac signal with negative and positive
parts. The zero crossings of this ac signal are
sensed, and the instrument records a data
point at the zero crossings. Electronically,
zero crossings are easier to detect than
maxima or minima because of the sign
change.
2.5 The Computer
The final requirement for an FT-IR
system is a computer. This discussion is
meant to be a discussion of the minimum
requirements only.
The data storage requirements depend
on the resolution used, and the capacity
must be fairly large if the interferogram is
stored. This requires about 100 kilobytes for
each interferogram recorded at 1-cm'1
resolution, and some means for archiving the
data must be available. Most software
packages that are currently available are
written for Windows'95, so a computer with
a Pentium processor is required. For ordinary
field work at monitoring sites such as
Superfund sites or waste sites, the ideal
system seems to be either a single computer
with the ability to operate in both foreground
and background modes or two
computers—one to control the instrument and
to record the data and the other, a much
more powerful machine, to be used for data
analysis.
In addition to the computer hardware,
a software package is required that will
control the FT-IR system and record either
the interferogram (preferably) or the single-
beam spectrum (Section 2.7.4) produced by
the Fourier transform performed on the
interferogram. There is currently one generic
software package that can be configured for
any of the commercially available FT-IR
systems. Other FT-IR systems use
proprietary software for data collection. In
addition to data collection, the software
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should also provide some means for data
analysis. This is discussed further in
Section 2.6.5.
2.6 The Data Output
This section contains a discussion of
the interferogram generated by the FT-IR
system, the Fourier transform that is applied
to the interferogram, and the single-beam
spectrum into which the interferogram is
transformed. The data reduction process,
starting with the interferogram and ending
with the unknown gas concentration, is
described. A discussion of Beer's law of how
energy diminishes as it traverses an
absorbing medium is presented first.
2.6.1 Beer's Law
The fundamental physical law that is
quoted as the basis for all FT-IR data analysis
is Beer's law (Beer 1852). It states that, for
a constant path length, the intensity of the
incident light energy traversing an absorbing
medium diminishes exponentially with
concentration. Mathematically, this is written
as
v) = I0(v)e
-a(v)CL
(2-4)
where 70(v) is the intensity of the incident
spectrum, a is the optical absorption
coefficient of the gas and is a function of the
wave number v, C is the concentration of the
gas, andZ, is the path length. There are many
possible sets of units for these quantities
that are variously used by the workers in
FT-IR open-path monitoring. Whatever the
set chosen, it must be noted that the product
aCL must be a unitless quantity. Thus, if the
absorption coefficient has units of (cm-atm)'1,
the concentration must be in atmospheres
and the path length must be in centimeters.
One primary difficulty that confronts the user
of FT-IR open-path monitors is determining
the quantity/0. This is discussed in detail in
Chapter 4, Background Spectra.
The mathematical functional form of
Beer's law explains many physical
phenomena. These include atmospheric
pressure as a function of altitude, thermal
expansion of metal rods, radioactive decay,
and the electrical discharge of capacitors, to
name but a few. Although- there is no
physical basis for doing so, in the field of
optical spectroscopy, this functional form is
often stated by using logarithm to the base
10. The available analysis software also uses
logarithms to the base 10. To understand
how the change is to be made, consider the
following.
The fundamental formula is Y = a?.
The problem is to solve this equation for the
quantity X, which is the power that a must
be raised to obtain Y. To solve this, the
concept of logarithms is introduced so that
\oga(Y) =X\oga(a). This is read as "the
logarithm of /to the base a equals Xtimes
the logarithm of a to the base a." By
definition, \oga(a) = 1 so that
X=\oga(Y}
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Logarithms can be determined by using any
number for the base, but only two are
commonly used in the physical sciences.
They are the base 10 and the base e. The
number e is defined as the limit of (1 + MN)N
as N goes to infinity. The number e occurs
naturally in mathematics, and particularly it
occurs naturally in equations like Beer' law.
The question is then how must Beer's law be
written to account for the change to base
10.
The logarithmic form of the equation
Y = c? can be written in any other base b
such that
\ogb(Y) = X\ogb(a)
Solving this for X gives
X = \ogb(X)/\ogb(aJ
Substituting this X into the original equation
gives
\ogb(Y) = \oga(Y)\ogb(a)
In terms of the bases e and 10, this is written
as
Iog10/r; = \OQ,0(e)\ogem
Historically, natural logarithms are
written by using the prefix In, while
logarithms to the base 10 are written with
the conventional log as a designator.
Logarithms to all other bases also use the
convention log as nomenclature, but then the
actual base is specified as a subscript.
If the power of 1 0 is used, Beer's law
is written as follows.
For convenience, the exponential term in this
expression is defined as the absorbance. The
mathematics given here is transparent to the
operator and of little significance throughout
the remainder of this document. However, it
should be noted that when absorbances are
given as numerical values, the logarithm to
the base 10 has been used.
Although most FT-IR workers cite and
discuss Beer's law, it is not directly used.
The absorption coefficient is generally not
known. One implication of Beer's law that is
used is the concept of reciprocity. That is, if
the concentration diminishes by a factor of 2
but the path length increases by a factor of
2, the measurement will yield the same
results. This is not always true, and it is
generally accepted that if the quantity aCL
becomes larger than about 0.1 , the concept
of reciprocity is no longer valid.
Beer's law has been restated so that
it includes many applications, and, as
restated, the law has assumed several other
names, as the Lambert-Beer law or the
Bouguer-Lambert-Beer law, but these other
names are not correctly used. Beer wrote the
law for a purpose other than the way it is
used today. When Beer published his original
work in 1852, he was conducting
experiments designed to measure the
absorption of various materials that were
then being used in the field of photometry.
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His entire endeavor was directed toward
investigating the effects of the thickness of
a material. He therefore did not write the law
in terms of concentration, nor is there any
evidence that he considered the effects of a
changing concentration. The law as used
today, with concentration as an explicit term
in the exponent, seems to have first been
published by B. Walter almost 40 years after
Beer's original work (Walter 1889).
2.6.2 The Interferogram
The primary data produced by an
FT-IR instrument is the interferogram, and it
is the piece of data that should be recorded.
However, the mechanics of the FT-IR
instrument itself can alter the appearance of
the interferogram, and this influence must be
accounted for during data analysis. Two of
these effects, truncation and phase shift, are
discussed below.
2.6.2.1 Truncation
As discussed earlier, the interferogram
is the intensity measured by the detector as
a function of the position of the moving
mirror. It contains all the information about
the spectrum that is familiar to most
operators. In actual operation, the mirror in
the interferometer moves, at most, a few
centimeters and stops and then returns to its
original position. This finite movement
truncates the interferogram at each end. It
can be shown that this truncation actually
limits the sharpness of the absorbing features
that are of interest to the experimentalist.
This is analogous to creating a square wave
from a series of sine and cosine functions.
There it is seen that the higher frequency
components sharpen the edges of the square
wave. The situation with the FT-IR data is
identical. The information at the ends of the
interferogram is really information about the
high-frequency components. A simple
truncation (stopping the mirror motion after
a certain distance) behaves mathematically
as though the interferogram were multiplied
by what is called a boxcar function. That is,
the interferogram is multiplied by a function
that is 1 in a region from mirror position 1 to
mirror position 2 and is zero elsewhere. The
effect of this multiplication is to broaden the
spectral line features. Truncation also causes
a phenomenon called ringing in the wings of
the spectral features. That is, the truncation
of the interferogram adds oscillations into the
wings of the spectral features. These
unwanted features can be removed by
applying an apodization function to the
interferogram prior to the Fourier transform.
There are several apodization functions (see
Filler or Norton and Beer) that can be applied
to the data, but an in-depth description is
beyond the scope of this chapter. They are
addressed briefly in Chapters 7 and 8. The
point is that the operator should be aware of
this effect and that some choices can be
made during data analysis that will affect the
shape and intensity of the spectral features.
2.6.2.2 Phase Shift
A second instrumental effect on the
data that occurs is a shifting in the relative
phase of the wavelength, which is caused by
the optics and the electronics. There are two
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components for each of the wavelengths
whose intensities are added to make up the
interferogram. They are the magnitude of the
intensity and the relative phase. The optics
and the electronics cause slight phase shifts
as the signals are processed, and these are
frequency dependent. The shifts are normally
accounted for when the Fourier transform is
done, but no record of them is saved.
Therefore, if the interferogram is not
recorded, it cannot be retrieved by simply
performing an inverse transform on the
spectrum itself. It is primarily for this reason
that the interferogram should be saved, even
though it is somewhat more costly in disk
space.
2.6.3 The Transform
The transform is performed on the
interferogram by machine and therefore is
done numerically. There are many algorithms
to accomplish this, and which of these is
used in the software provided with the
commercially available instruments is not
known. The mathematical basis for the
transform is described below.
The complex motion of items such as
vibrating strings or drumheads or other
periodically varying quantities can always be
described by a sum of sine and cosine terms
known as a Fourier series. The frequencies in
these terms are called the fundamental
frequencies at which the item or quantity can
vibrate. The actual motion is then a linear
combination of these fundamental
frequencies. When this summing of terms is
done, it is said that a harmonic analysis has
been performed on the original vibratory
motion. A study of such analyses shows that
there-are related pairs of variables such as
time and frequency or position and
momentum. In an analogous manner,
functions can be analyzed, but here the more
general Fourier transform must be used. The
Fourier series is used to describe a periodic
function as an infinite sum of sine and cosine
terms whose frequencies are multiples of
some fundamental. The transform allows the
analysis of nonperiodic functions as an
integral (also a summation) over a continuous
range of frequencies. In one of its forms that
relates time and frequency, the Fourier
transform /^co), a function of frequency, is
related to G(t), a function of time, as is
shown in Equation 2-5. In the present
situation, the function G(t) is the
interferogram produced by the system, and
F(co) is called the single-beam spectrum. The
t in the term G(t) is a dummy variable, but in
this case it is really the position of the
moving mirror from the center burst position.
-T**J
1 I —./ \ -«fl*
= -,—J(7(f)e
dt
(2-5)
2.6.4 The Single-Beam Spectrum
Some of the literature in this field
refers to the single-beam spectrum as the
inverse transform of the interferogram
because the instrument takes the transform
of the incoming signal to start with.
Mathematically, this merely changes the sign
in the exponent of Equation 2-5, which
implies a phase shift in the sine and cosine
terms. The term single-beam spectrum is a
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historical holdover from the time when
spectroscopists used a double-beam
instrument and determined the transmission
directly from a ratiometer in the electronics
of the instrument. The present-day FT-IR
systems do not use a double-beam system,
but some of the terminology remains.
The single-beam spectrum contains all
the information about the absorbing species
of interest. But most workers do not use this
spectrum for any direct data analysis. In
some systems, it is this spectrum that has
been stored on disk. At 1 -cm"1 resolution this
spectrum takes about 35 kilobytes of
memory, which is much less than the
interferogram (100 kilobytes). However,
storage capacity of the computers available -
today makes this a non-issue.
2.6.5 Data Analysis
the interferogram. Although in some cases
the interferogram is analyzed directly to
determine the concentration of the target
gas, more commonly, the interferogram is
automatically converted into a single-beam
spectrum through the numeric process that is
called a fast Fourier transform. A single-beam
spectrum is generated and recorded for each
sampling period. We call this spectrum the
analytical, or field, spectrum. A background
spectrum is generated by one of the methods
described in Chapter 4. Then a transmission
spectrum is obtained by dividing the field
spectrum by the background. The absorption
spectrum is obtained by taking the negative
logarithm of the transmission spectrum. The
absorption spectrum is used for all further
data analysis.
2.6.5.2 Generation of the Reference
Spectrum
The data analysis includes generating
an absorption spectrum from the raw
interferogram data, developing or obtaining
the appropriate reference spectra, and then
applying the chosen analytical method to
determine the concentration of the target
gases. The analytical methods and the
procedures for generating an absorption
spectrum from the interferogram and
reference spectra of the target compounds
are discussed below.
2.6.5.1 Generation of the Absorption
Spectrum
As shown in Figure 2-8, the data
analysis generally starts with the recording of
A reference spectrum is usually
generated by using a high concentration of
gas in a relatively short cell. The cell is
usually at least 1 m long, although multipass
cells with longer path lengths are also used.
A pure sample of gas mixed with an inert
gas, such as nitrogen, is used. The
concentration of gas used to generate the
reference spectrum should yield a range of
absorbance values that match as closely as
possible those expected to be found in
atmospheric measurements. The system can
use a flowing stream of gas, but the total
pressure should be around 1 atm. The
process of producing a reference spectrum is
then the same as outlined above.
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Interferogram
Single-Beam
Spectrum
0 1
Path Difference (cm)
1000 2000 3000 4000
Wave Number (crrr1)
Analytical Spectrum
Generated from Each
Sampling Period
Background Spectrum
Generated as Described
in Chapter 4
Transmission Spectrum =
Analytical Spectrum
Background Spectrum
I
Absorption Spectrum = -In [transmission]
The absorption spectrum is used for all further
data analysis.
Figure 2-8. Data Reduction Flow Chart.
The production of reference spectra is
an exacting undertaking and requires great
attention to the experimental details. It is not
likely that most users of the FT-IR technique
will prepare their own reference spectra.
Reference spectra are currently available
commercially. The National Institute for
Standards and Technology (NIST) has
undertaken the task of producing reference
spectra that are available at a minimal cost.
The investigators can at present (1999) be
contacted at 301-975-3108 or on the
Internet at http://gases.nist.gov.
2.6.5.3 Analytical Methods
After the reference spectra of the
target gases are obtained, the appropriate
wave number region for analysis must be
selected. The selection should be based on
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an examination of reference spectra and the
type of analytical method chosen. Two
issues must be addressed to make this
selection. Ideally, the gas should have a high
absorption coefficient in the selected region,
and the region should be free of absorption
bands from interfering species. If interfering
species are present they must be identified
and accounted for in the analysis methods.
Once an appropriate wave number
region is selected, data analysis can proceed.
The concentration of the unknown gas can
be determined in three general ways, as
described below: the comparison method,
scaled subtraction, and multicomponent
analysis techniques. Each method uses a
reference spectrum of the gas being
investigated.
2. 6. 5. 3. 1 Comparison Technique
One method of determining the
concentration is to measure the absorbance
at a particular wave number and compare it
with the absorbance of the reference
spectrum at the same wave number. Then, if
reciprocity holds (as implied by Beer's law),
the concentration is obtained as follows. The
absorbance (A) is the product of a, the optical
absorption coefficient, C, the concentration
of the gas and L, the path length. Thus A =
aCL and the unknown concentration can be
found from the following expression.
CunkLunk
(2-6)
Solving for the unknown concentration gives
the following.
^unk ~ ^ref^ref^unk ' ^unk^ref (2-7)
This concentration has the same units as the
units of the reference concentration, which
is prepared as described in Section 2.6.5.2.
2.6.5.3.2 Scaled Subtraction Technique
The scaled subtraction technique is
similar in principle to the comparison
technique. This technique is particularly
useful if there are spectral features due to
interfering species that overlap with those of
the target compound. However, for scaled
subtraction to be successful, either the
target compound or the interfering species
should have at least one unique absorption
band. High-resolution data can be used to an
advantage with this technique.
The scaled subtraction can be done as
follows. Most software packages allow two
spectra to be subtracted interactively. In this
case the reference spectrum should be
•subtracted from the analytical spectrum until
the absorption maximum of the band of
interest is zero. Once the subtraction is
completed the software reports a scaling
factor. This factor can be multiplied by the
concentration used to generate the reference
spectrum to obtain the concentration of the
target gas in the analytical spectrum. There
is some operator skill involved in subtracting
spectra interactively; therefore, some
practice in using this technique is
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recommended before the actual field spectra
are measured.
2,6.5.3.3 Multicomponen t A na lysis
Techniques
Multicomponent analysis techniques
can be used to advantage when there are
several target compounds to be analyzed for
and there are several interfering species
present. This is the case often encountered
in open-path FT-IR monitoring, so some type
of multicomponent analysis technique is
generally the preferred method of analysis.
There are several techniques that are used to
perform multicomponent analyses of IR
spectra. Multicomponent analysis techniques
encompass a discipline unto themselves, and
a complete discussion of the various
techniques is beyond the scope of this
document. Chapter 9 includes a discussion of
classical least squares analysis. But this is
intended to be only an introduction. The
reader is referred to an excellent review by
Haaland (1990). The most common
multicomponent analysis method used in
open-path FT-IR monitoring is based on a
classical least squares (CLS) fitting algorithm.
This is discussed below.
The CLS technique performs a linear
regression by using the unknown and the
reference spectra over a wave number
region. The slope calculated in the regression
is then used as a multiplier of the reference
concentration to obtain the unknown. The
ratio of the path lengths must also be
accounted for. Thus if the slope is found to
be 1 and the ratio of the reference path
length to the path length used for the
measurement is 1/10, then the unknown
concentration is 1/10 of the reference
concentration.
The process of using the linear
regression is more suitable than either the
comparison technique or the scaled
subtraction technique because the shape of
one spectrum is compared with the shape of
the reference spectrum. If the correlation
coefficient is also calculated, it gives a
measure of this comparison. There is one
significant problem with this technique that
has generally been overlooked. The
procedures are generally written by assuming
a linear response of the instrument to
changes in concentration. The response is
actually slightly nonlinear, and this
contributes to the overall error in the data.
This topic is discussed in depth in Chapter 8.
2.7 References
Beer, A. 1852. Ann. Physik. 86:78
Beer, R. 1992. Remote Sensing by Fourier
Transform Spectrometry, John Wiley & Sons,
New York.
Filler, A.S. 1964. Apodization and
Interpolation in Fourier Transform
Spectroscopy, J. Opt. Soc. Am. 54: 762
Haaland, D.M. 1 990. Multivariate Calibration
Methods Applied to Quantitative FT-IR
Analyses. Practical Fourier Transform
Infrared Spectroscopy-lndustrial and
Laboratory Chemical Analysis, J.R. Ferrar
and K. Krishnan, Eds., Academic Press, San
Diego, CA, pp. 396-468.
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Marshall, A.G., and F.R. Verdun. 1990. Michelson, A.A. 1881. The Relative Motion
Fourier Transforms in NMR, Optical, and of the Earth and the Luminiferous Ether. Am.
Mass Spectrometry, Elsevier, Amsterdam. J. Sci. 22: 120-129.
Norton, R.H. and Beer, R. 1976, New Rossi, B. 1957. Optics. Addison-Wesley
Apodizing Functions for Fourier Publishing Company, Inc., Reading, MA.
Spectrometry. J. Opt. Soc. Am. 66: 259.
Walter, B. 1889. Ann. Physik (Wiedemann)
36: 502, 518.
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Chapter 3
Initial Instrument Operation
SUMMARY
This chapter offers guidance and recommendations with respect to the initial
tests that should be performed on the FT-IR system to verify that the instrument is
set up to operate properly. Specific areas that are addressed include the following.
• The characteristic features of the single-beam spectrum
• The distance at which the detector is saturated and operating in a nonlinear
fashion
• The return signal intensity as a function of distance
• The uniformity of the IR beam intensity
• The contribution of stray light to the total return signal
• The determination of the system noise
• The effect of water vapor concentration on the return signal intensity
3.1 Introduction and Overview
The assumption made for the
discussion in this chapter is that the
manufacturer has set up the FT-IR and it is
running according to his specifications.
Initially, the setup procedure for each field
study should be the same, although certain
procedural differences are dictated by
specific data requirements.
Before putting the instrument into
continuous monitoring service, the operator
should conduct some initial tests and
determine the following.
• The distance at which the detector is
saturated and operating in a nonlinear
fashion (Section 3.4)
• The return signal as a function of
distance (Section 3.5)
• The stray light inside the instrument
(Section 3.6)
• The uniformity of the beam intensity
(Section 3.7)
The operator should become quite familiar
with the single-beam intensity profile and
with the gross features of the single-beam
spectrum. Beyond that, the operator must
start several control charts that will provide
long-term information about the return
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intensity and the noise levels. Some ancillary
items such as water vapor concentration,
ambient temperature, -and ambient pressure
should also be recorded.
This chapter includes a discussion of
each of these items and also addresses the
items that must be recorded so that
adequate information concerning the long-
term stability of the FT-IR can be obtained.
In addition, some data are presented that
have been recorded by FT-IR instruments in
the past.
The tests outlined in this chapter
should be performed before data are recorded
with the FT-IR monitor. A failure to do so
could result in the acquisition of erroneous
data that could lead to inaccurate
concentration measurements. Many of the
tests involving the initial instrument setup are
similar to those proposed for use in the
routine quality assurance procedures
presented in Chapter 10 of this document.
3.2 The Single-Beam Spectrum
Figure, 3-1 shows a single-beam
spectrum taken with 1-cm"1 resolution. The
total scan time was 5 min and the total path
length was 414 m. The vapor pressure of
water during this measurement was 1 2 torr.
There are several features in the spectrum
that should be noted. First, the regions 1415
to 1815 cm'1 and 3547 to 3900 cm'1 are
where the infrared energy in the beam is
totally absorbed by water vapor. The
operator will notice that, for a given path
length, the width of the region for complete
400 1000 2OOO 3000
Wave Number (cm-')
4000
Figure 3-1. Single-Beam Spectrum Along a
414-m Path. S indicates stray light.
absorption varies as the amount water vapor
in the atmosphere changes from one day to
the next. Also the center of the region
should become somewhat transparent as the
path is made shorter.
The strong absorption in the 2234- to
2389-cm"1 region is due to carbon dioxide,
and the atmosphere in this wave number
region should remain opaque at all times,
even when the instrument is used to monitor
over short paths. The opaque regions should
be flat, and they represent the baseline of
the spectrum. Any deviation from zero in
these regions indicates that something is
wrong with the instrument operation.
However, Figure 3-1 shows these regions to
be elevated. This is due to stray light in the
instrument, and these regions are marked
"S" in the figure.
The operator should pay particular
attention to the spectrum in the region
around 600-700 cm"1. The spectrum below
this wave number region should be flat and
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at the baseline. If the spectrum has an
elevated baseline below the detector cutoff,
in this-example the-650-cm'1-~region, the
instrument may be operating in a nonlinear
manner. If this is the case, the operator will
see what seems like a dip appear as the
retroreflector or source is brought closer to
the FT-IR. An example of this is given in
Figure 3-2 for a single-beam spectrum
recorded at a 20-m path length.
c
a
_
01
c
2000
Wave Number (cm'1)
4000
Figure 3-2. Single-Beam Spectrum Recorded
at a 20-m Total Path Length Indicating
Nonlinear Operation.
When the path is sufficiently long
(200 m and 10 torr H20) or the water vapor
concentration is large, an absorption band
should be noticeable at 2720 cm'1. This peak
is the Q-branch of deuterated water (HDO),
and it is also possible to observe the P and
the R branches.
The spectral region around 3000 cm"1 is
also strongly absorbed by water vapor,
although it is not opaque. The absorption
features .of methane are in this region. This
is also the region of the C-H stretching
frequencies. The atmosphere from 3500 to
3900 cm"1 is opaque, again because of water
vapor. There is still some sensitivity and
therefore an elevated signal return above
4200 cm"1, and this is the region where
hydrogen fluoride is absorbing.
The return beam intensity at
approximately 987, 2500, and 4400 cm"1
should be recorded so as to form a basic set
of data about the instrument's operation.
Along with this, the operator should record
the path length. The total return signal is
dependent on the path length and the
amount of water vapor in the atmosphere.
When using the single-beam spectrum to
gauge how well the instrument is
functioning, the operator should try to select
regions that are not greatly impacted by
water vapor.
Figure 3-3 shows the region between
1000 and 1025 cm'1 enlarged and plotted in
absorbance. The operator should notice that
there are water vapor lines at 1010, 1014,
and 1017 cm"1. These lines will be in every
spectrum as long as the product of the water
vapor concentration and the path length is
large enough. The lines at 1010 and 1017
are actually doublets and cannot be resolved
at 1-cm"1 resolution. The line at 1014.2 cm"1
is a singlet and can be used as a check for
wave number shifts and resolution. A
procedure for doing each of these is given in
the subsections below.
Both wave number shifts and resolution
changes indicate that something has
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1010 1020
Wave Number (cm'1)
Figure 3-3. Region Between 1000 and
1025 cm'1. The line at 1014.2 cm'1 can be
used as a check for wave number shifts and
resolution.
changed in the instrument geometry, and if
these occur they should be discussed with
the instrument manufacturer. A subtle,
apparent wave number shift can be observed
if the atmospheric absorption line used for a
shift determination is an unresolved doublet.
In this case, if one line becomes more
intense with respect to the other, the
envelope peak will appear to be shifted.
3.2.1 Wave Number Shift
To determine whether wave number
shifts have occurred, the operator should
have an absorption spectrum that contains
the water vapor line at 1014.2 cm"1 and one
for which there is no shift present. The
HITRAN database for water vapor is used in
this document as a guide (University of South
Florida 1993), and it positions this water
vapor line at 1014.2 cm"1.
For any particular instrument, the line
assignment may be slightly different
(±0.2 cm"1) because of the instrument's
geometry, but it should not shift in time.
However that may be, it is the responsibility
of the operator to determine precisely where
the water line is and whether shifts occur
with time. The operator may also choose to
determine wave number shifts by using the
HDD lines in the 2720-cm'1 region. This
measurement is somewhat more sensitive to
shifts in the higher wave number (shorter
wavelength) region.
In principle, any absorption or single
beam spectrum can be used as a guide to
determine wave number shifts. There are
two methods available for determining shifts.
The first is simply to compare the positions
of the peaks of the two spectra on the
computer monitor. The second is to subtract
the second spectrum from the first and study
the result. The second spectrum should be
normalized to the first by a simple
multiplication before the subtraction is done,
or the subtraction can be done interactively.
After subtraction, wave number shifts will
result in a curve that appears to be the first
derivative of the line shape. The wave
number where zero amplitude occurs will be
shifted from the original peak wave number
by an amount that is proportional to the
wave number shift. This is shown
schematically in Figure 3r4A.
3.2.2 Change in Resolution
The other possible change that can
occur in the spectra as time passes is a
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Suited
OngiruJ
Figure 3-4. Subtraction of Spectra for the
Determination of (A) Line Shifts and
(B) Resolution Changes.
resolution change in the instrument. If a
change in the resolution has occurred but
there is no peak shift, the result will appear
to have the shape of an 'M' or a 'W,
depending on which spectrum has been
recorded with the largest amount of water
vapor. This is shown schematically in
Figure 3-4B. If there are no changes in the
line, then the result of subtraction will be
random noise.
3.3 Distance to Saturation
One of the early pieces of information
to obtain with an FT-IR monitor is the path
length at which the detector is saturated. As
discussed in Section 3.2, this is easily
noticed by a negative dip in the single-beam
-return in the 650-750-cm'1 region below the
detector cutoff. As the retroreflector or the
light source is brought closer to the detector,
this dip will appear. This response is
opposite to the response that is due to an
absorption feature in the spectrum. This
distance is important because it represents
the minimum path length over which it is
possible to operate without making changes
to the instrument. In the monostatic case, it
is possible to rotate the retroreflector to
lower the return intensity. If necessary, it is
possible to lower the intensity of the FT-IR
instruments by simply using a fine wire mesh
screen to cover the aperture. A plastic
screen should not be used because plastics
have absorption features in the infrared.
To measure this distance, simply move
the light source or the retroreflector away
from . the transmitting telescope until the
negative dip just disappears from the single-
beam spectrum. This distance should be
recorded as the minimum working distance
available without making instrument
changes.
3.4 Return Intensity as a Function of
Distance
Some attempt is made to collimate the
infrared beam before it is transmitted along
the path. It is, however, impossible to
completely collimate the beam because of
the size of the light source. Therefore, most
beams either are always diverging as they
traverse the path or become diverging at
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some point along the path. Once the beam
is bigger than the retroreflector or the
receiving telescope, the return signal should
diminish as the square of the distance. That
is, beyond some distance the signal is
reduced by a factor of 4 when the path
length is doubled. The reason that this return
signal versus distance determination is
necessary is twofold. The first is that the
commercially available instruments that use
the monostatic configuration both have a
stray light signal when the telescope is
blocked. The return beam should never be
allowed to approach this signal. The second
is that at some distance the system noise
will become an appreciable part of the signal,
and -this represents the maximum usable
distance.
To determine the return signal as a
function of distance, the operator must start
with the retroreflector or the light source at
the minimum working distance as determined
above. Then, the operator should move the
light source or the retroreflector back by
some distance and record the signal. This
process should be continued until the signal
level reaches the noise level or just levels off.
It should be noted that the leveling-off effect
can also be caused by the return signal's
reaching the stray light level. These data
should then be plotted and used for quality
assurance/quality control purposes.
3.5 Determination of the Stray Light Signal
The stray light in the instrument can be
measured without regard to the distance to
the light source or the retroreflector. It is not
expected that instruments using the bistatic
configuration will have any measurable stray
-light, but a one-time check is appropriate.
To measure the stray light, the operator must
block the receiving telescope while the signal
is being recorded. It is important to use an
appropriate blocking material to do this. No
surface that can reflect any of the infrared
energy back to the instrument can be used,
nor any material that is transparent. The
best blocking material is a piece of black
cloth such as is used in the construction of a
photographic film changing bag. For systems
that transmit the beam through the
interferometer before transmitting it along
the path, the beam can simply be slewed
away from the retroreflector. This return
signal should be recorded and then plotted on
the graph as return signal versus distance,
discussed above. A record of the stray light
spectrum should be made and compared to
the single-beam spectrum recorded at the
selected working distance.
Stray light inside the instrument can
also be caused by strong sources of IR
energy that are in the field of view of the
instrument. For example, it is possible to
have the sun in the instrument's field of view
during sunrise and sunset. This will probably
give rise to an unwanted signal that actually
comes from reflections inside the instrument.
The stray light actually causes an error
in the determination of the gas
concentrations and must be subtracted from
the data spectra before processing. Thus it
has to be recorded at every monitoring
session and periodically in the case of a
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permanent installation. The effect of stray
light on photometric accuracy is illustrated by
the absorption feature-shown in Figure 3-5.
1.0-
0.5-
1.0
Wave Number
1.0-
0.5-
1.1
B
Wave Number
Figure 3-5. Effect of Stray Light. A. Spectral
feature without stray light. B. Spectral
feature with stray light.
The absorption line in Figure 3-5A has
a transmission of 0.5 at the peak. The base-
line (100% transmission) has unity
amplitude. Now suppose that stray light
exists in the instrument in the amount of
10% of the original return signal. This
means that the baseline goes to an amplitude
of 1.1, but the absorption feature goes to an
amplitude of 0.6, as shown in Figure 3-5B.
Thus the new transmission of the absorption
is 0.6/1.1, and this is not equal to 0.5 but to
0.5454, or is in error by about 9.2%.
Mathematically, this is just verifying
the fact that A/B * (A + C)/(B + C). It
might be questioned whether the effect of
this stray light is offset by the effect of the
air in the interferometer enclosure, which
most likely contains the pollutant gas also.
However, the transmission due to the
gas in the cell is increased from that along
the path in the ratio of the path lengths.
Thus, for our data taken at Research Triangle
Park, NC, along a 414-m path, the ratio of
the path lengths is at most 1/414, and
therefore the additional absorption is
negligible. A more in-depth analysis of the
problems introduced by stray light indicates
that actual line shape distortions may take
place. It is also quite likely that the simple
subtraction of stray light as suggested above
will not remove all the error incurred.
Therefore, all efforts should be made to at
least minimize the amount of stray light
reaching the detector.
3.6 Determination of the Random Noise of
the System
The random noise of the system is
determined from an absorption spectrum
made from two single-beam spectra taken
sequentially. These spectra are to be taken
under the same operating conditions as will
be used for the acquisition of data spectra.
That is, the same acquisition time and path
length should be used for the noise
determination as will be used for data
acquisition. There should be no time allowed
to elapse between the acquisition of the two
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spectra. This determination will be somewhat
dependent on the water vapor concentration
in the atmosphere, so the water vapor
concentration should also be determined.
The use of the word "noise" suggests
a random signal that is primarily produced by
the system electronics. When measurements
are taken in the open air, this may not
exactly be the case. If the period of data
acquisition for the two spectra is long
(because of a large number of scans, for
example), then atmospheric effects may
contribute to the measurement. For that
reason, the wave number regions that are
used for the determination should be
carefully chosen. Three regions are
suggested below, but the low wave number
region may not be suitable in all situations
because of the presence of gases other than
water vapor.
the three regions 958-1008 cm'1, 2480-
2530 cm'1, and 4380-4430 cm'1.
There are several ways that are
described in statistics texts to determine the
noise. We will specify the use of the root
mean square (RMS) deviation as the
appropriate measure of the noise. The first
step is to perform a linear regression over the
wave number region and determine the slope
and the intercept of the line. At each wave
number, the next step is then to calculate
the difference between the calculated line
and the actual ordinate value. The squares
of these differences are then used to
calculate the RMS deviation as is described
below.
To calculate the slope and the
intercept from a linear regression, use the
following expressions.
The actual wave number range over
which the noise should be calculated will
vary with the resolution used. Statistically,
it can be shown that about 98 data points is
an optimum number (Mark and Workman,
1991). For 1-cm"1 resolution, this means
that data should be taken over a 50-cm"1
region.
NUMERA TOR =7V~£ XtYf - £ x£ Y,
DENOMINATORS^, (*,)2-£*,£*,
SLOPE=NUMERA TORIDENOMINA TOR
Once the two spectra have been
acquired, an absorption spectrum should be
made by using one of the two spectra as a
reference or background spectrum. Which
one is used for the background is not
important. The noise is then determined in
INTERCEPT=—(£ Y-SLOPED X)
In this case the Xt values are the wave
numbers and the Yt values are the
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absorbance values at the particular wave
numbers.
The differences are then found as £>, =
Yi - yt , where now the Yt values are
calculated from the line by using the
expression Yt = slope*X( - intercept.
Once this is accomplished the RMS
deviation is determined with the following
expression.
RMSDEVIATION=
D;
N-2
1/2
Mathematical representations of the
RMS deviation vary in what the denominator
is. Quite often the denominator is written
simply as N. The term N-2 is used here
because the slope and the intercept are
calculated from the data. This reduces the
degrees of freedom by 2 and hence the N-2
(see, e.g., Mark and Workman 1991).
Some results of these measurements
are shown in Figure 3-6. The data shown in
the figure were taken over the region
980-1020 cm"1 in order to include the water
vapor peaks at 1014 cm"1. To reduce the
effect of water vapor to a minimum it is
possible to create two spectra by using an
artificial background, subtract the water
vapor of one from the other, and then make
the noise determination.
0.005
0.004 -
0)
tn 0.003 -
O
0.002 -
0.001 -
Date of Measurement
Figure 3-6. The RMS Baseline Noise Measured Between 980 and
1020 cm"1 (•), 2480 and 2520 cm"1 (•), and 4380 and 4420 cm"1 (A).
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3.7 Return Intensity as a Function of
Water Vapor
The return-beam intensity is a function
of the absorption due to water vapor in the
atmosphere. It is therefore a function not
only of the path length but also the water
vapor concentration in the atmosphere. It
must be clear to the operator that relative
humidity is not important in this case and has
no relevance to the FT-IR data, and it is
actually the water vapor partial pressure in
torr that must be used. However, over a
period of one day, the water vapor
concentration may not change very much, so
acquiring a set of data over a range of water
vapor concentrations will take some time.
Some thought must also be given to the
problem of measuring the water vapor
concentration when the temperature is below
freezing. The Smithsonian psychrometric
tables give data to an ambient temperature
of 5 °F, but it is not clear that a simple sling
psychrometer should be used to make the
wet and dry bulb measurements.
The measurements for water vapor can
be made at any place along the path. The
operator should note, however, that some
investigators feel that the concentration of
water vapor-along.the path actually changes.
We have made some measurements with a
sling psychrometer and have not seen any
appreciable changes along the path. We have
seen rather subtle changes in the absorption
due to water vapor from the spectra
themselves. This is most easily noticed if the
subtraction technique is used. For example,
we acquired a set of data taken at 1-min
intervals. After the spectra were converted
to absorption spectra, the first spectrum was
subtracted from the others in order. The
residual water in the spectra indicated that
minor but noticeable changes take place
minute by minute.
3.8 References
University of South Florida. 1993. USF
HITRAN-PC. University of South Florida,
Tampa, FL
Mark, H., and J. Workman. 1991. Statistics
in Spectroscopy. Academic Press, New
York.
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Chapter 4
Background Spectra
SUMMARY
The topics and specific points of emphasis discussed in this chapter include
the following.
• The generation of the transmission spectrum and the absorption spectrum
• The need for a background spectrum and the difficulties in obtaining one
that is adequate
• The methods for generating a suitable background spectrum
• Synthetic backgrounds
• Upwind backgrounds
• Short-path backgrounds
• Averaged backgrounds
• Specific field guidance for measuring the background spectrum
4.1 Introduction and Overview
In current use, long-path, open-path
FT-IR data are obtained from single-beam
measurements. That is, there is no
reference, or background, spectrum taken
simultaneously with the sample spectrum to
null the spectral features due to the
characteristics of the source, beam splitter,
detector, and interfering species in the
atmosphere. To remove these background
spectral features, the single-beam field
spectrum is divided by a single-beam
background spectrum, or I0 spectrum. This
operation (illustrated in Figure 2-8) generates
a transmission spectrum. According to
Beer's law, the absorption spectrum is then
calculated by taking the negative logarithm
of the transmission spectrum. It is the
absorption spectrum that is used for data
analysis.
Ideally, the background spectrum is
collected under the same experimental
conditions as those for the sample spectrum,
but without the target gas or gases present.
However, in the field it is not possible to
obtain the /0 spectrum directly because the
target gas cannot be easily removed from the
atmosphere. This chapter presents a
discussion of the problems associated with
obtaining the 70 spectrum and the methods
that are used to generate a background
spectrum.
There are currently four methods for
obtaining 70: synthetic, upwind, short-path,
and averaged background spectra. Synthetic
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background spectra can be generated by
selecting data points along a single-beam
spectrum and then calculating the high-order
polynomial function that best fits the
selected points or by repeatedly subtracting
the spectral features due to interfering
species from a single-beam spectrum. Both
of these methods can introduce distortions or
spurious features in the actual intensity
profile. Therefore, much care must be taken
when generating synthetic background
spectra.
For short-term monitoring efforts, the
FT-IR path is generally chosen to be
perpendicular to the wind field. If the area of
the emission source is relatively small, a
background spectrum can be acquired along
a path that is upwind from the source.
However, it is difficult to make this type of
measurement frequently if the FT-IR system
has to be moved from one side of the source
area to another. Also, errors may be
introduced in the measurements if the water
vapor in the atmosphere changes
significantly between the times that the
background spectrum and the sample spectra
are acquired.
Another option for obtaining the /0
spectrum is to bring the retroreflector or
external IR source close to the receiving
telescope. This effectively eliminates the
absorption caused by the target gases and
records a true instrument background. One
problem with this method is that the detector
can be saturated at short paths because too
much IR radiation is incident on the detector
element..
When the experimental conditions are
fairly constant over a measurement period, it
is possible-to average several backgrounds
that have been taken over this time. This
average 70 an then be used for the entire data
set for that period. However, most of the
time, the experimental conditions are not
constant enough to perform this type of long-
term averaging. For example, the
concentrations of water vapor, C02, and
gases emanating from other sources are
constantly changing.
The change in water vapor
concentration must be considered the
biggest potential source of error in the
background measurement. This is because
changes in water vapor concentration can
change the curvature of the baseline in the
field spectra. When that happens, the
background spectrum and the field spectra
do not properly match, and errors occur. An
accurate record of the partial pressure of
water vapor should be maintained. These
data should be taken continuously.
Acquisition of the 70 spectrum
represents one of the more difficult tasks in
FT-IR long-path, open-path monitoring.
Currently, there is not a universal method for
obtaining a satisfactory background
spectrum. The method chosen to obtain /0
must be determined on a site-by-site basis.
This chapter includes a rationale for the use
of an 70 spectrum, as well as advice on the
appropriate techniques for generating it.
These techniques are each discussed below.
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4.2 Synthetic Background Spectra
The software that is supplied with the
commercially available instruments has a
routine that allows a synthetic spectrum to
be generated. This is best accomplished by
selecting data points along some original
single-beam spectra and then calculating a
high-order polynomial function that best fits
the selected points. Generally, however, the
individual data points are connected .with
straight line segments, and in most instances
this is satisfactory. Thus, once a single-beam
spectrum is produced, it can be used to
generate a synthetic I0. Synthetic 70 spectra
can be made that cover only selected wave
number regions, or they can be made to
cover the entire wave number region that
the FT-IR uses. An example synthetic
spectrum is shown in Figure 4-1.
Original Spectrum
1000
Wave Number (cm )
Figure 4-1. Synthetic I0 Spectrum. The
peak at 1110 cm"1 has intentionally been
left in as a fiducial point.
Some care must be used when
synthetic 70 spectra are generated so that
distortions are not introduced into the
intensity, function. For this reason, when
data points are selected, they should never
be selected at the peaks or even within an
absorbing feature. The final curve that is
produced must be a smooth function without
artificial dips and peaks and must follow the
baseline of the single-beam spectrum from
which it is made.
It is essentially impossible to
construct a synthetic spectrum in the wave
number regions where water vapor and
carbon dioxide absorb strongly. The
individual lines are overlapping so that it is
very difficult to judge where the background
curve should be set, and in much of the
region there is almost no energy being
returned to the detector. Even at the shortest
path length possible, there are still portions
of the spectrum that are completely
absorbed by the water vapor and the carbon
dioxide. Because of this strong absorption,
these regions of the spectrum are not used in
the data analysis.
4.3 Upwind Background Spectra
For short-term monitoring efforts, the
path is generally set out so as to be
perpendicular to the wind field. If need be,
the operator can change the orientation of
the path so that this geometry is maintained.
If the area of the source is relatively small
and its upwind side is accessible, an upwind
/0 spectrum can be acquired. A usable
background spectrum can also be acquired
by taking data along the side of source. (See
Figure 4-2.) As long as the wind is not
blowing across the source area and
transporting the emissions across the path
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I tun- 'i-j -^j.-i ^=
TR-4423-99-03
used for 70, these spectra should be transport the entire system from one place to
satisfactory. another.
Retroreflector
Path for
I0 Measurements
Prevailing
Wind
J_D
FT-IR Retroreflector
Y— Primary Data Path -*j
Figure 4-2. A Possible Configuration for 70
Spectrum Acquisition.
Another technique for acquiring an
upwind background spectrum is to wait until
the wind shifts so that the path is along an
upwind side of the source. This works well
for isolated sources, but if there are other
places emitting chemicals, then this method
can lead to errors in identifying compounds
and in quantifying just what is.coming from
the source under study.
There are some advantages to taking
true upwind background spectra this way.
First, it is likely that sources are not isolated
and the chemical species of interest are
emanating from several places in the area.
The compounds entering the area being
investigated are thus included in the upwind
background spectrum. If the configuration
can be set up so the side of the source area
can be used, a second retroreflector or IR
source can be used, and the 70 spectrum can
be taken, frequently and without having to
There are also some disadvantages to
this procedure. It is difficult to take upwind
and downwind spectra frequently if the
system has to be moved from one side of the
source area to another. Generally, this type
of spectrum is taken once at the beginning of
the monitoring period and once at the end
(each day).
4.4 Short-Path Background Spectra
Another possible technique for
obtaining the 70 spectrum is to bring the
retroreflector or external IR source close to
the receiving telescope. This effectively
eliminates the absorption caused by the
compounds of interest and records a true
background. This background is called the
short-path 70. If two retroreflectors are
available, this task is fairly easy to perform.
The FT-IR monitor can be pointed first to one
retroreflector and then the other quite easily
with some regularity.
Figure 4-3 presents a procedure for
acquiring a short-path background spectrum.
The recommendation for the frequency of
repeating this procedure is that a background
should be considered valid for no longer than
one day or until there is a major change in
the operational parameters. Although a
short-path background spectrum may be
valid for an extended period, it should be
revalidated on a daily basis. Necessary
checks for a short-path background spectrum
include the following.
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ACQUIRING A SHORT-PATH BACKGROUND SPECTRUM
1. Calculate the required path length for each gas that is being measured.
a. Calculate the absorption coefficient of the gas in the wave number region that is being used
for analysis. From the reference spectrum, obtain the product of the concentration and the
path length used to generate the reference data. Then measure the absorbance of the peak that
is being used for analysis. The absorption coefficient is given by the following.
a=A/CL
b. Estimate the maximum anticipated concentration of the target gas. Express this in the same
units as the concentration of the reference has been expressed (generally, ppm).
c. Set the absorbance to the number that has been experimentally determined from the RMS
noise as an estimate of the lowest possible detection limit for the FT-IR system, for example,
10"*, and use the expression
L = A/aC
to find the path length to be used for the background spectrum.
d. A sample calculation with the toluene peak at 1031.6 cm"1 is given below.
a=A/CL
Read A at 1031.6 as 0.0203.
The CL product = 496 ppm-m
a = 0.0203/496 = 4.1 x 10'5
Estimate the maximum concentration to be 0.050 ppm.
Calculate L:
L =A/aC= 10-4/(0.000041 x 0.050)
or
L = 48.8m
2. Repeat Step 1 for each target gas and set up the retroreflector or light source at the minimum
calculated distance.
3. Take a spectrum at the same resolution as will be used to take data. So that the noise in the data
spectrum will be the predominant source of noise, take the background spectrum for at least 4
times the number of scans used for the data spectrum. (This judgement should be based on the
time involved with taking a spectrum.)
4. Use this spectrum for the background spectrum.
Figure 4-3. Procedure for Acquiring a Short-Path Background Spectrum.
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• Comparison of the curvature of the
baseline in the short-path spectrum
with the curvature of the baseline in the
field spectra
• Inspection of the spectrum for
wavelength shifts and resolution
changes, as discussed in Section 3.2
One difficulty with this procedure is
deciding on an appropriate distance for
placing the retroreflector or external IR
source. One difficulty is that the detector
can easily be saturated when the path length
is too short. However, if the reflector is
placed far enough away to overcome this
problem, then the absorption may become
large enough to be detrimental. Thus, this
distance must be determined for each
instrument at least once. When the detector
is saturated, the signal seems to drop below
zero at the low-wave-number end of the
single-beam spectrum, and the response of
the detector is nonlinear. The retroreflector
or external IR source must be far enough
away so that this dip in the signal strength
disappears. One way to accomplish this is to
reduce the light intensity by rotating the
retroreflector or using wire mesh screens to
attenuate the signal. (See Section 3.3.)
A second difficulty in monostatic
systems is that the retroreflector will subtend
different angles when it is at different
distances. The retroreflector may be the
actual optical field stop of the instrument,
and changing the distance can cause
distortions in the spectrum. When the
distance is increased, the retroreflector
subtends, smaller angles, and the instrument
uses different cones of light. This problem
can be overcome by placing a field stop in
the instrument that uses a smaller field of
view than the smallest anticipated from the
retroreflector. However, that is a job for the
manufacturer because stops cannot be
placed just anywhere in the optical train
without causing other problems
4.5 Averaged Background Spectra
When the experimental conditions are
fairly constant over a measurement period, it
is possible to average several background
spectra that have been taken over this time.
This average 70 can then be used for the
entire data set for that period. Because all
the individual spectra making up the average
should have the same noise and there should
be no other errors, the final error in this
average background should be smaller by a
factor of //V. Here, A/ is the number of
spectra in the average.
However, most of the time the
experimental conditions are not constant
enough to perform the averaging. The water
vapor concentration is changing most of the
time, and so is the concentration of carbon
dioxide. If other sources are in the area, the
concentrations of the gases emanating from
them are not likely to be constant. If any of
these gases are also being monitored, the
use of an average 70 will not give true
absorption spectra for the entire monitoring
period.
Currently, no published data seem to
be available that have been taken over
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periods of more than a few weeks.
Therefore it is not known whether 70 spectra
can be taken over-extended periods, sorted
according to the similarity of conditions, and
then averaged. If this could be done, it might
be possible to acquire a set of 70 spectra that
are universal. The experimenter could use
these as he uses the library of pure
compound spectra. Thus, with 10 torr of
water vapor and a path length of 200 m,
background VII might be used, etc.
Acquisition of the 70 spectrum
represents one of the more difficult tasks
associated with using an FT-IR spectrometer.
Most of the data that have been published
until now has come from short-term
monitoring programs. The 70 spectra that
have been used have been taken at various
times during the days of operation. These
spectra have then been used for the next
series of atmospheric spectra to be analyzed
until the next background is taken. Although
shifts in the wind direction have been used to
determine the need for a new background,
changes in water vapor concentration have
not. Little information has been published on
the stability of the instrument itself or on the
effect of taking a new background after
some instability develops. There is some
evidence that has been derived from bench-
top laboratory work that indicates the I0
should be taken as often as every other
atmospheric spectrum. There is also some
evidence that a single 70 can be used over a
long period of time with no detrimental
effects. Neither of these observations has
been corroborated by any in-depth study of
the background spectra.
The work performed at Research
Triangle Park, NC, indicates that a synthetic
background (70)-spectrum can-be used for
extended periods with some care. After one
year of operation, the 70 spectrum had to be
changed four times. Three times were
caused by instrument component changes,
and only one time did the atmospheric
conditions require a change in 70. That time
the water vapor concentration changed from
23 torr to 9 torr in a 1 5-min period.
Thus, much work is yet to be done in
establishing the appropriate manner and
frequency for acquiring the 70 data.
4.6 Why Use a Background
The primary data that is produced by
an FT-IR is the interferogram. It contains all
the information that is required to obtain the
concentrations of the gases that the
experimenter wants. However, the
information in the interferogram is in a form
that is somewhat cumbersome to most
people that are familiar with spectroscopy.
In addition, the primary physical law that
governs the analysis of the data is Beer's
law, and this is defined in terms of the more
conventional spectra that are familiar to most
people. Thus, with few exceptions, the
interferogram is converted to a single-beam
spectrum via a Fourier transform and divided
by a background, or 70, spectrum to get a
transmission spectrum. This is then
converted to an absorption spectrum by
finding the negative logarithm of the
transmission spectrum. At this point, the
absorption spectrum is compared with the
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absorption spectrum (after it has undergone
the same mathematical processing) of a pure
gas to obtain the concentration.
All this mathematical processing is
performed by computer and therefore is done
numerically with whatever algorithms were
available at the time the analysis software
was written. A relevant question is whether
all the processing is necessary, or if it is
being done merely because it has always
been done that way.
It is likely that most workers would
essentially refuse to work with the
interferogram directly because spectra have
historically been used. However, this does
not seem to be true of the single-beam
spectrum. The single-beam spectrum also
contains all the information about the
concentrations, and it looks like a normal
spectrum. The water vapor and the carbon
dioxide absorption peaks are readily
discernable, and any absorption due to other
gases should also be discernable. Thus, for
identification purposes, using the single-beam
spectrum should not be a problem.
The problem seems to arise when
quantitation is required. If the reference
spectrum were also available in terms of a
single-beam spectrum, a direct comparison
could be made between the data spectrum
and the reference spectrum, but only if the
intensity levels of each were known on some
absolute basis. Beer's law gives no hint of
how the data are to be analyzed in the
absence of an /0 spectrum. It is true that the
single-beam spectrum is recorded with some
intensity level for the ordinate. But unless it
is put on an absolute basis, the single-beam
spectrum alone is not a sufficient piece of
information to determine the transmission
through the atmosphere.
Currently, there does not seem to be
a satisfactory way to use the single-beam
spectrum alone for the final analysis.
4.7 General Advice About Background
Spectra
All of the currently used methods for
generating a background spectrum are
fraught with difficulties. No one method is
generally accepted as the best method for
acquiring a background. It is crucial for the
operator to be aware of the importance of
this spectrum and of two criteria for a valid
background.
1. The background cannot contain any
absorption features due to the target
gas or gases.
2. The background spectrum must be
valid for the time period over which it
is used. .
Although there seems to be agreement that
the first point above is a requirement, no
such consensus has been reached for the
second. The time periods over which single
backgrounds are used by various workers
vary from a day to several months.
However, one point has become clear.
Whenever any optical component (light
source, mirror, window, etc.) is changed in
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s ~ ss 7ai =••=
TR-4423-99-03
the instrument, a new background must be
acquired.
There are few guidelines as to what
represents a valid background spectrum for
the production of accurate data. One point
is that the curvature of the baseline
(maximum intensity) must be quite close to
the curvature of the baseline of the field
spectra.
There are two primary choices for the
background that is to be used with a specific
data set. If the absorbing peaks are narrow,
as they are for methane or hydrogen fluoride,
it is possible to construct a synthetic
background for the analysis. But for broad
absorbing features like those exhibited by
acetone, this is difficult. With broad features,
even small changes in the curvature of the
baseline can produce large errors. In general,
the operator is advised to use a synthetic
background whenever possible. Taking a
short-path background should be considered
only when the absorption feature of the
target gas is very broad. A final reason to
consider the use of a synthetic background is
that it is essentially the only background that
allows actual atmospheric concentrations to
be determined.
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•
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TCFU- ~:~ss~sj. =••==
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Chapter 5
Water Vapor Spectra
SUMMARY
Specific topics that are addressed in this chapter are the following.
• Selection of spectra that can be used for generating a water vapor
reference spectrum
• Creation of the water vapor reference spectrum itself
• Subtraction from the water vapor spectrum all absorption features of
C02, N20, CH4, CO, and the so-called pollutant gases
• Example water vapor spectra for methane and ozone, selected because
they present different problems to the operator
5.1 Introduction and Overview
Water vapor absorption lines are
present in all regions of the mid-IR
wavelength region, as was shown in
Figure 3-1. The water vapor spectrum
interferes with the spectrum of almost every
volatile organic compound in the atmosphere.
Because of this, the absorption features of
water vapor have to be accounted for during
the analysis of field spectra.
Some amount of the water vapor
absorption is accounted for if there is water
vapor absorption in the background
spectrum, as described in the previous
chapter. However, when a synthetic
background is used, all the water will still be
in the field spectrum, and some residual
amount will be there when other
backgrounds are used. It is possible to
account for the water vapor by considering it
as an interfering species in the analysis
package. The software commercially
available for performing a classical least
squares analysis allows the operator to
choose interfering gas species that are
present in the wave number region of
interest. To do this, however, a water vapor
spectrum must be available. Although there
are water vapor spectra available
commercially, they are not suitable for use in
this application because of line shape
differences and other small instrumental
effects, as well as insufficient path length.
This chapter explains how to use field
spectra on site to produce a spectrum of
pure water that can subsequently be used in
the analysis of field spectra. Examples of
water vapor spectra that can be used for the
analysis of methane and ozone are
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discussed, as these gases represent,
perhaps, the extreme challenges that the
operator will encounter.
5.2 Water Vapor Spectra Considerations
Any single-beam spectrum that
exhibits a sufficient amount of water vapor
absorption in the wave number region of
interest can be used for the production of a
water vapor reference spectrum. Spectra
taken at short path lengths or during very dry
periods may not be satisfactory. At
Research Triangle Park, NC, we have seen
the water vapor partial pressure change from
a low of less than 1 torr in the winter to a
high of 28 torr during the summer. Changes
in the water vapor concentration of this
magnitude, along with any instrument
changes, may require that a new water vapor
spectrum be produced. It is the responsibility
of the operator to determine when the water
vapor spectrum has to be remade, and no
hard and fast rules on the frequency for
creating a new spectrum are presently
available. If the error bars of the analysis
increase from one data set to another, a first
step in determining the cause is to compare
the water vapor reference spectrum with the
water vapor in the field spectra.
The primary concern for the
production of a water vapor spectrum is that
the final result must not contain any of the
target gas. If the water vapor spectrum does
contain even a small amount of a target gas,
the analysis will be in error by that amount.
The ease with which the absorption features
of the target gas can be removed from the
water vapor reference spectrum is dependent
on many instrumental factors, and the
process can be quite time-consuming. The
removal of the target gas absorption is done
by subtraction and in some instances
requires great attention to detail.
5.3 General Process for the Production of
a Water Vapor Spectrum
The general procedure that is to be
followed to produce a water vapor reference
spectrum is given below.
1. Select two single-beam spectra that
will be combined into a water vapor
absorption spectrum.
2. Use one of the spectra to create a
synthetic spectrum that is to be used
as the background.
3. Create the absorption spectrum that
is to be used as the water vapor
reference spectrum.
4. Subtract any absorption features that
are known to be present from the
target gas.
5. Analyze a number of the field spectra
for the target gas, using the water
vapor reference spectrum as an
interfering species.
6. Determine if any of the target gas
absorption remains in the water vapor
spectrum.
7. Repeat Steps 4-6 until you are sure
that there is no absorbance due to the
target gases remaining.
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A word of caution is necessary here. If
analysis is to be done for more than one gas,
the synthetic background in Step 2 should be
created for all the gases of interest at the
same time. Otherwise, when the absorption
spectrum is created, some or all of the water
vapor absorbance will disappear. If this
occurs the process has to be started over.
5.3.1 Selection of Spectra
The spectra selected in Step 1 that
are to be used to produce a water vapor
reference spectrum should be taken at the
same resolution as the field spectra. The
water vapor spectrum should have a signal-
to-noise ratio that is the same as or better
than the field spectra. If possible, the water
vapor concentration for these two spectra
should be representative of the water vapor
concentration in the field spectra to be
analyzed. Curvatures and any other special
features of the baselines of these spectra
should be the same as those of the field
spectra baselines over the wave number
regions of interest. If both of these spectra
are closely spaced in time, they should
contain approximately the same amount of
the target gas. The operator should select
spectra at times when a minimum of the
target gas is expected to be present.
However, the operator should be aware that
the target gas will be present in both spectra
and should consider the ramifications of that
fact.
5.3.2 Generation of Synthetic Background
Either of the two spectra selected
above (Step 1} can be used to create a
synthetic background that is then used to
create an absorption spectrum. The synthetic
background must be created over the same
wave number region as will be used for the
final analysis. The wave number region can
be larger than that used for analysis, but it
cannot be smaller. If the two spectra
selected above are closely spaced in time
they will probably both contain approximately
the same amount of the target gas. This will
certainly be the case with methane and
nitrous oxide regardless of the time selected,
but any set of spectra for ozone may have
widely varying absorption due to ozone.
Again, which one of the spectra is used for
the synthetic background generation is
arbitrary. Once the synthetic background
has been prepared, it should be stored with
an appropriate name.
5.3.3 Generation of the Absorption
Spectrum
Use the remaining spectrum (after
Step 2) as the data spectrum and the newly
created synthetic background to create an
absorption spectrum (Step 3). This is done
exactly as all the other absorption spectra
are created. (See Figure 2-8.) At this point
it is not likely that the baseline of the
absorption spectrum is at zero absorbance.
To make the baseline zero, measure the
height of the baseline above zero and simply
subtract that amount from the spectrum.
This completes the process of creating an
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absorption spectrum, and it should be saved
with an appropriate name.
5.3.4 Subtraction of the Target Gas
This step (Step 4) is really an iterative
process. The newly created water vapor
spectrum must be used in the analysis of
other spectra. The results of these analyses
must be examined in an attempt to determine
whether any of the target gas remains. If
some remains, it must be subtracted from
the water vapor spectrum. The process
must then be repeated until the operator is
sure that no target gas absorbance remains.
To analyze the water vapor spectrum,
the operator must process several data
spectra and use the newly created water
vapor spectrum as an interfering species
spectrum. The field spectra to be used
should be chosen so that the target gas is a
minimum. If the analysis shows the target
gas to go through zero and actually become
negative, then the water vapor spectrum still
contains an absorbance due to the target
gas. The negative concentration should be
subtracted from the water vapor reference
spectrum. Some gas concentrations will not
go to zero at any time but will reach a
minimum. This minimum can be set to zero
in some instances, but it should at least be
set to the minimum that the gas is known to
achieve from other sources.
The actual subtraction can be done in
two ways. The first way is to use the
reference spectrum of the target gas and
create a spectrum that represents the
amount of the target gas to be subtracted.
This is done by multiplying the reference
- spectrum by an appropriate factor. This
factor can be calculated by using the
concentration path length product used in the
reference gas and the path length that was
used for data acquisition.
The second way is to do the
subtraction interactively with the software.
In this way, the operator can see the results
of the subtraction directly and has a little
more control of the process. Both
procedures require some practice, and the
operator must be aware that his first attempt
may not be satisfactory.
5.4 Calculated Water Spectra
Some time ago investigators at the Air
Force Geophysics Laboratory in Cambridge,
Massachusetts, compiled a high-resolution
transmission molecular absorption database
for the primary atmospheric gaseous
constituents. This database is known as
HITRAN and contains the data for calculating
a water spectrum. Software has been
developed that allows for the actual
generation of the spectrum, and that
software is called FASCODE. FASCODE
generates a high-resolution spectrum using
Lorentzian line shapes. These calculated
spectra can then be mathematically shaped
to fit the spectra produced by a particular
FT-IR instrument by using the mathematics
described in Chapter 8.
While the software is not readily
available, this procedure has been tested for
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several different resolutions and for several
different FTIR . instruments. It has been
determined that this -procedure works well,
and all of the observable absorption features
are quite accurately reproduced.
The above-referenced mathematical
procedure will probably be used by NIST to
generate lower resolution reference spectra
from the high-resolution spectra that they are
acquiring.
If this procedure can be used, it is
recommended as the method of choice for
the production of a water vapor reference. It
eliminates all of the difficulties described in
the previous sections about having to remove
the .absorptions of the other gases in the
atmosphere. It has a flat baseline, and once
the procedure is determined, a new reference
can be generated in a few minutes' time.
5.5 Methane and Ozone Examples
Figure 5-1 shows the portion of a
single-beam spectrum over which methane
absorbs. The methane concentrations at
Research Triangle Park are generally
measured at about 2.5 ppm. We have seen
methane concentrations as high as about
6 ppm in this area. The spectrum in
Figure 5-1 actually contains water vapor and
methane, although the methane is not very
noticeable. Figure 5-2 has superimposed on
it the synthetic background that will be used
to manufacture an absorption spectrum. The
synthetic background has been raised slightly
above the single beam spectrum for clarity.
•e
W«v» Number (cm-')
Figure 5-1. The Portion of a Single-Beam
Spectrum Over Which Methane Absorbs.
2900
2950
3000
Wave Number (cnr1)
Figure 5-2. Methane Region with Synthetic
Background Spectrum Superimposed.
Figure 5-3 shows the absorption
spectrum that has been made from the two
spectra shown in Figure 5-2. Also shown in
this figure is the methane reference
spectrum. The task is now to subtract out
the methane that is present in this absorption
spectrum. There are two absorption peaks in
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TECHmOHm
TR-4423-99-03
o
o
c
n
a
o
in
a
Methane Reference Spectrum
Absorption Spectrum
2900 2950
Wave Number (cm-1)
3000
Figure 5-3. Methane Reference Spectrum
and the Calculated Absorption Spectrum.
the methane spectrum that are virtually not
impacted by water vapor. They are at
2916.7 and 2926.8 cm'1. The methane
concentration can be calculated from the
peak height of these two peaks. The
concentration path length product of the
reference spectrum is 81 ppm-m. The field
spectrum was taken at a path length of
414 m, so the reference spectrum represents
a concentration of 81/414 = 196ppb. The
measured peak height of the .2926.8-cm"1
line is 0.00771 absorbance units for the
reference spectrum and 0.1069 absorbance
units for the field spectrum. Thus if the
reference spectrum is multiplied by the factor
0.1069/0.00771 = 13.9 it will represent the
same amount of methane as is in the field
spectrum. That is to say that the absorbance
in the data spectrum is indicative of
196 ppb x 13.9 = 2.7 ppm of methane.
After multiplication, the reference can be
subtracted from the field spectrum, and the
methane should be removed from the water
vapor spectrum.
Figure 5-4 shows the spectrum that
has the methane removed and is now usable
as a water vapor spectrum in the region of
the methane absorbance. The operator must
note, however, that many gases other than
methane absorb in this region and, if they are
still in the spectrum, they will cause errors in
the analysis.
_ Water Vapor over Mithane Region
2900 2950
Wave Number (crrr1)
3000
Figure 5-4. Water Vapor Spectrum Made for
the Methane Absorption Region.
Removal of ozone from the water
vapor spectrum is much more difficult,
primarily because the absorption feature is
broad. Figure 5-5 shows an atmospheric
.Q
<
Field Spectrum
Showing Ozone Absorbance
1000
1050
1100
Wave Number (crrr1)
Figure 5-5. Atmospheric Ozone Absorption
Spectrum and Ozone Reference Spectrum.
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ozone absorption spectrum and the ozone
reference spectrum. The slight elevation of
the absorption spectrum in the vicinity of
1050 cm"1 is indicative of an absorbance due
to ozone with a concentration of about
100 ppb. A significant problem with ozone
occurs when the synthetic background is
made. Here the absorption spectrum is so
broad that at least one point in the ozone
spectrum region must be chosen for the
baseline. It is easiest to think that the point
in the center of the spectrum where the
absorbance dips almost to the baseline
should be used. However, the ozone
absorbance does not go to zero at that wave
number. So, a very careful estimate for
where that point should be placed needs to
be made. A difficulty arises that is associated
with the MCT detector, for which there is a
curvature of the baseline in this wave
number region. This means that the baseline
cannot be made by connecting a line
between two points along the curve.
Once the synthetic background has
been made and the operator has an
absorption spectrum, the ozone still has to be
subtracted from it. There is almost no
possibility that the ozone concentration will
actually go to zero at any location but it
should go through a minimum. For areas
such as Research Triangle Park, where the
atmospheric ozone is produced locally and
not transported into the area from elsewhere,
that minimum occurs at about 6:00 in the
morning.
A plot of several days of ozone
concentration taken at Research Triangle
Park during the month of June is shown in
Figure 5-6. The negative values indicate that
there is a significant amount of ozone in the
water vapor spectrum. The question is just
c
o
O
0.08 -
0.06 -
0.04 •
0.02 -
0.00 -
-0.02 -
-O.04 -
-0.06 -
—I—
20
—r—
40
—I—
60
—1—
80
—I—
100
—I—
120
Elapsed Time (hrs)
Figure 5-6. Ozone Measured at Research
Triangle Park During June.
how much to subtract from the spectrum,
because the ozone concentration does not go
to zero. In this area, we are fortunate
because there are other instruments that
make measurements of ozone, and they can
be used to determine the ozone minimum.
Ozone is a criteria pollutant and is also
monitored by the individual states. These
data are generally available as hourly
averages and may be useful to the operator
who is trying to subtract the correct amount
of ozone from the water vapor reference
spectrum.
The operator must be aware that
gases other than methane and ozone must be
subtracted from the water vapor reference
spectrum, even though they are all not
covered here. Certainly the gases C02, N20,
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TCFU- "slssJs^ '•==
itUft: 'it.! -.?• > • ^
and CO must be subtracted from the water
vapor reference. When data are taken at
industrial sites, any gas that is to be
monitored or used as an interfering species
must be subtracted from the water vapor
reference spectrum.
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Chapter 6
Siting
SUMMARY
The topics and specific points of emphasis discussed in this chapter include
the following
• Siting considerations for long-term and short-term monitoring efforts
• Factors to consider when selecting the path
• Short path versus long path
• Prevailing winds
• Slant path versus horizontal path
• What conditions warrant changing the path
• What ancillary measurements are required
• Calculation of the minimum path length required to detect specific
concentrations of selected target gases
• An example of a specific monitoring site
6.1 Introduction and Overview
There are two kinds of monitoring
programs for which siting needs to be
discussed. One is a long-term effort with the
instrument placed in a more or less permanent
position. The second is a short-term program
designed to take data at a site for a period
from a few days to a few weeks. Each of
these situations, while similar, requires
somewhat different thinking to actually site
the instrument. The short-term program is
more flexible in that the path configuration
can be based on the meteorological conditions
at the time of the monitoring program. Long-
term monitoring programs must be designed
to allow for changes in the direction of the
path as dictated by changing meteorological
conditions, or useful data might be lost.
Siting considerations for both situations are
described in this chapter. Criteria for
selecting the path, changing the path, and
choosing the ancillary measurements to
make at a monitoring site are also discussed.
There is little information in the
literature pertaining to the long-term
monitoring program. Even for the short-term
program, the parameters that were
considered in selecting the actual direction
and length of the path have been discussed
in only a cursory manner. A typical
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statement is "The path was set up based on
a knowledge of the prevailing winds." But
what the wind field actually, was during the
observation period or where the prevailing
wind data were taken is almost never
presented. There is a similar lack of
information concerning the selection of the
path length and the partial pressure of water
vapor in the atmosphere. For that matter,
there is almost no discussion in the literature
about how the length of the path is selected.
There are some sophisticated methods
being studied by various groups that use real-
time meteorological data for making decisions
about the path. It seems that these.
techniques are more suited for permanent
monitoring installations and not for short-term
programs such as monitoring at small waste
sites. Under any circumstances these
methods have not been adequately tested,
and an evaluation of these methods is
considered to be beyond the scope of this
document at the present time.
Other ongoing relevant work is being
documented by the U.S. Environmental
Protection Agency, which has prepared a set
of changes to Part 58 of Chapter 1 of Title 40
of the Code of Federal Regulations (40CFR58)
that define the appropriate ambient air
monitoring criteria for open-path (long-path)
monitors (U.S. Environmental Protection
Agency, 1994). These amendments have
been finalized and approved, and they
specifically address the monitoring of the
gases called the criteria pollutants. The
amendments are significant in that they
describe just how the path is to be chosen in
terms of obstructions, height above the
ground, and changes in path height. They
also describe the appropriate positioning of
the path in relation to buildings, stacks, and
roadways.
Several factors must be considered
when selecting the path. These factors
include (1) instrumental parameters, such as
the signal-to-noise ratio (S/N) of the system
and the divergence of the IR beam; (2) the
characteristics of the target gases, such as
concentrations and absorption coefficients;
(3) the presence and concentrations of
interfering species, such as water vapor and
C02; (4) meteorological data, such as wind
direction and speed; and (5) physical
constraints, such as the area of the emission
source, the extent of the plume, and the
availability of suitable sites to accommodate
the instrument and peripherals.
Example calculations using Beer's law
are given in this chapter to illustrate the
minimum path length required to measure a
specific concentration of a target gas. For
example, the minimum path length required
to measure ammonia at a concentration of
10 ppb would be approximately 21 m,
assuming a minimum detection limit of
3 x 10"4 absorbance units, no interfering
species, and a uniform concentration
throughout the path. In contrast, the
minimum path length required to measure
10 ppb of chlorobenzene would be 230 m.
In general, the length of the path must be
chosen to be the minimum length that will
allow the measurement to be made with a
meaningful statistical accuracy.
As an aid to the operator, Table 6-1,
listing minimum detection limits for various
6-2
-------
TR-4423-99-03
gases, is included. The limits in Table 6-1
were calculated by using a minimum
detectable absorbance of 10"3...The units used.
in this table are ppm«m.
An example using a specific Superfund
site is given in this chapter. Procedures are
described for selecting a usable path for a
short-term intensive study.
6.2 Selecting the Path
To select the length and the position of
the path, the investigator must have some
understanding of the ramifications of these
choices. The immediate questions concern
(1) the effect that the path has on the data
that is produced and (2) the procedure that
the operator follows for selecting a path.
Preliminary answers to those questions
are found by referring to Beer's law. But the
complete answers are more complicated.
They include scattering and absorption by
aerosols, the effects of water vapor and
carbon dioxide on the S/N, and spectral
interferences. When measuring plumes of
finite extent, a path longer than the width of
the plume is actually detrimental.
The amendments to 40CFR58 describe
the following considerations for selecting the
path.
• At least 80% of the path must be
between 3 and 15 m above the
ground.
• At least 90% of the path must be at
least 1 m vertically or horizontally
away .from, walls, etc.
• If the path has to be near a building,
then it must be on the windward side
of the building.
• Buildings or other obstructions may
possibly scavenge the gases of
interest. At least 90% of the path
must have unrestricted airflow and be
located away from obstructions so
that it is removed by at least twice
the height that the obstacle protrudes
above the path.
• At least 90% of the path must be at
least 20 m from the drip lines of
trees.
• When monitoring is done for ozone,
90% of the path must be at least
10m from a road that carries fewer
than 10,000 cars a day. This criterion
changes to 250 m for heavily traveled
roads (> 110,000 cars per day).
There are other changes to 40 CFR
Part 58 that are applicable to the use of
FT-IR open-path monitors, but they are for
concerns other than siting. The interested
reader should obtain a copy of 40 CFR Part
58 from the Office of Federal Register,
National Archives and Records Adminis-
tration, Washington, DC. It is also available
in most public libraries.
6-3
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•\i:s:'::s-.'= =
mm
TR-4423-99-03
TABLE 6-1. Estimated Method Detection Limits (MDLs) for Selected Gases1
Compound
acetaldehyde
acetonitrile
acrolein
acrylic acid
acrylonitrile
ammonia
benzene
bis-(2-chloroethyl)ether
bromomethane
1,3-butadiene
2-butanone
carbon dioxide
. carbon disulfide
carbon monoxide
carbon tetrachloride
carbonyl sulfide
chlorobenzene
chloroethane
chloroform
chloromethane
m-dichlorobenzene
o-dichlorobenzene
dichlorodifluoromethane
1,1-dichloroethane
1,2-dichloroethane
1,1-dichloroethene
1,2-dichloroethene
dichloromethane
1,1-dimethylhydrazine
ethylbenzene
ethylene oxide
formaldehyde
hexane
hydrogen chloride
hydrogen fluoride
hydrogen sulfide
isooctane
methane
methanol
methylmethacrylate
nitric oxide
nitrobenzene
nitrogen dioxide
nitrous oxide
ozone
phosgene
phosphine
propionaldehyde
propylene oxide
styrene
sulfur dioxide
sulfur hexafluoride
tetrachloroethene
toluene
1,1,1-trichloroethane
1,1,2-trichloroethane
Class"
caa
caa
pp.caa
caa
pp,caa
PP
pp.caa
pp.caa
pp.caa
caa
pp.caa
ag
pp.caa
cp
pp.caa
caa
pp.caa
pp.caa
pp.caa
pp.caa
PP
PP
PP
pp.caa
pp.caa
PP
pp.caa
pp.caa
caa
pp.caa
pp.caa
caa
caa
caa
caa
caa
caa
ag
caa
caa
pp.caa
cp
ag
cp
caa
caa
caa
caa
caa
cp
tracer
pp.caa
pp.caa
pp.caa
pp.caa
v b
'max
(cm-1)
1761
1463
1730
1726
954
967
673
1138
1306
908
1745
2361
1541
2173
795
2070
740
1288
772
732
1581
749
1161
705
731
869
864
750
2775
2975
3066
1745
2964
2945
4038
1293
2961
3017
1033
1169
1894
1553
1629
2213
1054
849
2326
1762
3001
695
1377
947
915
728
725
742
MDLb
(ppb-m)
2063
8403
1297
639
3398
620
266
2157
11547
1445
1483
637
191
4583
178
240
1341
6744
359
6652
1266
1428
294
2049
1983
1241
5024
1174
1962
2031
987
1248
1023
3164
578
535003
554
1597
1249
1199
4388
852
540
932
2533
318
7699
2305
2838
1720
372
42
708
1632
533
1615
v c
max
(cm-1)
2729
1042
958
1439
971
931
3047
767
2983
1014
1175
668
1527
2112
773
2051
1483
677
1219
1459
784
1462
921
1060
1237
793
1276
909
697
872
2802
1467
2822
3877
1305
2982
1748
1843
1355
1599
1300
1040
1832
992
2992
837
909
615
781
3018
1088
941
MDLC
(ppb-m)
6674
46095
4509 '
1326
4548
718
4449
4372
12455
5719
3224
608
266
5417
1027
330
3980
6871
1927
9517
1305
5142
303
3053
6803
1814
4113
3774
2277
3327
2581
7710
3620
761
2998
5933
1341
6816
1049
742
3946
3971
667
12468
4107
4549
2908
420
2654
3583
1183
7933
6-4
-------
TR-4423-99-03
refi/.-rs-ssT^i -^
/CUfts •i.-J -.=i J ; ^=
TABLE 6-1. Estimated Method Detection Limits (MDLs) for Selected Gases1
Compound
trichloroethene
trichlorofluoromethane
vinyl acetate
vinyl chloride
vinylidene chloride
m-xylenc
o-xylene
p-xylene
Class3
pp.caa
PP
caa
pp.caa
caa
pp.caa
pp.caa
pp.caa
v b
max
(cm'1)
849
846
1225
942
868
768
741
795
MDLb
(ppb-m)
1173
178
688
2824
1669
1601
1070
1765
v c
max
(cm-1)
944
1084
1790
1620
1086
690
2949
2936
MDLC
(ppb-m)
1578
634
1327
3643
2501
3825
5797
3340
MDLs were estimated by using value's of the absorptivity calculated from 1-crrr1 reference spectra with
triangular apodization from a commercially available spectral library and a minimum detectable absorbance of
1 * irj-3.
"Pollutant classification: priority pollutant (pp); criteria pollutant (cp); hazardous air pollutant from the 1990 Clean
Air Act Amendment (caa); atmospheric gas (ag).
"Peak position and MDL for the most intense absorption band.
cPeak position and MDL for the second most intense absorption band in a different spectral region.
6.2.1 The Longest Path
It is possible to determine the
maximum usable path in several ways. One
is to use the noise equivalent power of the
detector as the minimum signal that can be
recorded. Another is to use a minimum S/N
that the operator is willing to accept. Then
if either the noise equivalent power (NEP)
signal or the S/N is known at one distance
and the energy falls off as the inverse square
of the distance, the maximum possible path
can be calculated. Any attempt to actually
do this calculation results in the conclusion
that the maximum path is essentially infinite.
In a practical sense the absorption due
to water vapor will limit the usable path long
before the theoretical limit calculated above
can be reached. The water vapor line at
1014.2 cm"1 has an absorbance of 0.01 at a
total path length of about 30 m when the
water vapor partial pressure is 10 torr. If an
absorbance of 1 is considered the maximum
allowable for this line, then the maximum
usable total path is about 3 km.
The companion to this document
(Russwurm 1997) describes a method for
determining the minimum detection limit for
open-path FTIR systems. It has recently been
shown by investigators in Germany (Dovard
et al. 1 997) that this detection limit does not
vary with path length as is predicted by
Beer's law. This is probably caused by the
variability in the atmospheric constituents
themselves. At any rate, the work by Dovard
et al. implies that a maximum usable path is
more on the order of 400-500 m.
6.2.2 Shortest Path Requirements
The shortest path for various gases can
be calculated from the absorbance measured
in the reference spectra, a knowledge of the
minimum measurable absorbance, and the
assumption that reciprocity holds. To make
this calculation, the operator must have
chosen the wave number region that will be
6-5
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TR-4423-99-03
used for analysis and obtained the
absorbance of the gas from the reference
spectrum over that region. The.operator
must also choose a minimum concentration
that is to be measured. Then, by using the
minimum detectable absorbance, the
minimum path can be calculated as follows.
1. Measure the absorbance at the
appropriate wave number for the
target gas from the reference
spectrum. Record the concentration
path length product at which this
spectrum was taken.
2. Calculate the absorption coefficient a
for this gas by using the following
formula.
CL=Ar/CrLr
where A is the absorbance and CL is
the concentration-path length
product. The subscript r refers to the
reference spectrum.
3. Assume a minimum concentration
that will be measured, and set the
minimum detectable absorbance at
3 times the RMS baseline noise as
measured under normal operating
conditions, for example, 3 x 10~4.
4. Calculate the minimum usable path
(Lm) from
Lm = Am/aCm
where Am is the minimum absorbance
(3 x 10~4) and Cm is the minimum
concentration assumed in Step 3, and
a is the absorption coefficient
calculated in Step 2.
The results of the above calculations
for four different gases are given in
Table 6-2. . - -
6.2.3 Short Path Versus Long Path
As shown in the previous section, the
selection of the path length begins by
calculating the minimum usable length from
Beer's law. If a retroreflector is used, the
physical path can be half the optical path
determined above. This is advantageous
when plumes of finite size are being
measured because the path length may be
chosen close to the physical extent of the
plume.
The length of the path must be
chosen to be the minimum length that will
allow the measurement to be made with a
meaningful statistical accuracy. For the
calculations above, this distance was
determined by using a minimum absorbance
of 3 x 10'4, or about 3 times the best
detection limit that is achievable at the
present time. For homogeneously distributed
gases, the path can be made longer with
some advantage. But for plumes of finite
extent, making the path longer than the
plume is wide would be a detriment and
should not be done. This is because the
measurement actually determines the path
average concentration, and if a portion of the
path has zero concentration, there is a
dilution effect. Another reason for choosing
a path that is as short as possible is that the
effects of spectral interferences will be
minimized.
6-6
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TR-4423-99-03
Table 6-2. Minimum Usable Path LengthsH
Wave
Number CrLr
Gas
p-dichlorobenzene
chlorobenzene
toluene
benzene
(cm'1}
822
1025
1031
1038
Ar (ppm-m) a
0.085
0.0227
0.0203
0.0027
500
170
496
27
1.7 x 10'4
1.34 x 10"4
4.09 x 10"5
1.0 x 10"4
cm
-
(ppb) (m)
10
10
10 '
10
176
223
734
300
* A, = absorbance of the reference spectrum, C,L, = concentration-path length product at
which the reference spectrum was taken, a = absorption coefficient, Cm = minimum
concentration, Lm = minimum usable path length.
A different example can be described
as follows. There are times when a release
of a tracer gas such as SF6 is desirable. The
question is how much must be in the path if
it is to be detected. From Figure 6-1, it is
seen that the absorbance of SF6 at 947 cm"1
is 1.56. The concentration path length is
66 ppm • m. Thus for a working detection
limit of 3 x 10"4 absorbance units and a path
length of 50 m, the minimum average
concentration in the path must be C = A/aL.
The absorption coefficient a is obtained from
a = A/CL = 1.56/66. Thus C= (3 x 10'4 x
66)7(1.56 x 50) = 0.25 ppb. It is clearly
seen in this example that because of its large
absorption coefficient, not much SF6 is
required for detection. '.
There is no distance with any of the
available instruments that will reduce the
absorption due to water vapor and carbon
dioxide below the detection limits. In fact, in
the wave number region of strongest
absorbance for these gases the atmosphere
is genera.lly totaljy opaque. That is, there is
so much light being absorbed that none
returns to the detector. These regions are
not usable for data analysis with the FT-IR
systems.
1.71S
0.156
0.000
007 816 924 933 942 950 959 968 976 985
Wave Number (cm-')
Figure 6-1. Sulfur Hexafluoride Reference
Spectrum. (Used with permission of P.L.
Hanst)
For long-term monitoring programs
with permanent installations, the only real
option is to place retroreflectors or light
sources (depending on the instrument
configuration) at various distances and
switch from one to the other periodically or
6-7
-------
TR-4423-99-03
on some predetermined schedule. A
scanning system is available with some
versions of open-path FT--IR-monitors that
facilitates this. Currently, almost no work
has been done to define various lengths for
various conditions. Thus, this chore must be
individually repeated for each monitoring
program.
6.2.4 Prevailing Winds
When using the FT-IR long-path
technique, the operator depends on the wind
to deliver the gases being emitted by a
source to the infrared beam. Knowledge of
the prevailing winds is important when
setting up the path for long-term monitoring
programs, but may be much less important
for short-term programs. Most operators of
open-path monitors have been concerned
with short-term programs and know that the
wind almost never comes from where the
prevailing wind rose predicts. The short-term
program usually demands that the operator
be prepared to change the path configuration
when the wind changes. For either the long-
term or the short-term program, the ideal
situation is to have more than one
retroreflector or light source. This allows the
path direction and length to be changed as
the requirements of the program dictate
without having to transport the instrument
itself.
When emission rates need to be
calculated from data taken with an FT-IR
instrument, the wind direction and speed
must be known. The direction of the path
with respect to the wind must also be
known. A knowledge of the historical
prevailing winds is of little use for this task.
When emission rates are required, the wind
field at the path must be measured directly.
6.2.5 Slant Path Versus Horizontal Path
Path orientation is important because
the wind is the primary mode of
transportation of the gases being monitored.
Wind speed and direction can change
dramatically over small regions when
measured close to the ground. This is true
not only because of the changing terrain but
also because the motion of the air (a wind)
must at least approach zero at the surface.
There is some indication that the
concentration contours of gases become very
complex with altitude, at least in part
because of turbulence. There are no data in
the FT-IR literature that describe the variation
of concentration with altitude. Because of
these uncertainties, a comparison of the use
of a slant path and a horizontal path cannot
be made.
6.3 Changing the Path
The beginning of this chapter included
a discussion of some of the ramifications of
path selection. The question here is when
should the path length or direction be
changed? Obviously, if the plume from a
point source or an area source is being
monitored and the wind changes direction,
the path should be changed. Changing the
path, however, should be done in accordance
with some plan. Items that need to be
covered in the plan include the conditions
6-8
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TCfU r~s75s~si ~.^=
ItUtl- -i-J -.-i * : ^=
TR-4423-99-03
that make a change necessary, as described
above. They should also consider the
ramifications of the change, both -the
advantages and the disadvantages. For
example, if the concentrations of gases
crossing a fence line are being monitored,
there is iittle point in changing the direction
of the path.
Change in the length of the path
should be considered only for purposes of
taking a background spectrum or when
spectral interferences from compounds like
water vapor become so strong that the
absorption due to the target compounds is
overwhelmed. Whether any accurate
monitoring can be done under that condition
has not been studied. Certainly, it makes no
sense to reduce the path length to the point
where the target compounds cannot be
monitored.
6.4 Ancillary Measurements
There are several reasons why some
ancillary measurements must be made when
taking data with an FT-IR open-path sensor.
One is the requirement to take data that can
be used for quality control and quality
assurance purposes. (See Chapter 10 for a
discussion of quality control and quality
assurance procedures.) Another is that many
programs will require ancillary data such as
wind speed and direction. Also, for the
foreseeable future, the amount of water
vapor in the atmosphere should be monitored
because too many unanswered questions
about water vapor exist. By far, water vapor
represents the strongest spectral
interference, and unless it is measured
separately, problems may arise when the
data are analyzed. It should be noted that a
measurement of relative humidity is not
satisfactory for this work. The actual partial
pressure of water vapor must be found, and
if relative humidity is measured, then the
temperature must also be measured. The
ambient pressure should also be recorded.
At any one monitoring location operators can
expect to experience a small change in
ambient atmospheric pressure. In some
cases, the data may have to be corrected for
these changes. However, when acquiring
data in places of high altitude, such as
Denver, CO, a substantial change in pressure
can be expected when compared to sea
level. The operator must determine whether
his experiment demands that these changes
be accounted for in the data.
Guidance for selecting and setting up
the instruments for making meteorological
measurements can be found in a government
handbook (U.S. Environmental Protection
Agency 1989). Although this document
does not directly address the long-path
measurements, it does present useful
information about meteorological
instrumentation and measurements. For the
long-path situation, the only measurements
that should be obtained are probably those at
or along the path itself.
6.5 A Specific Case
The literature offers very little
information about procedures for selecting
the path at any given site. The task is again
6-9
-------
TR-4423-99-03
divided into two parts: (1) selecting a path
or set of paths for long-term monitoring at a
fixed installation and (2) selecting a usable
path for short-term intensive studies. For
this document, we will discuss the latter
case only and do so by presenting a real
case.
Figure 6-2 is an aerial photograph of
a Superfund site undergoing remediation.
The active region of the site is at the middle
left of the photograph. Two large repository
pits can be seen, one in the top middle of the
photograph and the other in the top right.
The former pit has been filled and capped
with dirt while the latter is open and in the
process of being lined. To gauge the size of
the site, note that the vehicles immediately
to the left of the FT-IR monitor are D8
bulldozers.
The site lies between two ridges (not
shown), and the prevailing winds blow along
the valley through the site from upper left to
lower right. The first pit rises sharply from
the active area for about 50 ft, and then the
terrain falls off about 20 ft to the second pit.
The road in front of the FT-IR monitor rises
sharply in front of the second pit. The
surrounding terrain is forest, with the trees
rising about 40 ft above the ground level.
Permission had been obtained to make
measurements with the FT-IR monitor with
the proviso that there would be no
interference with the ongoing remediation.
The FT-IR operators were not given access to
the active area, which was defined as
starting at the buildings in the foreground and
extending to the forested region to the left of
and behind the capped pit. The remediation
operation entailed digging soil from the active
area,- repacking it-in metal drums, and
moving it to the lined pit areas. Fluids that
were encountered in the active area or in old
drums were brought to the settling tanks
seen in the middle of the photograph. The
predominant chemical in the site was the
herbicide Dicamba. Dicamba has a very low
vapor pressure, but two by-products were
thought to be present. They were
benzonitrile and benzaldehyde, and the goal
of the FT-IR study was specifically to
measure these two compounds. Funding had
been allocated for one week of field work.
Although the proposed amendments to 40
CFR Part 58 were not available at the time of
this study, they were almost exactly
followed.
Benzonitrile has a single usable
absorption band at 757 cm"1. The
absorbance of this band is 0.0346 when the
concentration-path length product is
186 ppm-m. Repeating the calculation
described above for the absorption
coefficient gives a = 0.0346/186 =
1.9 x 10~4. It was thought that benzonitrile
would have a concentration of about 10 ppb.
At the time of this study, the FT-IR
instrument had a minimum detection limit of
about 1 x 10"3 absorbance units. The
minimum usable path is calculated as
follows.
Lm = 1 x 10'3/{1.9 x 10'4 * 10 x 10'3)
= 525 m
(Eq. 6-1)
6-10
-------
Figure 6-2. Aerial Photograph of a Superfund Site Undergoing Remediation.
M
CO
CD
CD
6
CO
-------
TR-4423-99-03
The problem is somewhat more
cqmplicated than this because there is a
weak interfering carbon dioxide peak at
757 cm'1. The task was then to site the
instrument so that the retroreflector could be
placed 250 m away while adhering to the
constraints imposed by the remediation
process. To obtain electrical power without
the use of a generator, the only logical place
to put the FT-IR monitor was at the main
entrance to the site, as it is shown in the
Figure 6-2 photograph. From there, only two
possible paths of 250 m were available.
They are shown in the photograph at the RR
positions. The path that extends from the
FT-IR monitor to the right RR position in the
photograph was selected as the primary path
because this would encompass the entire
plume coming from the active area according
to the prevailing winds. The secondary path,
extending from the FT-IR monitor to the
bottom of the capped repository pit (at the
left RR position), was not really satisfactory
because it rose too high above the ground
level and went directly over the settling
tanks. A path that is too high above the
active area would leave the possibility that
the plume might go under the beam. If the
beam were to go directly over the settling
tanks, flux calculations would be virtually
impossible.
As an aside, during the week-long
field program the remediation process was
halted because of a problem with the lining
of the second pit. Also, during this time, the
wind never blew more than 0.5 mph, and its
direction was almost always from the bottom
to the top of the photograph, contrary to
expectation.
6.6
References
Douard, M., J. Zentzius-Reitz, T. Lamp,
A. Ropertz, and K. Weber. 1997. Quality
Assurance Procedures and Measurements for
Open Path FTIR Spectroscopy Europto
Series. Proceedings of the Envirosense '97
Meeting in Munich, Germany. SPIE
3107:114-125.
Russwurm, G.M. 1 997. Compendium Method
TO-16. Long-Path Open-Path Fourier
Transform Infrared Monitoring of
Atmospheric Gases. In Compendium of
Methods for the Determination of Toxic
Organic Compounds in Ambient Air, Second
Edition, EPA/625/R-96/01 Ob, U.S.
Environmental Protection Agency, Research
Triangle Park, NC.
U.S. Environmental Protection Agency.
1989. Quality Assurance Handbook for Air
Pollution Measurement Systems, Vol. IV -
Meteorological Measurements. U.S.
Environmental Protection Agency, Research
Triangle Park, NC.
U.S. Environmental Protection Agency.
1994. Ambient air quality surveillance siting
criteria for open path analyzers (proposed
rule). Fed. Reg. 59(1 59):42541-42552.
6-12
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TR-4423-99-03
- 'if -.- - •
Chapter 7
Resolution Considerations in FT-IR Long-Path, Open-Path Spectrometry
SUMMARY
The topics and specific points of emphasis discussed in this chapter include
the following.
• The definition of resolution in FT-IR spectrometry
• The trading rules between resolution, the signal-to-noise (S/N) ratio, and
measurement time
• Example spectra of atmospheric constituents and selected VOCs that
illustrate the following effects.
• Effect of resolution on peak shape and intensity
• Effect of apodization and zero filling on peak shape and intensity
• A discussion of the effect of resolution on quantitative analysis
• A case study illustrating the effects of resolution, zero filling, and baseline
noise on the CLS analysis of multicomponent mixtures
7.1 Introduction and Overview
One important issue regarding the use
of long-path, open-path FT-IR systems for
monitoring hazardous air pollutants is the
appropriate spectral resolution to be used
during data acquisition. A resolution should
be chosen to maximize the ability to resolve
spectral overlap while maintaining a balance
between the S/N, analysis time, and data
storage requirements. Several factors must
be considered when determining the optimum
resolution for measuring the IR spectra of
atmospheric constituents along an open long
path. These factors include (1) the ability to
distinguish between the spectral features of
target analytes and those of ambient
interfering species in the atmosphere, such
as water vapor and CO2; (2) the trade-offs
between resolution, IR peak absorbance,
and S/N; and (3) practical considerations,
such as measurement time, computational
time to process the interferogram, and the
size of the interferogram file for data
storage. The use of an inadequate
instrumental resolution can distort the true
absorption spectrum, affect the quantitative
relationship between absorbance and
concentration, and diminish the ability to
resolve spectral overlap. Resolutions ranging
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from 0.25 to 2 cm"1 have been suggested for
use in FT-IR monitoring, but there currently is
no consensus as to what resolution is
generally applicable. The nonlinear response
caused by the apodization function discussed
in Chapter 8 strongly indicates that higher
resolution improves the accuracy of the data.
practical terms this means that the scan
time will be approximately twice as long,
the interferogram file will be approximately
twice the size for data storage, and the time
required to process the interferogram will be
longer for the higher resolution
measurement.
This chapter describes the
fundamental aspects of resolution in FT-IR
spectrometry and illustrates the effects of
resolution and related instrumental
parameters on the measured spectrum. The
trading rules that determine the balance
between resolution and S/N are discussed.
Test spectra were obtained in the laboratory
and along an open path to illustrate the
effects of resolution, apodization, and zero
filling on the IR spectra of C02 and water
vapor, common atmospheric species that can
interfere with analytical measurements, and
selected gases and VOCs. Studies from the
literature that address resolution
requirements in long-path FT-IR monitoring
are discussed. A case study illustrating the
effects of resolution, zero filling, and baseline
noise on the CLS analysis of multicomponent
mixtures is also presented.
In FT-IR spectrometry, the minimum
separation in wave numbers (cm"1) of two
spectral features that can be just resolved is
inversely related to the maximum optical path
difference in centimeters of the two mirrors
employed in the Michelson interferometer. If
the desired resolution is increased by a factor
of 2, for example, from 1- to 0.5-cm"1
resolution, the moving mirror in the
interferometer must travel twice as far. In
The instrumental resolution also
affects the S/N. In general, if the size of
the aperture, or Jacquinot stop, in the
interferometer is held constant, the baseline
noise in an FT-IR spectrum is directly
proportional to the resolution of the
interferometer for measurements made in
equal times. For example, changing the
resolution from 1- to 0.5-cm'1 increases the
noise level by a factor of 2 for equal
measurement times. Therefore, to obtain
the same baseline noise level for the
0.5-cm"1 spectrum as was measured for the
1-cm"1 spectrum, the measurement time
would have to be quadrupled (because the
S/N is proportional to the square root of the
measurement time).
As described in Chapter 8, resolution
also affects the peak absorbance of the
bands being measured. For narrow spectral
features, the peak absorbance will only
approximately double on halving the
resolution. In this case, the S/N is nearly
the same for the spectra acquired at the
higher and lower resolution settings,
provided the measurement time is equal.
For broad spectral features whose peak
absorbance does not change appreciably as
a function of resolution, the lower resolution
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measurement is preferable. For strongly
absorbing bands, whether they are broad or
narrow, calibration curves of absorbance
values measured at different resolutions and
plotted versus concentration must be
developed to ascertain the optimum
resolution to be used. In light of the work
outlined in Chapter 8 it seems to be better to
use the highest resolution at which the
instrument can operate.
In general, the minimum limit of
detection (LOD) should be found for
measurements made at the lowest possible
resolution that adequately resolves the
spectral features of the analyte from those of
interfering species. The use of an inadequate
resolution can distort the true absorption
spectrum, affect the quantitative relationship
between absorbance and concentration, and
diminish the ability to resolve spectral
overlap. Conversely, the use of a higher
resolution than is required can result in a
poorer S/N and an unnecessary increase in
measurement time, processing time, and
data storage requirements.
There is currently no consensus as to
what resolution and related parameters are
generally applicable in long-path, open-path
FT-IR monitoring. Most likely, the optimum
resolution will need to be determined on a
case-by-case basis, depending on the
spectral characteristics of the target
compounds and their concentration, the path
length, and the presence of interfering
species. In field measurements, a qualified
judgement must by made taking into account
these factors in addition to the practical
considerations discussed above and in
Chapter 8.
7.2 Definition of Resolution
An understanding of the resolution
requirements in FT-IR long-path, open-path
monitoring requires an understanding of the
basic principles involved in generating an
interferogram and the operations performed
on the interferogram prior to converting it to
a spectrum. The following discussion is an
attempt to describe these basic principles in
a way that will be of general use to analysts
in FT-IR monitoring. For a more rigorous
treatment of the fundamentals in FT-IR
spectrometry, the reader is referred to the
definitive text by Griffiths and de Haseth
(1 986) or several other excellent references
(Horlick 1968; Bell 1972; Herres and
Gronholz 1984) and Section 2.4.2 of this
document.
As shown in Section 2.4.2, the
minimum separation in wave numbers of
two spectral features that can be resolved
is inversely related to the maximum optical
path difference, in centimeters, of the two
interferometer mirrors employed in the
Michelson interferometer. The closer the
separation of the two spectral features, the
greater the optical path difference must be
before the spectral features can be resolved.
In terms of the measured spectrum,
resolution can be defined as the minimum
separation that two spectral features can
have and still be distinguished from one
another. A commonly used requirement for
7-3
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two spectral features to be considered
resolved is the Raleigh criterion. This
criterion states that two bands that have
identical intensity, band shape, and peak
width are resolved when the minimum of one
band falls on the maximum of the other.
When this is the case, there is a dip
corresponding to approximately 20% of the
absorption maxima between the two
overlapping spectral features. It should be
noted that this criterion is valid only for a
sine2 instrument line shape, such as that
found in a dispersive spectrometer or an
FT-IR instrument using triangular apodization.
The actual spectral resolution in the
frequency domain that can be obtained by an
interferometer is also affected by the
truncation of the interferogram and the
application of various apodization functions.
The apodization functions can increase the
bandwidth and also change the line shape.
Apodization is discussed further in
Section 7.3.3 and in Chapter 8.
7.3 Trading Rules in FT-IR Spectrometry
The quantitative relationships
between the S/N, resolution, and
measurement time in FT-IR spectrometry are
referred to as "trading rules". The factors
that affect the S/N and dictate the trading
rules are expressed in Equation 7-1, which
gives the S/N of a spectrum measured with
a rapid-scanning Michelson interferometer.
(The derivation of Equation 7-1 is given by
Griffiths and de Haseth [1986].)
N
where t/v(T) =
9
Av
t =
£>» =
AD =
1/2
(Eq. 7-1)
the spectral energy density
at wave number v from a
blackbody source at a
temperature T
the optical throughput of
the spectrometric system
is the resolution of the
interferometer
is the measurement time in
seconds
the efficiency of the
interferometer
the specific detectivity, a
measure of the sensitivity
of the detector
the area of the detector
element
As shown in Equation 7-1, the S/N of
a spectrum is proportional to the square root
of the measurement time (tK). For
measurements made with a rapid scanning
interferometer operating at a constant mirror
velocity at a given resolution, as would
most likely be the case in FT-IR monitoring
applications, the S/N increases with the
square root of the number of scans being
averaged.
The relationship between the S/N
and resolution is not as straightforward as
implied in Equation 7-1. If the physical
parameters of the spectrometric system,
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TR-4423-99-03
such as the measurement time, optical
throughput, and the interferometer
efficiency, are assumed to be constant for
measurements made at both high and low
resolution, the S/N will be halved on doubling
the maximum retardation of the
interferometer (Amax) or halving the resolution
(Av/2). Because the S/N is proportional to the
square root of the measurement time, the
measurement time required to maintain the
original baseline noise level must be
increased by a factor of 4 each time Amax is
doubled, or Av is halved, for measurements
made at a constant optical throughput.
The optical throughput does not
necessarily remain constant throughout the
range of resolutions that could be used to
measure atmospheric gases. In low-resolution
measurements, a large optical throughput is
allowed for the interferometer, and the
throughput is limited by the area of the
detector element or the detector foreoptics.
Most commercial low-resolution FT-IR
spectrometers operate with a constant
throughput for all resolution settings.
Instruments capable of high-resolution
measurements are equipped with adjustable
or interchangeable aperture (Jacquinot) stops
installed in the source optics that reduce the
solid angle of the beam passing through the
interferometer. Spectra collected at high
resolutions are generally measured with a
variable throughput, which decreases as the
spectral resolution increases.
In high-resolution measurements made
under variable throughput conditions, the
throughput is halved as Amax is doubled.
This results in an additional decrease in the
S/N by one-half, which requires increasing
the number of co-averaged scans by another
factor of 4 to obtain the original S/N. Thus,
for high-resolution FT-IR spectrometers
operating under variable throughput
conditions, the total measurement time is
increased by a factor of 16 when Amax is
.. doubled, if the S/N ratio is to stay the same.
' The above discussions apply only to
the effect of resolution on the baseline noise
level. Resolution may also affect the peak
absorbance of the bands being measured.
For a narrow spectral feature whose full
width at half height (FWHH) is much less
than the instrumental resolution, the peak
absorbance will only approximately double
on doubling Amax. Assuming this band was
measured under constant-throughput
conditions, its S/N would be the same for
measurements taken at the higher and lower
resolution settings, provided the
measurement times are equal. However,
the degree of overlap by nearby spectral
features will be reduced when the
measurement is taken at a higher resolution.
Therefore, in this case the higher resolution
measurement is preferred.
For weak, broad spectral features
whose peak absorbance does not change as
a function of resolution, the lower resolution
measurement is preferable when the optical
throughput is constant. For strongly
absorbing bands, whether they are broad or
narrow, calibration curves of absorbance
values measured at different resolutions and
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: •.>•=••••• -.••= =
TR-4423-99-03
plotted versus concentration must be
developed to ascertain the optimum
resolution to be used.
In general, the minimum LOD should
be found for measurements made at the
lowest possible resolution that adequately
• resolves the spectral features of the analyte
from those of interfering species. Increasing
the resolution beyond this point degrades the
S/N. In FT-IR monitoring, the optimum
resolution will be determined by the band
widths of the absorption lines in the spectra
of the target compounds, the presence of
interfering species, and the S/N of the
system. The optimum resolution will most
likely vary with respect to specific analytes
and measurement conditions.
7.4 Example Spectra of CO2 and Water
Vapor
Water vapor and CO2 have IR
absorption bands with theoretical bandwidths
as narrow as 0.1 cm"1, according to the USF
HITRAN-PC database (University of South
Florida 1993). To fully characterize the IR
spectra of these compounds, which have
absorption bands that may overlap with
those of target compounds, an FT-IR
spectrometer capable of high-resolution
measurements must be employed.
A series of experiments was
conducted on a benchtop FT-IR
spectrometer in the laboratory and with a
transportable FT-IR monitor in the field to
illustrate the effects of resolution on the IR
spectra of C02 and water vapor. Three
separate series of experiments were
performed. In the first set of experiments,
single-beam sample and background spectra
were collected at various instrumental
resolution settings with the benchtop
spectrometer purged with nitrogen. These
spectra were used to generate the data
given below in Section 7.4.1.1 (Table 7-1).
Table 7-1. Resolution Test Data
Resolution
(cm'1)
0.25
0.50
1.0
2.0
4.0
8.0
16.0
Fourier
Transform
Points
131072
65536
32768
16384
8192
4096
2048
File Size
(bytes)
300268
168268
100267
67803
35034
18650
10266
Scan Time
(s)*
194
112
69
49
28
18
13
Process
Time
(s)
249
119
60
32
16
10
8
RMS Noise
2150-2100 cm'1
(10-3 Abs)**
1.5115
0.9007
0.4504
0.2347
0.1102
0.0590
0.0225
Time to collect 100 scans.
* RMS noise for 1-min measurement times.
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In the second set of experiments, a
background interferogram was collected at
0.125 cm"1 with the spectrometer purged,
and a sample interferogram was collected
with the sample compartment open to the
laboratory air. These interferograms were
used to generate lower resolution spectra by
reducing the number of data points used for
the Fourier transform. These spectra are
shown in Figures 7-1 and 7-2. In the third
set of experiments, single-beam spectra were
collected along an open path of 1 50 m at
0.5-, 1.0-, and 2.0-cm'1 resolution with a
transportable FT-IR monitor. These spectra
are shown in Figure 7-3.
Wive Number (cur')
Figure 7-2. Single-Beam IR Spectra of Water
Vapor Measured at (A) 0.25-cm1,
(B) 0.50-cm"1, (C) 1.0-cm'1, and (D) 2.0-cm'1
Resolution with No Apodization and No
Additional Zero Filling.
Wov« Number (err1)
Figure 7-1. Single-Beam IR Spectra of C02
Measured at (A) 0.25-cm'1, (B) 0.50-cm1,
(C) 1.0-cm"1, and (D) 2.0-cm"1 Resolution
with No Apodization and No Additional Zero
Filling.
All laboratory spectra were collected
on a benchtop FT-IR spectrometer, which has
a nominal instrumental resolution selectable
to 0.125 cm'1. The data system uses two
68000 data processors and contains
2 megabytes of RAM. The long-path spectra
of water vapor were obtained on a portable
FT-IR spectrometer with resolutions
selectable to a nominal 0.5 cm"1. Data
acquisition and manipulations were carried
out by using a commercial software package
on a 486/33-MHz personal computer with
8 megabytes of RAM.
1020 1040
Wave Number (cm-')
1060
Figure 7-3. Single-Beam IR Spectra of Water
Vapor Measured at (A) 2-cm"1, (B) 1-cm'1,
and (C) 0.5-cm'1 Resolution over a 150-m
Path.
7-7
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7.4.1 Resolution Effects
The effects of resolution on the IR
spectra of C02 and water vapor obtained
from laboratory measurements and long-path
measurements are addressed in this section.
The laboratory measurements illustrate the
relationship between resolution and scan
time, data processing time, data storage
requirements, spectral definition, and.S/N.
The long-path measurements are used to
characterize the water vapor spectrum in a
region in which it interferes with the analysis
of an example target compound, toluene.
7.4.1.1 Laboratory Measurements
Single-beam spectra of the p- and
r-branch of CO2 were recorded at resolutions
ranging from 0.25 to 2 cm"1 as shown in
Figure 7-1. No apodization or additional zero
filling was applied to the interferograms prior
to performing the Fourier transform. When
plotted on the scale from 2400 to
2280 cm"1, the spectral features of the C02
bands appear to be defined equally well at
0.25- and 0.5-cm"1 resolution, although slight
differences were observed in the FWHH
measurements. In the spectrum measured at
1-cm"1 resolution, there is a more noticeable
degradation of the rotational fine structure.
This structure is completely lost in the
spectrum measured at 2-cm'1 resolution, and
the r-branch appears as a broad continuum.
The absorption bands that make up the
rotational fine structure of CO2 have
bandwidths of approximately 0.2 cm"1,
according to the USF HITRAN-PC database
(University of South Florida 1993). Thus,
these bands are not fully resolved, even at
0.25-cm'1 resolution, and a resolution of
0.125 cm"1 is required to fully characterize
these bands.
Similar results were observed in
spectra of water vapor measured at
resolutions of 0.25, 0.5, 1, and 2 cm"1 with
no apodization or additional zero filling
(Figure 7-2). The single-beam spectrum of
water vapor between 3720 and 3620 cm"1
exhibits several isolated, sharp features as
well as overlapping features that are nearly
baseline resolved in the spectrum measured
at 0.25-cm"1 resolution. The spectrum
measured at 0.5-cm"1 resolution exhibits a
slight degradation in spectral definition as
compared to the 0.25-cm'1 spectrum,
although the general characteristics of the
bands are retained. The overall band
structure is still present in the spectrum
measured at 1-cm"1 resolution; however, the
distinction between some of the closely
spaced, weaker bands is lost. In the
spectrum measured at 2-cm"1 resolution,
there is no longer any evidence of the
spectral definition exhibited in the previous
spectra, and the -bands are significantly
broader.
The effect of resolution on scan time,
data processing time, data storage
requirements, and baseline noise levels was
also determined. For these tests, single-beam
sample and background spectra were
measured independently at each resolution
setting, while holding the Jacquinot stop
constant. The number of scans for each
spectrum was 100. The RMS noise levels
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TR-4423-99-03
were calculated from spectra with a 1-min
measurement time. The results from this
test are presented in Table 7-1.
As shown in Table 7-1, the time
required to collect 100 scans increases
significantly upon acquiring data at higher
resolutions. This is because the moving
mirror in the interferometer must travel a
greater distance as Amax is increased for
higher resolution scans. On average, the
total scan time for 100 scans for this
particular instrument increased by a factor of
1.6 each time Amax was doubled, indicating
the poor duty cycle efficiency.
The time required to process the
interferogram also increases as Amax (and as
the number of data points collected for. the
interferogram) increases. In these examples,
the processing time is that required to
perform the Fourier transform and related
operations on both the background and
sample interferograms and to calculate the
absorption spectrum. The time required to
process the interferogram increased on
average 1.8 times each time Amax was
doubled. It should be noted that these data
were processed on a relatively old data
system using a 68000 processor chip. With
newer and faster computers the time
required to perform the Fourier transform is
not as much of a factor. For example, on a
486/33MHz machine with 8 megabytes of
RAM, the time required to perform the
Fourier transform and plot a single-beam
spectrum is 1.65, 3.23, and 7.74 s for 2-,
1-, and 0.5-cm"1-resolution interferograms,
respectively. However, if time resolution is an
important parameter in a specific FT-IR
monitoring application, then the combination
of scan time and processing time should be
considered, or the interferograms should be
stored for post-run processing.
The amount of disk space required for
data storage increases almost by a factor
of 2 each time the resolution is increased by
a factor of 2. For 3.5-in floppy disks with
1.4 megabytes of storage capacity, this
means that, for example, 14 interferograms
collected at 1-cm"1 resolution could be stored
on one disk, whereas only eight 0.5-cm"1
interferograms could be stored on one disk at
a time. The newer data acquisition software
packages and data stations make more
efficient use of disk space. For example,
21 interferograms collected at 1-cm"1
resolution on a newer system could be stored
on one 3.5-in. floppy disk. If large amounts
of data are expected to be collected, such as
might be the case in routine FT-IR monitoring
studies, data storage requirements could be
an important consideration.
The RMS noise measured between
2200 and 2100 cm'1 increases as Amax
increases. The data in Table 7-1 were taken
from absorption spectra created from
background and sample spectra collected
over a 1-min scan time with a constant
aperture at each resolution setting. These
data follow closely the twofold increases in
baseline noise expected each time the
resolution is increased by a factor of 2. It
should be noted that only the baseline noise
level was measured in this experiment.
Resolution may also affect the peak
7-9
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TR-4423-99-03
absorbance of the bands being measured.
For example, for a weak spectral feature
whose FWHH .is much less than the
instrumental resolution, the peak absorbance
will approximately double on increasing the
resolution by a factor of 2. Therefore, the
S/N would be the same for measurements
taken at the higher and lower resolution
settings, provided the measurement times
are equal. For broad bands, the peak
absorbance will not be affected by changes
in resolution, and the lower resolution
measurement would be preferred.
7.4.1.2 Long-Path Measurements
The laboratory measurements
described above illustrate some of the trade-
offs encountered between resolution and
other experimental parameters. However,
the path length used in those studies was
insufficient to detect many of the water
vapor bands that interfere' with bands of
target pollutants, such as toluene.
Russwurm (1992) has addressed the
limitations that the presence of overlapping
water vapor bands impose on the ability to
detect and quantify toluene by long-path
FT-IR spectrometry. With a CIS analysis of
the toluene band at 1031 cm"1, the detection
limit for toluene in the presence of 10.5 torr
of water vapor was estimated to be
approximately 1 ppm. In this spectral region
over a path length of 420 m, the absorbance
due to water vapor was found to be strong
compared to that of toluene. These data
clearly indicate that to optimize the detection
limits of FT-IR monitors for difficult target
compounds, such as toluene, the water
vapor spectrum must be well characterized.
Single-beam spectra measured at 2-,
1-, and 0.5-cm"1 over a 1 50-m path length
are shown in Figure 7-3. The interferograms
were processed with triangular apodization
and no additional zero filling. The spectra are
plotted over the wave number region used to
quantify toluene. As expected, the FWHHs
of the water vapor absorption bands between
1000 and 1060 cm"1 are narrower in the
0.5-cm"1 resolution spectrum as compared to
the 1- and 2-crrf1 resolution spectra. In
addition, spectral features are resolved in the
0.5-cm"1 spectrum that appear as a single
band.in the other two spectra. For example,
the band at 1010 cm"1 in the 1-cm"1
spectrum is resolved into a doublet at 1010
and 1010.7 cm"1 in the 0.5-cm"1 spectrum.
Also, bands appearing at 1028.3 and 1029.5
cm'1 are much better resolved in the 0.5-cm'1
spectrum. In fact, they are not resolved at
all in the 2-cm"1 spectrum.
To completely resolve all of the
overlapping bands in the spectrum of water
vapor over this wave number region, the
spectrum must be recorded at 0.125-cm'1
resolution. The theoretical spectrum of
water vapor from the USF HITRAN-PC
database is shown in Figure 7-4A.
A 0.125-cm'1 resolution spectrum of
water vapor recorded on the ROSE system
(Herget 1992) is shown in Figure 7-4B. In
these spectra the band at 1018 cm"1 can be
resolved into two components, and the
bands at 1010 and 1010.7 cm"1 are
7-10
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TR-4423-99-03
|
A.
1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 10161019 1020
W«vo Number (cm-1)
Figure 7-4. IR Spectra of Water. (A) 10 torr
of water vapor over a 300-m path, from the
USF HITRAN-PC database (University of
South Florida 1993). (B) Water vapor
recorded at 0.125-cm"1 resolution of the
ROSE system (reproduced with permission
from W.F. Herget).
completely baseline resolved. Whether or
not measuring ambient spectra at 0.1 25-cm"1
resolution improves the results of
quantitative analyses for difficult target
compounds, such as toluene, has not yet
been fully investigated.
7.4.2 Zero-Filling Effects
When the interferogram contains
frequencies that do not coincide with the
frequency sample points, the spectrum
resembles a "picket fence" (Herres and
Gronholz 1 984). An example of this effect is
shown in Figure 7-5 in the spectrum of C02
measured on a benchtop FT-IR instrument.
In this example, the spectrum of CO2
measured at 0.25-cm"1 resolution with no
apodization and a zero-filling factor of 1
(Figure 7-5A) exhibits excellent peak shape.
However, in the spectrum measured at
0.5 cm"1 with no additional zero filling
(Figure 7-5B), the peaks of several absorption
bands are squared off. This effect can be
overcome by adding zeros to the end of the
interferogram before the Fourier transform is
performed. This operation is referred to as
zero filling. Zero filling increases the number
of points per wave number in the spectrum,
and, in effect, interpolates the spectrum.
Normally, some multiple (e.g., 2, 4, etc.) of
the original number of data points is added to
the interferogram. This improves the
photometric accuracy of the FT-IR spectrum
Figure 7-5. Absorption Spectra of CO2
Measured at (A) 0.25 cm"1 with a Zero-
Filling Factor of 1, (B) 0.5 cm"1 with No
Zero Filling, and (C) 0.5 cm"1 with a Zero-
Filling Factor of 2.
7-11
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and increases the digital resolution. As
shown in Figure 7-5C, zero filling the
interferogram measured at 0.5 cm"1 by an
additional factor of 2 eliminated the picket
fence effect.
It should be noted that zero filling
improves only the digital resolution, and not
the resolution of the FT-IR spectrum. An
example of this is illustrated in Figure 7-6 for
spectra of water vapor measured at 0.25-,
0.5-, and 1-cm'1 resolution. The spectrum
measured at 0.25-cm"1 resolution was zero
filled by a factor of 1, the 0.5-cm"1 spectrum
was zero filled by a factor of 2, and .the
1-cm"1 spectrum by a factor of 4. In this
case, each of the interferograms contained
the same number of data points after being
zero filled. Even with additional zero filling,
the 0.5-cm"1 spectrum does not match the
spectral definition of the spectrum obtained
at 0.25-cm"1 resolution. (Compare Spectra A
Wave Number (cnr<)
Figure 7-6. Absorption Spectra of Water
Vapor Measured at (A) 0.25-cm 1 Resolution
with a Zero-Filling Factor of 1, (B) 0.5-cm°
Resolution with a Zero-Filling Factor of 2,
and (C) 1-cm'1 Resolution with a Zero-Filling
Factor of 4.
and B in Figure 7-6.) The loss of spectral
features is more dramatic in the zero-filled
1-cm"1 spectrum. For example, shoulders at
3905 and 3884 cm"1 that are detectable in
the 0.25- and 0.5-cm"1 spectra were not
observed in the 1-cm'1 spectrum. Also, side
lobes appear in the 1 -cm"1 spectrum that was
zero filled by a factor of 4 (Figure 7-6,
Spectrum C). These side lobes are also
present, but are not as severe, in the
0.5-cm'1 spectrum zero filled by a factor of 2
(Spectrum B in Figure 7-6).
The picket fence effect is less
extreme if the spectral components are broad
enough to be spread over several sampling
positions. As a rule of thumb, the original
interferogram size should be doubled by zero
filling by an additional factor of 2. When a
CIS analysis of the spectral data is
performed, in general it has been found that
one order of zero filling (which is 2 times the
original number of data points used in the
Fourier transform) yields a factor of 2 lower
error than that with no additional zero filling.
An example of this is given in Section
7.5.2.2.1. It should be noted that zero filling
does increase the file size and the time
required for data processing.
7.4.3 Apodization Effects
As shown in Chapter 2, the Fourier
transform integral has infinite limits for the
optical path difference. Thus, to measure
the true spectrum of the source, the
interferometer must scan infinite distances.
However, because the mirror can move only
a finite distance, the exact reconstruction of
7-12
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TcCH,!i=J3.=i.*S==5
TR-4423-99-03
the spectrum is impossible. The finite
movement of the interferometer mirror
truncates, or cuts-off, the interferogram.
This, in effect, multiplies the interferogram
by a boxcar truncation function. This
function may cause the appearance of side
lobes on both sides of the absorption
band. The corrective procedure for
eliminating these side lobes is called
apodization. (For an in-depth discussion of
the effects of apodization, see Chapter 8).
Apodization is performed by multiplying the
measured interferogram by a mathematical
function. Typical apodization functions
include triangular, Happ-Genzel, and Norton-
Beer functions. An example of the effect of
these apodization functions on the FT-IR
spectrum of CO is shown in Figure 7-7.
Apodization affects the effective
spectral resolution, the apparent peak
absorbance, and the noise of any. FT-IR
spectrum. The apparent absorbance of
narrow bands will be most affected by the
n« JIM
Wave Number (cnr1)
Figure 7-7. Absorption Spectra of CO
Measured at a Nominal 0.125-cm 1
Resolution with (A) No, (B) Triangular,
(C) Happ-Genzel, and (D) Norton-Beer-
Medium Apodization Functions.
choice of apodization function. In general,
the bands in a spectrum computed with no
apodization will be more intense than bands
in the spectrum of the same sample
computed from the same interferogram after
applying an apodization function.
.Apodization also degrades resolution.
An example of this is illustrated by the
spectra of water vapor in Figure 7-8. In this
case, subtle differences are observed, for
example, at 3948 and 3947 cm'1 and
3924.4 cm"1, in the spectrum generated with
no apodization (Figure 7-8A) and the spectra
generated by using the three types of
apodization functions.
In general, to obtain the optimum S/N
for spectra of small molecules with
resolvable fine structure, the use of no
apodization is preferable if side lobes from
neighboring intense lines do not present an
interference. If side lobes are present and
Wive Number (cnr>)
Figure 7-8. Absorption Spectra of Water
Vapor Measured at 0.5-cm'1 Resolution
with an Additional Zero-Filling Factor of 2
and with (A) No, (B) Triangular, (C) Happ-
Genzel, and (D) Norton-Beer-Medium
Apodization Functions.
7-13
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TR-4423-99-03
interfere with either qualitative or
quantitative analyses, apodization becomes
necessary. However, when classical least
squares is performed, the field spectra must
be processed by using the same apodization
function that was used for the reference
spectra. For broad absorption bands, the
measured absorbance is about the same in
apodized and unapodized spectra. This can
pose some problem in the analysis using
classical least squares. Gases that exhibit
broadband features in the P and the R
branches, but also have a sharp Q branch like
that of the gas toluene, will exhibit a
different response in these branches
because of the apodization function. Overall,
the greatest noise suppression will be
obtained with the strongest apodization
function, but the spectral resolution and band
intensities will be greatest for weaker
apodization functions (Griffiths and
de Haseth 1986). The optimum apodization
function has yet to be determined for general
use in long-path FT-IR monitoring. In general,
there is a reciprocal relation between the
suppression of the side lobes and the
broadening of the absorption feature for any
of the apodization functions. That is, as the
side lobes became smaller relative to the
peak, the feature becomes broader compared
to the unapodized feature.
Triangular and Happ-Genzel
apodization functions are commonly used in
OP/FT-IR monitoring, although Griffiths et al.
(1995) have indicated that a Norton-Beer
medium function actually gives a better
representation of the true absorbance. In all
cases, however, the same parameters should
be used to collect the field spectra that were
used to record the reference spectra. The
choice of apodization function may be limited
by this requirement. If spectra from a
commercial or user-generated library are to
be the reference spectra for quantitative
analysis, then the parameters that were used
to generate those reference spectra should
be used to collect the field spectra.
Otherwise, errors in the concentration
measurement will occur.
7.5 Effect of Resolution on Quantitative
Analyses
The determination of analyte
concentrations by FT-IR spectrometry
depends on the linear relationship between IR
absorbance and concentration as described
by Beer's law. The discussion in Chapter 8
shows that this seems never to be true if an
apodization function is used, particularly at
low resolution. If the FWHH of the band is
narrower than the instrumental resolution,
the measured spectrum is actually a
convolution of the instrument line shape and
true band shape. As a result, the measured
absorbance will be only approximately linear
with concentration. The higher the resolution
for the spectral features of the IR band
chosen for quantification, the better the
approximation. The apodization function also
has an effect on linearity. This section
describes studies from the literature that
have addressed the effects of resolution and
related parameters on quantitative analyses.
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7.5.1 Studies from the Literature
Strang et ai. (1989) designed and
evaluated an FT-IR system for monitoring
toxic emissions from semiconductor
manufacturing processes. This system was
used to analyze part-per-billion levels of
organic vapors and metal hydrides such as
arsine, phosphine, and diborane in simulated
workplace environments. The optimal wave
number, region for quantification and the
effects of resolution and spectral overlap on
the accuracy of quantitative results were
studied. Spectral measurements were taken
at resolutions ranging from 0.5 to 8 cm"1 to
determine the optimum balance between
(1) analysis time, (2) data storage space,
(3) S/N, (4) accuracy of quantitative analyses
using a CIS program, and (5) the ability to
differentiate compounds with overlapping
spectra. It should be noted that these data
were acquired over a 20.25-m path in a
multipass cell. Therefore, findings from this
study may not be applicable to long, open-
path measurements. Discussion of this study
is included in this text because of the interest
in workplace monitoring. Also, the
methodology used to determine the optimum
resolution for the short-path measurements
can also be applied to longer path
measurements.
The authors specified the following
four issues that must be resolved for a CLS
analysis at a given resolution to be
acceptable.
1. Whether the CLS result varies by
more than 50% of the theoretical
value
2. Whether false positives or false
negatives develop as a result of
degraded resolution
3. Whether the amount of error in the
measurement will cause potentially
toxic concentrations of the target
analyte in air to be measured
incorrectly
4. Whether the detection limit obtained
with the CLS program changes as a
function of resolution
Using these criteria, the authors determined
the minimum allowable resolution for the
target compounds. The results are
summarized below in Table 7-2.
In this study, the higher resolutions
required for the metal hydrides arsine,
diborane, and phosphine were a result of
spectral overlap with other target analytes
and with interfering atmospheric compounds.
For example, phosphine overlaps with C02
and arsine overlaps with water vapor. The
authors also determined the effects of
decreased resolution on the accuracy of the
quantitative results. In the case of diborane,
only the 0.5-cm'1 resolution measurements
exhibited a linear relationship for all
concentrations. Measurements taken at 2-
and 4-cm"1 resolution deviated from linearity
as the concentration decreased.
The effect of resolution on the ability
to quantify overlapping compounds by the
CLS analysis was investigated by using
mixtures of Freons 11, 1 3B1, and 22. These
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Table 7-2. Optimal Wave Number Region and Minimum Resolution1
Compound
Acetone
Arsine
Diborane
o-Dichlorobenzene
2-Ethoxyethanol
Freon 1 1
Freon 13B1
Freon 22
Nitrogen trifluoride
Phosphine
Sulfur hexafluoride
Wave Number
Region
(cm'1)
1287-1167
2132-2106
2522-2515
1060-1002
1192-984
876-813
1137-1031
1193-1063
960-833
2440-2390
965-915
Minimum
Resolution
(cm'1)
8
2
0.5
8
8
8
8
8
8
4
8
'From Strang et a/. (1989). These data are applicable to a 20.25-m path.
compounds have relatively broad spectral
features that overlap. The mixtures were
analyzed at 0.5-, 2-, 4-, and 8-cnrv1
resolution. Each of the individual compounds
could be quantified accurately at each
resolution in a 1:1:1 mixture at
concentrations of 10, 1, and 0.1 ppm.
Strang and Levine (1989) have also
determined the LODs for the same target
compounds in the previous study as a
function of resolution. For most compounds,
there was very little difference in the LODs
estimated at resolutions of 0.5, 2, 4, and
8 cm'1. However, for diborane and
phosphine the LOD was difficult or
impossible to measure at 8 cm"1 resolution.
In the case of diborane, the peak selected for
quantification had a FWHH of 7 cm"1. At 8-
cm'1 resolution there are only two data points
every 8 cm"1, so a peak 7 cm'1 in width is not
defined well enough to be quantified by the
CLS program. For phosphine, the peak
shape is severely degraded at 8 cm'1.
Although the CLS program could quantify the
peak, the LOD was significantly higher
(0.7 ppm-v/v) for spectra measured at 8 cm'1
resolution as compared to those measured at
0.5 cm'1 resolution (0.07 ppm-v/v). This
example also illustrates one of the
advantages of the CLS program over single
peak absorbance measurements in
quantitative analysis. The single peak
absorbance measurement is difficult to make
for broad bands, whereas the CLS program
uses multiple data points over the entire
spectral range of the broad band.
Spellicy et al. (1991) addressed
several issues regarding spectroscopic
remote sensing with respect to the Clean Air
Act. One issue that was addressed was the
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optimum resolution for remote sensing FT-IR
applications. The authors presented
theoretical calculations describing the
relationship between absorbance and
concentration for a single Lorentzian line with
a half-width of 0.1 cm"1 measured at
resolutions from 0.01 to 0.1 cm"1. Under
these conditions, linearity was observed only
at a highest resolution case and at the lowest
concentrations. The deviation from linearity
most likely would be observed in small
molecules such as HCI, CO, C02, and H20,
which have sharp spectral features. For
larger compounds, such as heavy
hydrocarbons that exhibit broader IR bands,
the linear relationship between absorbance
and concentration is more likely to be
followed.
More recently, Marshall et al. (1994)
conducted a laboratory study to determine
the effect of resolution on the
multicomponent analysis of VOCs with a CLS
program. When they analyzed for target
VOCs, such as acetone, chloroform, toluene,
methanol, 1,1,1 -trichloroethane, methyl ethyl
ketone, carbon tetrachloride, and the xylene
isomers, over a short path, resolutions lower
than 4 cm"1 had an adverse effect on the
multicomponent analysis. Resolutions of 1 to
2 cm"1 were found to be adequate for these
target compounds when the CLS program
was used.
Griffiths et al. (1993) reported the
advantages and disadvantages of using low-
resolution measurements in long-path FT-IR
monitoring. Among the advantages cited
were the.smaller size and greater portability
of the instrument, an improved S/N, and a
lower cost. The disadvantages included a
greater difficulty in visualizing the IR bands
of the target compounds and potential
deviations from Beer's law. A test case of
measuring the xylene isomers at resolutions
of 2, 4, 8, and 16 cm"1 was presented. By
using a partial least squares (PLS) program,
good quantitative results were obtained at
the relatively low resolution measurements.
These results also indicated that the PLS
program might be better than the CLS
program for distinguishing and quantifying
target compounds with overlapping features.
Bittner et al. (1 994) have reported on
high-resolution FT-IR measurements of VOCs
at a variety of monitoring sites. By recording
spectra at 0.125-cm"1 resolution, detection
limits for benzene of 0.5 ppm-m were
achieved at path lengths between 60 and
100 m at a fuel storage area. The high-
resolution measurements allowed the narrow
benzene band at 674 cm"1 to be separated
from the strong C02 absorption bands in that
spectral region.
7.5.2 Case Study: The Effect of Resolution
and Related Parameters on the CLS
Analysis of Multicomponent Mixtures
A study using laboratory-generated
spectral mixtures that have overlapping
features was conducted to investigate the
effect of instrumental resolution and related
parameters on the CLS analysis results
(Childers and Thompson 1994). The study
was designed to simulate conditions that
might be encountered in long-path
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TR-4423-99-03
measurements. The results from three
separate cases are discussed.
1. Analytes with narrow bands that
overlap, such as those for CO and
13C-labeled CO
2. Analytes with broad bands that
overlap, such as those for acetone,
methylene chloride, and ethanol
3. Analytes with narrow and broad
bands that overlap, such as those for
nitrous oxide and methylene chloride.
The effect of the number of data points and
the noise level on the CIS analysis is also
illustrated. Because the mixtures analyzed in
this study were created from a linear
combination of reference spectra, the effect
of resolution on the relationship between
concentration and absorbance is not
addressed.
The spectra were collected on a
research-grade, benchtop FT-IR spectrometer
equipped with an MCT detector. A gas cell,
50 mm long and 32 mm in diameter, was
used to obtain reference spectra of CO,
13CO, acetone, methylene chloride, ethanol,
and nitrous oxide at room temperature and
atmospheric pressure. The reference spectra
were acquired at resolution settings of 0.1 25
and 1 cm'1. The original interferograms were
processed by using the appropriate number
of data points to yield spectra with nominal
resolutions ranging from 0.25 to 8 cm"1. No
additional zero filling was used on the
0.25-cm"1 spectra because of memory
limitations in the data system. The 0.5-cm'1
spectra were zero filled by an additional
factor of 2, and the 1.0-cm"1 spectra were
zero filled by an additional factor of 4. As a
result, the 0.25-, 0.5-, and 1.0-cm'1-
resolution spectra had the same number of
data points, that is 1 31,072. The 2,- 4-, and
8-cnY1 spectra were generated from
interferograms that contained 16,384, 81 92,
and 4096 data points, respectively. No
additional zero filling was performed on these
interferograms. A triangular apodization
function was applied to each interferogram
prior to performing the fast Fourier
transform.
The concentrations of the individual
analytes in the gas cell were determined by
comparing the maximum absorbance values
of the 0.5-cm'1 spectra to those of reference
spectra in a commercial spectral library. The
absorbance values of the reference spectra
were then normalized to values cor-
responding to a concentration'of 100 ppm.
These spectra were added mathematically to
produce synthetic mixtures with varying
concentrations of each analyte. Synthetic
noise corresponding to an amplitude of 1, 5,
10, and 25% of the most intense peak in
each spectrum was added to the mixtures.
Mixtures with 10% noise added were then
analyzed by using a CLS algorithm.
7.5.2.1 Mixtures of CO and 13CO
Synthetic mixtures of CO and 13CO
were generated by adding reference spectra
of CO corresponding to concentrations of
150, 300, 450, and 600 ppm to reference
spectra of 100 ppm 13CO. The 0.25-cm'1
7-18
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TR-4423-99-03
reference spectra and the spectra of the
synthetic mixtures corresponding to 1 50 ppm
of CO and 100 ppm of 13CO recorded at
0.25, 0.5, 1.0, and 2.0 cm"1 resolution are
shown in Figure 7-9. CO and 13CO have
several bands that overlap or nearly overlap
in the spectral region between 2118 and
2137 cm'1. For example, overlapping bands
at 2123.6 and 2124.2 cm"1 and at 2131.0
and 21 31.6 cm"1 are nearly baseline resolved
in the 0.25 cm"1 spectrum. These bands can
2120 2125 2130 2135
Wave Number (cm'1)
Figure 7-9. Reference 0.25-cm"1 Spectra of
(A) 13CO and (B) CO and Spectra of
Synthetic Mixtures of 150 ppm CO and
100 ppm 13CO Measured at (C) 0.25-,
(D) 0.5-, (E) 1.0-. and (F) 2.0-cm1
Resolution.
still be distinguished at a resolution of
0.5 cm"1, but appear as only one band in the
1.0- and 2.0-cm"1 spectra. Even though
these bands are not resolved at 1.0- and
2.0-cm"1 resolution, the CLS analysis
accurately determined the concentration of
CO in the mixture when it was analyzed for
both CO and 13CO. Plots of the calculated
concentration versus the known
concentration of CO were linear over the
range of 0 to 600 ppm of CO in the presence
of 100 ppm 13CO. When the mixtures were
analyzed for only CO, a positive bias and an
increase in the magnitude of the errors in the
measurements were observed. Although the
bias was relatively constant, the error
increased as the resolution decreased from
0.25 to 1.0 cm"1. In the case of the 2-cm"1
measurements, CO could not be detected at
1 50 ppm in the mixture if 13CO was excluded
from the analysis. (See Figure 7-10.)
TOO
100 MO MO 400 MO tOO 700
Known Concentration (ppm)
Figure 7-10. Concentration Calculated from
CLS Analysis vs. Known Concentration for
13CO/CO Mixtures Measured at 2-cm"1
Resolution. The (•) represents a value
obtained during analysis for both 13CO and
CO, and the (+) represents a value obtained
during analysis for CO only.
7.5.2.2 Mixtures of Acetone, Methylene
Chloride, and Ethanol
Synthetic mixtures of acetone,
methylene chloride, and ethanol were
generated by adding reference spectra of
ethanol corresponding to concentrations of
125, 250, 375, and 500 ppm to reference
spectra of 100 ppm each of acetone and
methylene chloride. The 0.25-cm"1 reference
7-19
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MAi&m
TECHm^
TR-4423-99-03
spectra and the spectra of the synthetic
mixtures corresponding to 500 ppm of
ethanol and 100 ppm each of acetone and
methylene chloride recorded at 1.0-, 2.0-,
and 4.0-cm"1 resolution are shown in
Figure 7-11. In this case, the spectrum of
each analyte could be adequately measured
at 1.0-cm"1 resolution. At 4-cm"1 resolution,
the Q-branches of these compounds were no
longer detected. However, this did not
diminish the ability to quantify ethanol in
these mixtures with the CLS algorithm. Plots
of the calculated concentration versus the
known concentration of ethanol were linear
over the entire range from 0 to 500 ppm
ethanol in the presence of 100 ppm of
acetone and -100 ppm of methylene chloride
for each resolution setting. Although the
concentration of ethanol could be determined
in the low-resolution measurements, the
errors in the CLS analysis increased with
decreasing spectral resolution. The high-
0>
o
c
a
a
Wave Number (cm'1)
Figure 7-11. Reference 0.25-cm'1 Spectra
of (A) Acetone, (B) Methylene Chloride, and
(C) Ethanol and Spectra of Synthetic
Mixtures of 100 ppm Acetone, 100 ppm
Methylene Chloride, and 500 ppm Ethanol
Measured at (D) 1.0-, (E) 2.0-, and
(F) 4.0-cm 1 Resolution.
resolution spectra contain more data points
per wave number than do the low-resolution
measurements. To determine if this
contributed to the increase in the magnitude
of the errors, the effect of the number of
data points on the CLS analysis was
investigated. The effect of S/N on CLS was
also investigated.
7.5.2.2.1 Effect of the Number of Data
Points on the CLS Analysis
The average error in the CLS analysis
for ethanol in the acetone, methylene
chloride, ethanol synthetic mixtures for each
resolution setting is shown in Table 7-3.
For the 0.25-, 0.5-, and 1.0-cm"1
measurements, in which additional zero filling
was used to keep the number of data points
the same, the average error was relatively
constant at approximately 9%. However, for
the 2.0-, 4.0-, and 8.0-cm"1 measurements,
in which no additional zero filling was used,
the average error increased with a decrease
in the number of data points. (Note that the
0.25-, 0.5-, and 1.0-cm'1 spectra were
generated from an original interferogram
collected at 0.125-cm"1 resolution, whereas
the 2.0-, 4.0-, and 8.0-cm"1 spectra were
generated from an original interferogram
collected at 1.0-cm"1 resolution.)
To show that the increase in error is
related to the number of data points per
wave number, and is not necessarily a direct
result of degrading the spectral resolution,
spectral mixtures of acetone, methylene
7-20
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rs.-=».f./s.fa =
TFFH ^"^Va; r=
I tUtii i=v -. -^ « r ^=
TR-4423-99-03
Table 7-3. Effect of The Number of Data Points on the CLS Analysis
Resolution
(cm'1)
0.25
0.5
1.0
2.0
4.0 ...
8.0
Additional Zero
Filling
None
2x
4x
None
None.
None
Data
Points
131072
131072
131072
16384
8192
4096
Average
Error
9.13
8.93
9.55
24.54
32.73
42.27
chloride, and ethanol obtained at 1-cm"1
resolution were processed by using no
additional zero filling, an additional zero filling
factor of 2, and an additional zero filling
factor of 4. This resulted in interferograms
having 32,768, 65,536, and 131,072 data
points, respectively. These results were also
compared to those obtained for spectra
measured at 2 cm'1, which were generated
from interferograms containing 16,384 data
points.
As can be seen in Table 7-4, the
accuracy of the measurements was not
affected by the number of data points per
spectral element. However, the magnitude
of the error in the measurements was related
to the number of interferogram data points
used to generate the spectra. On average,
the error in the CLS analysis decreased by a
factor of 1.4 each time the number of data
points used to process the interferogram was
doubled.
Table 7-4. The Effect of Zero Filling on the CLS Analysis
Cone.
(ppm)
0
125
250
375
500
1-cm'1
Resolution
4 x Zero Fill
Below MDL
121.40 (8.49)
248.33 (9.35)
379.85 (9.58)
500.81 (10.29)
1-cm-1
Resolution
2 x Zero Fill
Below MDL
119.65 (11.89)
248.87 (12.87)
368.40 (13.83)
509.94 (14.73)
1-cm-1
Resolution
No Zero Fill
Below MDL
124.53 (17.24)
252.07 (18.15)
380.78 (17.94)
492.42 (20.83)
2-cm-1
Resolution
No Zero Fill
Below MDL
119.85 (22.47)
252.18 (22.53)
373.87 (24.27)
509.24 (28.90)
7-21
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• -L-J -,-j. • /
TR-4423-99-03
7.5.2.2.2 Effect of S/N
Analysis
on the CLS
Table 7-5. Effect of Noise on the CLS
Analysis
Synthetic noise was added to 1-cm'1
spectral mixtures containing 100 ppm
acetone, 100 ppm methylene chloride, and 0
to 500 ppm ethanol at levels corresponding
to 1, 5, 10, and 25%.of the maximum
absorbance value in each spectrum.
Spectral mixtures containing 100 ppm
acetone, 100 ppm methylene chloride, and
500 ppm ethanol at each noise level are
shown in Figure 7-1 2. In these mixtures, the
average error in the CLS analysis was found
to be directly proportional to the percentage
of noise added to the spectrum. (See
Table 7-5.)
1200 1250 1300
Wave Number (cm'1)
Figure 7-12. Spectra of Synthetic Mixtures of
100 ppm Acetone, 100 ppm Methylene
Chloride, and 500 ppm Ethanol Measured at
1-cm"1 Resolution with (A) 0, (B) 1, (C) 5,
(D) 10, and (E) 25% Noise Added.
% Noise
Average Error
0
1
5
10
25
0.07
0.96
4.78
9.55
23.89
7.5.2.3 Mixtures of Methylene Chloride
and Nitrous Oxide
Synthetic mixtures of methylene
chloride and nitrous oxide were generated by
adding reference spectra of nitrous oxide
corresponding to concentrations of 1 2.5, 25,
37.5, 50, 75, and 100 ppm to reference
spectra of 100 ppm methylene chloride. The
0.25-cm"1 reference spectra and the spectra
of the synthetic mixtures corresponding to
50 ppm of nitrous oxide with both 0 and
100 ppm of methylene chloride recorded at
0.25-, 0.5-, and 1.0-cm"1 resolution are
shown in Figure 7-13.
The spectrum of nitrous oxide exhibits
sharp bands that are resolved at 0.25 cm'1,
but are not as well resolved at 0.5-cm'1
resolution. These bands become a broad
continuum in the 1.0-cm"1 spectrum. At first
glance, one would expect the CLS analysis
to perform better for the 0.25-cm"1 spectra,
in which the N20 bands are fully resolved.
However, this is not the case in these
mixtures. When analyses are performed for
N20 over the entire band envelope from
1231 to 1329 cm'1, N20 is not detected at
concentrations less than 75 ppm in the
0.25-cm"1 spectra. (See Figure 7-14.)
7-22
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MAIWiin
TECH
TR-4423-99-03
0)
g
ra
o
(0
<
1250 1300
Wave Number (cm"1)
Figure 7-13. Reference 0.25-cm"1 Spectra of
(A) N2O and (B) Methylene Chloride and
Spectra of Synthetic Mixtures of 50 ppm
N2O and 100 ppm Methylene Chloride
Measured at (C) 0.25-, (D) 0.5-, and
(E) 1.0-cm1 Resolution.
120
20 40 «0 BO 100
Known Concentration (pom)
120
Figure 7-14. Concentration Calculated from
CIS Analysis vs. Known Concentration for
N2O/ Methylene Chloride Mixtures Measured
at 0.25-cm"1 Resolution. The (•) represents
a value obtained during analysis over the
methylene chloride region, and the (4)
represents a value obtained during analysis
over the N2O region.
However, when the mixture was analyzed for
N2O by using the methylene chloride region
from 1243 to 1292 cm"1, N2O was
accurately quantified with a high precision.
Similar results were obtained for the 0.5-cm'1
resolution spectra. In contrast, the mixtures
recorded at 1.0-cm"1 resolution could be
analyzed successfully over both regions. At
2-cm"1 resolution, the CLS analysis
performed best over the N20 region.
Apparently, in multicomponent mixtures, the
CLS algorithm does not perform well in
regions where one or more components
exhibit only baseline noise.
This effect seems to be amplified in
higher resolution measurements of
compounds with sharp spectral features,
such as N20. These results indicate that for
spectra with sharp features the CLS should
be performed over a narrow range that
contains absorbing features.
7.5.2.4 Conclusions and Recommendations
Based on Case Study
The following conclusions regarding
resolution requirements in long-path FT-IR
monitoring can be drawn from this simulated
study using well-characterized spectral data
sets.
In spectra with overlapping sharp
features, the CLS algorithm can accurately
quantify target analytes, even when the
bands used for analysis are not fully
resolved. However, a failure to identify all of
the overlapping components in a mixture can
result in a bias and an increase in the error in
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the CLS analysis. Thus, the real value in
performing higher resolution measurements
might be to facilitate identifying the species
present to be included in the CLS analysis
set.
In the case of spectra with
overlapping broad features, such as those
found in acetone, methylene chloride, and
ethanol, the accuracy of the CLS analysis is
not affected by the resolution setting.
However, the magnitude of the errors in the
CLS analysis is related to the number of data
points per wave number in the analyte
spectrum. Therefore, the errors in the CLS
analysis will increase with decreasing
resolution unless additional zero filling, or
some other means, is used to increase the
number of data points in the spectrum.
However, the use of zero filling or
interpolation to indiscriminately increase the
number of data points in the spectrum is not
recommended, because interpolated data
points do not contain independent
information. In these mixtures, the errors in
the CLS analyses were also found to increase
proportionally with increases in the noise
level.
The results from the CLS analysis of
spectral mixtures with overlapping broad and
sharp bands, as was the case with
methylene chloride and nitrous oxide, were
not as straightforward to interpret. When
analyzing for nitrous oxide in spectral regions
where methylene chloride did not exhibit any
absorption bands, the CLS algorithm
performed better at lower resolutions. In
regions where the two compounds exhibited
overlapping spectral features, comparable
results were obtained for measurements
taken at 0.25-, 0.5-, and 1.0-cm"1 resolution.
In summary, resolution requirements
will vary for different target compounds and
sampling conditions. In field measurements
-these requirements will depend on several
factors, such as path length, concentration
of the target compounds, and the presence
of interfering species. Although the
simulated studies described here do not
provide a definitive answer regarding the
resolution question, similar studies using
target analytes and possible interfering
species should be performed prior to field
studies to establish guidelines for data
acquisition and analysis.
7.6 General Conclusions and
Recommendations
As stated in the introduction of this
chapter, there is currently no consensus as
to what resolution is generally applicable in
FT-IR long-path, open-path monitoring. A
spectral resolution of 0.125 cm'1 is required
to fully characterize the spectra of
atmospheric C02 and water vapor. Spectra
taken along a 1 50-m path show that there
are significant differences in the water vapor
spectra measured at nominal resolutions of
2, 1, and 0.5 cm'1. The effect of these
differences on the computer-assisted
quantitative analyses for target pollutants
has not, however, been fully examined for
long-path FT-IR measurements. In previous
studies, Strang et al. (1989) have shown
that for several organic vapors a resolution of
7-24
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TR-4423-99-03
8 cm"1 is sufficient to obtain quantitative
results over a short path if a CIS program is
used. In contrast, Spellicy et al. (1 991) have
presented theoretical results that suggest
that the FT-IR spectra of small molecules
with very fine spectral features will obey
Beer's law at only high resolution (0.01 cm'1)
and at very-low concentrations. Recently,
Marshall et al. (1994) and Griffiths et al.
(1995) have indicated that 1- to 4-cnrT1
resolution, or possibly a lower resolution, is
adequate for measuring certain VOCs using
CIS and PLS multicomponent analysis
programs.
Clearly, there is much fundamental
research that must be done to "resolve" the
resolution question. Experiments similar to
those done by Strang et al. (1989), Strang
and Levine (1989), Marshall et al. (1993),
and Griffiths et al. (1993) should be
conducted over a long, open path for the
hazardous air pollutants stipulated under the
Clean Air Act Amendments of 1990.
Measurements of these compounds should
be taken at different resolutions,
concentrations, and path lengths to
determine the optimum experimental
conditions for obtaining the best S/N and
detection limits. Most likely, the optimum
resolution will be different for the various
compounds. However, at least minimum
resolution requirements could be determined.
Although the question of what
resolution should be used in FT-IR long-path,
open-path monitoring has not been
answered, the reader should have an
appreciation for the factors related to
resolution that affect spectral measurements.
Instrument manufacturers and software
vendors have made great strides in
simplifying the use of FT-IR instruments.
Most FT-IR software is menu driven and
some instruments can be operated at the
push of a button. Although these
developments facilitate the collection of
FT-IR data, they also allow data to be
collected without a knowledge of the
principles behind the measurement. Analysts
working in this field must be aware of the
effects of different instrumental parameters
on the measured spectrum. Grasselli et al.
(1982) have published criteria for presenting
spectra from computerized IR instruments,
with an emphasis on FT-IR measurements.
The authors established recommendations
and guidelines for reporting experimental
conditions, instrumental parameters, and
other pertinent information describing the
acquisition of FT-IR spectra. These guidelines
should be followed when reporting FT-IR
data.
7.7 Guidance for Selecting Resolution and
Related Parameters
In this section, general criteria and
guidelines are suggested for choosing the
optimum resolution for acquiring spectral
data. The choice of resolution and related
parameters, such as apodization and zero
filling, to be used for data collection will be
determined by several factors. As stated
before, there is no consensus as to what the
optimum parameters should be. The
parameters need to be optimized for the
specific experiments planned, taking into
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TR-4423-99-03
consideration the goals of the monitoring
study. The following guidelines should be
taken into account when choosing the
optimum instrumental parameters.
7. Consider the bane/widths of the
absorption features used to analyze for
specific target compounds. If the absorption
bands of the target compounds are relatively
broad, there may be no need to acquire high-
resolution spectra. When this is the case, no
additional information will be gained, and the
measurements will have a poorer S/N and
will require longer data collection,
computational times, and larger data storage
space. The analyst must be aware,
however, that the spectral features of
atmospheric constituents such as CO2, H2O,
and CH4 can be completely resolved only at
a resolution of 0.125 cm"1. Because these
compounds are in every long-path spectrum
and often overlap with the target analyte,
access to high-resolution data may be
required to develop the analysis method.
There is some thought that the real
advantage of high-resolution spectral data is
the ability to visualize the spectral features
and to identify interfering species. This
information can then be used in developing
the analysis method.
2. Determine if interfering species are
present. If the comparison method or scaled
subtraction is used for quantitative analysis,
the resolution should be sufficient to
separate spectral features of the target
compounds from those of interfering species.
For example, in the case of toluene the
absorption band used for analysis at
1031 cm"1 is relatively broad. At first, this
would indicate that a low-resolution
measurement would be sufficient. However,
this band overlaps with bands due to
atmospheric water vapor and CO2.
Therefore, a higher resolution measurement
is required to separate the toluene from
those of interfering species.
3. Acquire reference spectra of the target
compounds. If the specific target
compounds are known prior to beginning the
monitoring study, reference spectra of the
compounds of interest should be recorded at
various resolutions. This can be
accomplished by collecting a reference
spectrum at the highest resolution setting on
the instrument, and then processing the data
by using the required number of Fourier
transform data points for each desired
resolution. When this method is used, only
one -spectrum has to be 'collected. By
comparing the spectra processed at different
resolutions, the operator can determine the
lowest resolution measurement that still
resolves the spectral features of interest.
This resolution setting should be used as a
starting point for future measurements. If
this is not possible, the operator should
consult reference libraries to help determine
the optimum resolution setting required to
characterize the target analyte.
4. Develop calibration curves of the target
compounds. If an inadequate resolution is
used, the relationship between absorbance
and concentration will not be linear. This
relationship is also affected by the
apodization function. Calibration curves
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TECH:
TR-4423-99-03
covering the concentration range of the
target compounds expected in the ambient
measurements must be developed at
different resolutions and with the use of
different apodization functions to determine
the optimum settings. If the compound of
interest does not respond linearly with
respect to concentration, a correction curve
will need to be fitted to the data and. used in
the quantitative analysis package.
5. Use the same parameters to collect field
spectra as were used to record the reference
spectra. If spectra from a commercial or
user-generated library are to be the reference
spectra for quantitative analysis, then the
parameters that were used to generate those
reference spectra should be used to collect
the field spectra. Otherwise, errors in the
measurement will occur.
6. Determine that the instrument is
producing data at the specified resolution.
The following factors should be considered
here: (a) that the operator has selected the
proper parameters, and (b) that the
instrument is operating to the manufacturer's
specifications and that the manufacturer's
specifications are a true indication of the
capabilities of the instrument.
a. Most software packages allow the
resolution to be selected from a menu.
The software then automatically sets the
proper parameters to collect data at the
selected resolution. Therefore, there is
very little opportunity for operator error.
In older versions of software that are not
menu driven, but instead require entering
line commands, many of the parameters
affecting resolution, such as the number
of data points used for the Fourier
transform, must be entered manually. In
this case, the operator must know, and
enter correctly, all of the proper
parameters, and there is a greater chance
of error.
b. If the instrument is not producing data
of the selected resolution, it is also
possible that the instrument is
malfunctioning or that the manufacturer
overstated the capabilities of the
instrument. The following procedure can
be used to determine if the instrument is
producing data at the specified
resolution. There is a cluster of
absorption bands between 1008 and
1020 cm"1 due to water vapor that can
be used to verify the resolution of the
FT-IR monitor. There is -a doublet
centered at 1010.5 cm"1, a single band at
1014.2 cm"1, and a pair of bands at
1017.5 and 1018 cm'1. The singlet at
1014.2 cm"1 has a theoretical bandwidth
of approximately 0.3 cm"1 (USF HITRAN-
PC [University of South Florida 1993]).
This band is a good reference band for
determining the actual resolution
measured by a medium- or low-resolution
spectrometer. For example, if this band
is measured at an instrument setting of
0.5cm"1, the FWHH should be 0.5cm"1.
If measured with an instrument capable
of achieving a higher resolution, for
example 0.25 cm"1, the FWHH should be
the theoretical value of 0.3 cm"1. The
doublet centered at 1010.5 cm"1 is just
7-27
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TR-4423-99-03
resolved at 0.5-cm"1 resolution, but is not
resolved at 1-cm~1 resolution. The
theoretical bandwidth of each of these
two absorption bands is approximately
0.1 cm'1 (USF HITRAN-PC), which makes
them good reference peaks for
instruments capable of measuring at a
resolution of 0.125 cm"1. The two peaks
at 1017.5 and 1018 cm'1 are resolved at
0.125 cm'1, but not at lower resolutions.
If the instrument is not performing to
specifications, there is most likely
an alignment problem with the
interferometer or source optics. Unless
the operator is trained to perform this
alignment, a representative from the
manufacturer must service the
instrument.
The bands centered at 1014.2 cm"1 are a
good test of resolution, but they are not
as sensitive to misalignment in the
interferometer. Other bands that may
also be used are the 2169-cm"1 band of
CO and the HDD doublet centered at
approximately 2720 cm"1. These bands
at shorter wavelength (higher wave
number) are more sensitive to
interferometer misalignment and can also
be used to determine the stability of the
interferometer.
These are general guidelines to be
used when choosing instrumental parameters
to collect data. In reality, the user's choice
of parameters that can be actually used may
be limited by either the specifications of the
spectrometer or by the software. For
example, one software package supplied
with FT-IR long-path,-open-path systems
allows only triangular apodization with no
additional zero filling for processing the
interferogram with the menu-driven
commands. These parameters cannot be
changed unless the user has the capability of
editing the software code. As the resolution
requirements of long-path, open-path FT-IR
monitors become better defined, the
manufacturers will most likely produce
instruments and software to meet those
needs.
7.8 References
Bell, R.J. 1972. Introductory Fourier
Transform Spectroscopy. Academic Press,
New York.
Bittner, H., T. Eisenmann, H. Mosebach,
M. Erhard, and M. Resch. 1994.
Measurements of Diffuse Emissions of
Volatile Organic Compounds by High
Resolution FTIR Remote Sensing. SP-89
Optical Sensing for Environmental
Monitoring, Air & Waste Management
Association, Pittsburgh, PA, pp. 443-454.
Childers, J.W., and E.L. Thompson, Jr.
1994. Resolution Requirements in Long-Path
FT-IR Spectrometry, SP-89 Optical Sensing
for Environmental Monitoring, Air & Waste
Management Association, Pittsburgh, PA, pp.
38-46.
Grasselli, J.G., P.R. Griffiths, and
R.W. Hannah. 1982. Criteria for Presentation
of Spectra from Computerized IR
Instruments. Appl. Spectrosc. 36:87-91.
Griffiths, P.R., and J.A. de Haseth. 1986.
Fourier Transform Infrared Spectrometry.
John Wiley and Sons, New York.
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I f,\ffl: i'j -.-j-j
TR-4423-99-03
Griffiths, P.P., D. Qin, R.L. Richardson, and
C. Zhu. 1993. Atmospheric Monitoring with
FT-IR Spectrometry: Strengths and
Weaknesses of Measurement at Low
Resolution. Presented at the 44th Pittsburgh
Conference and Exposition on Analytical
Chemistry and .Applied Spectroscopy,
Atlanta, GA, March 7-12, paper no. 1142.
Griffiths, P.R., Richardson, R.L., Qin, D., and
Zhu, C. 1995. Open-Path Atmospheric
Monitoring with a Low-resolution FT-IR
Spectrometer. Proceedings of Optical
Sensing for Environmental and Process
Monitoring, O.A. Simpson, Ed., VIP-37, Air &
Waste Management Association, Pittsburgh,
PA, pp. 274-284.
Herres, W., and J. Gronholz. 1984.
Understanding FT-IR data Processing Part 1:
Data Acquisition and Fourier Transformation.
Computer Applications in the Laboratory
4:216-220.
Horlick, G. 1968. Introduction to Fourier
Transform Spectroscopy. Appl. Spectrosc.
22:617-626.
Marshall, T.M., C.T. Chaffin, V.S.
Makepeace, R.M. Hoffman, R.M. Hammaker,
W.G. Fateley, et al. 1994. Investigation of
the Effects of Resolution on the Performance
of Classical Least-Squares (CLS) Spectral
Interpretation Programs When Applied to
Volatile Organic Compounds (VOCs) of
Interest in Remote Sensing Using Open-Air
Long-Path Fourier Transform Infrared (FT-IR)
Spectrometry. J. Mo/. Structure 324:19.
Russwurm, G.M. 1992. Quality Assurance,
Water Vapor, and Analysis of FTIR Data,
Presented at the Air & Waste Management
Association Annual Meeting, Kansas City,
MO, June.
Spellicy, R.L., W.L. Crow, J.A. Draves,
W.F. Buchholtz, and W.F. Herget. 1991.
Spectroscopic Remote Sensing: Addressing
Requirements of the Clean Air Act.
Spectroscopy 6:24-34.
Strang, C.R., and S.P. Levine. 1989. The
Limits of Detection for the Monitoring of
Semiconductor Manufacturing Gas and Vapor
Emissions by Fourier Transform Infrared
(FTIR) Spectroscopy. Am. Ind. Hyg. Assoc.
J. 50:78-84.
Strang, C.R., S.P. Levine, and W.F. Herget.
1989. A Preliminary Evaluation of the
Fourier Transform Infrared (FTIR)
Spectrometer as a Quantitative Air Monitor
for Semiconductor Manufacturing Process
Emissions. Am. Ind. Hyg. Assoc. J.
50:70 77.
University of South Florida. 1993. USF
HITRAN-PC, University of South Florida,
Tampa, FL.
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Chapter 8
Nonlinear Response Caused by Apodization Functions and
Its Effect on FT-IR Data
SUMMARY
This chapter discusses the effects of apodization and temperature on the accuracy
of the FT-IR data. It places special emphasis on the following.
• Why apodization causes the FT-IR response to be nonlinear and how this
response is affected by resolution.
• The FT-IR response to absorption of water, methane, and ammonia as functions
of concentration, temperature, and resolution.
• The errors incurred by using classical least squares and assuming a linear
response.
This chapter uses a set of spectra calculated by using the HITRAN database over a 207-m
path at various concentrations and temperatures.
8.1 Introduction and Overview
The technique of using an FT-IR
system over a long, open atmospheric path
to monitor atmospheric pollutants has
undergone a vigorous development over the
past several years. However, an in-depth
analysis of the error associated with the data
has never been reported. One source of error
in an FT-IR measurement is the application of
an apodization function to the interferogram,
causing a nonlinear response to changes in
gas concentration.
In an FT-IR instrument, the moving
mirror of the interferometer must travel a
certain distance in order to achieve a specific
resolution. At the end of the travel, the
mirror returns to its original position and
repeats the movement. The abrupt cutting
off of the interferogram at the end of the
mirror travel is called truncation. When the
Fourier transform of the truncated
interferogram is performed, an exact
spectrum is not reproduced, and there are
spurious oscillations in the reproduced
spectrum. These oscillations distort the
shape of the spectral features, both in the
bandwidth and in the amplitude of the
various spectral peaks. A graph of an
unapodized (boxcar) water spectrum is
shown in Figure 8-1 a. The graph in
Figure 8-1 b is the same portion of the water
spectrum, but it has been processed with
triangular apodization. Both spectra are at
0.25-cm'1 resolution and are calculated for a
8-1
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UJ
o
m
a
o
tn
m
A. boxcar apodization
B. triangular apodization
1010
1012 1014 1016
WAVE NUMBER (CM-1)
1018
1020
Figure 8-1. A Portion of a Water Spectrum Using (A) Boxcar Apodization and
(B) Triangular Apodization.
path length of 207 m and a partial pressure
of water of 1 5 torr. The spurious oscillations
are clearly visible in the upper curve.
changes in absorbance. This is separate from
the detector's nonlinearity, which has not
been considered in this discussion.
To reduce the magnitude of these
oscillations, various apodization functions
can be applied to the interferogram before
the transform is performed. Many
mathematical forms of the apodization
functions have been investigated (Happ and
Genzel 1961; Filler 1964; Norton and Beer
1976; Kauppinen et al. 1981) and are
available for use by the operator. In general,
these apodization functions create a broader
line width than is available in the unapodized
spectrum and are also partly responsible for
a nonlinear response of the instrument to
The FT-IR instruments commercially
available for remote sensing generally do not
provide a large selection of apodization
functions for the operator, and triangular
apodization is commonly used. This means
that the interferogram is multiplied by a
triangular mathematical function with the
peak at the so-called center burst before the
Fourier transform is performed."
The analysis of the spectra for
concentration is generally done by using the
method of classical least squares and using
8-2
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jECHmimm
TR-4423-99-03
reference spectra of known concentration-
path length products, and these spectra
have also been processed with triangular
apodization. Included in these reference
spectra is a water vapor reference that is
generally manufactured by the operator
(Russwurm 1996) from a field spectrum
taken during an actual monitoring program.
Generally, there is only one reference
spectrum per gas, and it has been acquired
for a single concentration-path length
product at a specific temperature, although
the temperature information is normally not
supplied with the spectrum.
The procedure is usually set up so
that the least squares calculation is
performed over a range of wave numbers
that encompasses a major absorption peak of
the target gas and generally accounts for all
known spectral interferences. The ensuing
mathematical analysis process assumes a
linear relation between absorbance and
concentration, as described by Beer's law.
Since the apodization function produces a
nonlinear instrument response with
concentration but the mathematical data
process, usually classical least squares,
assumes linearity, an error in the data
occurs.
How this manifests itself is shown
schematically in Figure 8-2. The linear curve
in Figure 8-2 represents the assumed change
in absorbance with concentration-path length
product while the quadratic curve represents
the actual response expected in the field
Actual response calculated using triangular apodization
o
ca
< 0.2
0 200 400 600 800 1000
concentration path length product (PPMM)
Figure 8-2. Schematic of Actual and
Assumed FT-IR Responses.
spectra. While Figure 8-2 is intended to be
indicative of the instrument response, the
actual curve is the response for methane at
2927 cm"1. The point where the two curves
cross is the concentration-path length
product of the reference spectrum. From
Figure 8-2 it is seen that if the
concentration-path length product of the
field spectrum is less than that of the
reference, the actual concentration is
overestimated, and the actual concentration
is underestimated when the concentration-
path length product of the field spectrum is
greater than that of the reference. Evidently,
triangular apodization creates a broader final
absorption feature (Marshall and Verdun
1990) than most of the other commonly
used functions and therefore a more
pronounced nonlinear response. Triangular
apodization has been used exclusively
throughout the remainder of this chapter
because use of this apodization function is
considered a worst case.
8-3
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This chapter examines the magnitude
of the error in several ways—by examining
the error for a single line in a pure gas, then
considering the effects of the spectral
interference created by water vapor, and
finally examining the error created when a
range of wavelengths is used with the
classical least-squares technique.
8.2 Procedure and Theoretical Basis
The primary data used in this chapter
is a set of spectra calculated from the
HITRAN database.1 The three gases used are
ammonia, methane, and water vapor. These
three gases were chosen because
absorbance due to ammonia is not heavily
impacted by water, and the absorbance due
to methane is strongly affected by water.
Water is the primary interfering species, and
it perhaps presents the largest problem in the
atmospheric spectroscopy of the mid-infrared
region. Indeed, the spectrum obtained from
the open atmosphere is primarily a water
vapor and carbon dioxide spectrum, and the
gases of interest (the target gases) represent
only small perturbations to that spectrum.
The HITRAN database was used to calculate
Lorentzian absorption lines over a 207-m
path at a total pressure of one atmosphere
and with varying concentrations and
temperatures. Following that calculation, the
spectra were reprocessed with an algorithm
that allows an apodization function to be
TR-4423-99-03
applied to the spectra and also allows
changing the resolution to some other
desired resolution. To match the wanted
resolution and to apply the apodization
function, the following mathematical
procedure has been used.
• Calculate an unapodized high-
resolution spectrum 7 from HITRAN.
• Calculate the inverse Fourier
transform of the spectrum T.
• Multiply this inverse transform by
the apodization function.
• Calculate the Fourier transform of
the product spectrum from the step
above.
The mathematical justification for this
procedure is straightforward and is described
as follows. The spectrum actually measured
by an FT-IR instrument, Tr (w), is given by the
convolution of the true spectrum 7"(o)) and
the instrument line function 5(o)) as
(8-1
However, the instrument line function for an
FT-IR instrument is the Fourier transform of
the apodization function /4(6), where 6 is the
optical path difference in the two legs of the
interferometer. That is, 5(co) = F[/4(6)], or
X(8) = F -'[5(0))]. Therefore, Equation (8-1)
can be rewritten as
(8-2)
'The AFGL HITRAN molecular absorption
parameters database. See, for example, Rothman
etal. (1987).
8-4
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Application of the inverse transform
followed by the forward transform to the
right-hand side of Equation (8-2) yields
(8-3)
The convolution theorem for Fourier
transforms states that the Fourier transform
(or inverse) of the convolution of two
functions is equal to the product of their
Fourier transforms (or inverses). Applying this
theorem to Equation (8-3) gives the final
expression that
and all the spectra that were calculated from
HITRAN and FASCODE and used for this
effort were processed in this manner.
It is convenient to discuss here two
other points about the linearity of the
response of the FT-IR instrument to changes
in concentration of the atmospheric gases.
These points consider what concentration
levels must be exceeded to make the
response nonlinear and what resolution will
make the response nonlinear. To evaluate
these points, note that the intensity 7(co) that
is measured by a Fourier transform
spectrometer is proportional to the
convolution of the incident intensity and the
Fourier transform of the instrument line
function S(u>). But the function 5(co) is a
function of the resolution, which in turn is
dependent upon the maximum optical path
difference between the two mirrors of the
interferometer. The measured intensity can
be written as
/m(o>) = D(a>)/7(co+8)S(8,7?)d8
In keeping with Beer's law, the measured
background intensity is given as
7mo(co) = D(G))//0(&>+6)S(6,/?)d8
where -D(co) is the response of the instrument
optics and the electronics. The actual
transmission 7"(a)) through the absorbing
medium can be written (from Beer's law) as
= /0(o))3Tto)
and for a single gas component 7*(co) =
exp(-ca(o))). Here cis the concentration-path
length product (with units of ppm-m) and ), can then be written as
If the background intensity is a slowly
varying function over the instrument line
function 5, then it can be taken outside the
integral sign, and the measured transmission,
Tr (co), can be rewritten as
Because the instrument line function has a
unity normalized integral (^S(b,R)db = 1), the
measured transmission T, can simply be
written as
8-5
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r±J=r.?. ia.Is =
•.-• -.: •••=•••= =
TR-4423-99-03
(8-5)
The measured absorbance can be
obtained by taking the negative logarithm of
Equation (8-5). Substituting for Tfrom Beer's
law, the expression
is obtained. From Equation (8-6), the above
two points can be examined. If the exponent
ca(o)) is small, only the first two terms of the
expanded exponential term can be retained,
and the expression can be written as
Am((*>) = -log{/[l-ca(cj + 5)]S(5,/?)rf§}
Then, making use of the unity integral of S
and the fact that logd - x) - - x for small x,
the measured absorbance can be written as
Xm(w) = c/a(o)
and this expression is linear with
concentration. The assumption that is
important here is that the product ca must
be small, at least compared to the quadratic
term in the expansion of the exponential.
Another limiting case is that of high
spectral resolution; that is, the instrument
line function should be small compared to the
half width of the gas absorption features.
With that assumption, the transmission
function is a slowly varying term in
comparison with the instrument line function
and can be brought outside the integral.
Then, again using the unity normal integral of
5, the absorbance A can simply be written as
Am(u>) = -log[exp(-ca(o)))] = ca(co)
which is again linear with concentration.
The predominant absorption features
in spectra taken over an open path come
from water vapor in the atmosphere, and
these features have a FWHH of about
0.1-0.2 cm"1. Therefore, the assumption
above implies that the instrument resolution
should be about 0.05 cm"1. However, this
requirement is not satisfied at present by any
of the commercially available instruments for
OP/FT-IR monitoring. Therefore, the response
of the instruments that are available should
be expected to be nonlinear, at least for
water.
It is not easy to verify experimentally
the nonlinear response of an FT-IR instrument
since the concentrations normally present in
the open air do not encompass a large
enough range. The nonlinear response has
been verified experimentally for methane by
Ropertz (1997), and a copy of a portion of
his data is shown in Figure 8-3. Additionally,
reference spectra made from known
concentrations of pure gases are available
commercially. One ammonia reference that is
commonly used has a concentration-path
length product of 550 ppm-m. When the
absorption of that spectrum is compared to
the absorption of the calculated spectrum at
the same concentration-path length product,
the agreement is within about 7%.
8-6
-------
TR-4423-99-03
PolynomiKfte Rttgntsion 2.0r4xng d«r
MvQargibniiM bd dner opUcnen Weg-
Iflng* von 96.88m
PdynomJscfia Regression 2.0nJnung d«f
MeOeigebnlsM t>d «ln«r optiscfwn W«j-
Urga von 20.7Vm
aooo loooo
ZuttindMctu* CM, / ppfn*m
Figure 8-3. Measured Concentration of
Methane vs. the Experimental Response of
the FT-IR (reprinted with permission of
A. Ropertz).
8.3 Results of Calculations
The effect of the nonlinear response
has been studied for three gases: methane,
ammonia, and water vapor. All the
absorbances were calculated for a range of
concentration-path length products at
specific wavelengths and then fit to a
polynomial of order 2, since this seemed to
be the best fit. In one case (an ammonia line
at 1046 cm"1), the quadratic fit was not
really satisfactory. The absorbance at that
ammonia line was best fit with a linear
approximation over a portion of the data and
a quadratic approximation over the
remainder. This is a clear indication that the
functions describing the absorbance at
various wave numbers are different. The
absorbance was also calculated as a function
of temperature and for the four resolutions
0.25, 0.5,1.0, and 4.0 cm'1.
The coefficients for the various
polynomials were calculated by using
nonlinear regression. It was then possible to
determine the maximum value of either the
concentration-path length product or the
temperature that can be used before the
response must be considered nonlinear. To
do that, the ratio of the quadratic to linear
terms of the polynomial fit should be small,
and this ratio was arbitrarily set equal to 0.1.
This is equivalent to requiring that the
concentration-path length product or the
temperature be less than the term 0.1c, lcq,
where the c, and the cq are the linear and the
quadratic coefficients, respectively.
The methane absorbance was
measured at various points in the
2900-3000-cm'1 region because that is the
region most commonly used for the analysis.
Within this region the absorbance was
calculated for the concentration-path length
product range from 300 to 2100 ppm-m. This
corresponds to a path length of 200 m and a
range of concentrations from 1.5 to 10 ppm.
This range was selected because it covers
the range from slightly below accepted
ambient levels to slightly above the levels
that could be expected at coal mines, land
fills, or hog farms.
The ammonia absorbance was
measured at various points in the
850-1050-cm'1 region and covering the
range from essentially 0 to 1100 ppm-m. For
a 200-m path length, this range covers the
concentration from the ambient levels to
5 ppm, or that concentration seen at hog
farms.
8-7
-------
TR-4423-99-03
The water spectra were calculated
over the wavelength ranges of methane and
ammonia since the absorbance due to water
is the predominant interfering absorbance in
the mid-infrared atmospheric spectrum. The
water vapor absorbance was calculated in
terms of the partial pressure of water from
0.5 to 35 torr, or from slightly below to
slightly above that range seen here at
Research Triangle Park (RTP), North Carolina,
over a year. The various graphs for water
that follow are plotted with the partial
pressure in torr along the abscissa. The
water absorbances were calculated for a
path length of 207 m, which is the path
length used when we take measurements at
RTP.
All the absorbances were calculated
over the temperature range from 250 K to
310 K in 5-K increments. This range was
chosen because it covers the yearly range
normally seen at RTP. This range is
appropriate also in that it encompasses the
temperature range over which the
commercially available instruments can work.
Finally, all the spectra were calculated for
the following four resolutions: 0.25, 0.5,
1.0, and 4.0 cm'1.
Figures 8-4, 8-5, and 8-6 show the
overall absorbance due to methane at
2927 cm'1, ammonia at 967 cm"1, and water
at 1014.5 cm"1, respectively. The plots for
methane and ammonia show the absorbance
as a function of the concentration-path
length product and the temperature. The
water absorbance is shown as a function of
the partial pressure of water and
temperature, with the absorbance being
calculated for a path length of 207 m.
Figures 8-7 and 8-8 show,
respectively, the absorbance for methane
and ammonia as a function of
concentration-path length product at a
constant temperature of 295 K. Figure 8-9
shows the absorbance due to water as a
function of the partial pressure of water, also
at a constant temperature of 295 K. These
graphs also contain the second-order
polynomial that best describes the curvature
of the absorbance.
As stated above, the dependence of
the absorbance on temperature was also
calculated for these three gases. The change
in absorbance as a function of temperature
for methane and ammonia is not very strong,
as is depicted in Figures 8-4 and 8-5, but
that is not the case for water. The change in
absorbance with temperature for water is
shown in more detail in Figures 8-10 and
8-11. Figure 8-10 shows the dependence of
water absorbance on temperature at a partial
pressure of 0.5 torr, and Figure 8-11 shows
this dependence at a partial pressure of
35 torr.
8-8
-------
TR-4423-99-03
A. METHANE AT 1/4 CM"1 RESOLUTION
B. METHANE AT 1/2 CM"' RESOLUTION
C. METHANE AT 1.0 CM"' RESOLUTION
D. METHANE AT 4.0 CM "RESOLUTION
Figure 8-4. Methane Absorbance at 2927 cm'1.
A. AMMONIA AT 1/4 CM"' RESOLUTION
8. AMMONIA AT 1/2 CM"' RESOLUTION
C. AMMONIA AT 1.0 CM"' RESOLUTION
0. AMMONIA AT 4.0 CM'1
Figure 8-5. Ammonia Absorbance at 967 cm .
8-9
-------
TR-4423-99-03
A. WATER AT 1/4 CM "' RESOLUTION
8. WATER AT 1/2 CM*1 RESOLUTION
C. WATER AT 1.0 CM'1 RESOLUTION
D. WATER AT 4.0 CM"' RESOLUTION
Figure 8-6.Water Absorbance at 1014.5 cm1.
A. 114 CW1 RESOLUTION
ADS n -2.7eS«10^ » 2.401I10~*(CL) - 1.0323«»10*(CL)*
400 100 1200 1600 2000 2400
CL (PPM-M)
e. in CM 'RESOLUTION
r'(CL|'
0.35
S 0.25
I «•"
0.05
-O.OS
400 100 1200 1000 2000 2400
CL (PPM*M)
C. 1 CM-' RESOLUTION
ABS • 1.892110-" + 1.931Iia^(CL) • 1.258X1Q*(CL)2
400 100 1200 1100 2000 2400
CL (PPWM)
D. 4 CM*1 RESOLUTION
ABS» 3.737x10^ * 6.21 x10~ft(CL)-
fj 0.07
I
400 100 1200 1000 2000 2400
CL (PPM-M)
Figure 8-7. Methane Absorbance vs. CL at 2927 cm"
8-10
-------
wmm
TR-4423-99-03
A. 1M CM'1 RESOLUTION
i1ffD» 1.73t4HOaCL -S.i72623i1ff'|CL|1
200 400 100 100 1000 1100
CL (PPMM)
B, iaCM 'RESOLUTION
I193* 1.H73i10':lCL.3.713J44X10''(CL)a
100 400 100 100 1000 1200
CL (PPMM)
C. 1.0 CM'1 RESOLUTION
ABS s 1.4M4i«3 * 1.077x10°CL • 3.1S021x1'"'
_»-"-*
.- ,•"•''" : :
^••*'** •
><"'": • " i
S IS IS JS
PARTIAL PRESSURE fTORR)
0.22
| 0.11
a
0 O.lQ
0.04
' .
0.10
0
a
or
o
! 0.01
.
.«•"
.*"*
..-**
»""**
S i 1* 21 31
PARTIAL PRESSURE FTORR)
o. 4.0 CM* 'RESOLUTION
ABS a 0.117X10T4* 1.4l07i10'~V * I.SJilO^P1
• ' "- XI-'-
„***
^r*' ';. . . ; . .
• —•**".. .'..:. • -
5 15 15 35
PARTIAL PRESSURE fTORR)
Figure 8-9. Water Absorbance vs. fat 1014.5 cm'1.
8-11
-------
TR-4423-99-03
A.1HCM •'RESOLUTION
Mi10 J.2*43110 "*T*6J172i10 -
240 210
TEMPERATURE (K)
300 320
6.112 CM •' RESOLUTION
ABS.1.7H49110 J-1.«U10 •*T»4.C04T««10 '7(
g 0*3
240 260
no MO
TEMPERATURE (K)
C. I CM1 RESOLUTION
ABS-1.02741110 J-8J9itO <5T*224S7S4t10 -'ft)3
230 300
TEMPERATURE [K]
D.
-------
8.4 Analysis
Once the absorbance function is
determined, it is instructive to find the
maximum value in concentration for which
the absorbance can be considered linear.
This can be done by requiring that the
quadratic term in the polynomial representing
the absorbance be small in comparison with
the linear term. That is, if the absorbance is
represented by the polynomial ABS = a0 +
a^X + a2X2, then for the absorbance to be
considered linear, the ratio a2X2/a{X must be
small. The value of X can be found by
requiring that this ratio be less than some
value k, which is equivalent to requiring that
the independent variable X must be less than
the quantity atk/a2. These values have been
calculated for a k value of 0.1 and a
temperature of 295 K and are shown for
methane and ammonia in column 4 of
Table 8-1.
Next, the error is estimated. The error
made when a linear response is assumed
depends on how far removed the
TR-4423-99-03
concentration-path length product of the
field spectrum (the actual measurement) is
from the concentration-path length product
of the reference spectrum. (See Figure 8-2.)
Column 5 of Table 8-1 shows the predicted
error at the calculated maximum values Xmca
when references at 81 and 550 pprrvm are
used for methane and ammonia, respectively.
These reference values come from two
commercial sources that are commonly used
by the instrument users. The errors have
been calculated in the following way. The
linear response is simply based on the
assumption that the absorbance goes
through the 0 and the reference absorbance.
at the concentration-path length product
listed. Thus the linear response is given by
the expression ABSL = (ABSREF )(CLj/CLR£/r
where the (CL)REF is the concentration-path
length product of the reference spectrum.
The absorbances for both the linear response
and the quadratic response can be calculated
for the same CL and the error found from
%E = (ABSQ-ABSL)/ABSQ. The results of these
calculations are given in Table 8-1.
Table 8-1. Maximum Values Over Which Response Can Be Considered Linear and Associated Errors
Gas v (cm"1)
Methane 2927
Ammonia 967
Resolution (cm"1)
0.25
0.5
1.0
4.0
0.25
0.5
1.0
4.0
Xmax (ppm-m)
2367
1799
1232
861
307
330
342
305
% Error at Xm(Lr
-9.3, Ref. at 81 ppm-rn
-10.2
-11.9
-17.4
+ 8.9, Ref. at 550 ppm
+ 7.6
+ 6.9
+ 9.2
•m
8-13
-------
TR-4423-99-03
Similar calculations can be carried out
for water, but in that case it is found that the
absorbance is not linear for resolutions poorer
than 0.5 cm "1 throughout the entire range of
partial pressures for which the absorbances
were calculated. This is also true for the
water absorbance as a function of
temperature. The water absorbance was also
examined at 1012.4 cm"1, which is
considered to be at the baseline between
peaks. As the partial pressure of water rises
and the absorbance increases, the wings of
the individual peaks merge to become a
continuum, which then forms the spectral
baseline. This is particularly troublesome for
the least-squares analysis because the
absorbance at the baseline changes in a
nonlinear way over the entire range of partial
pressures for which the calculations were
done.
While the actual concentration of
water is of little interest as an atmospheric
pollutant and water is seldom a target
compound, it must almost always be
included in the least-squares analysis as an
interfering species. One question that this
work set out to answer is how to overcome
the difficulty with matching the water vapor
reference to the actual water in the field
spectrum. The concentration of water can
and does change rapidly and dramatically in
the atmosphere. Therefore, it was instructive
to look at the case where the water vapor
reference was obtained from a spectrum that
was taken when the partial pressure was
10 torr but the actual partial pressure of
water for the spectra being analyzed was
20 torr.
Figure 8-12 is a plot of the water
absorbance in the 1014.5-cm'1 region. The
solid curve is a water spectrum calculated for
20 torr of water at 207 m. The dotted curve
is a 10 torr spectrum that has been
normalized to the 20 torr spectrum at
1014.5 cm"1. Note that the only place where
the curves seem to match is at that peak,
and there is a particularly large discrepancy
in the baseline. But this kind of normalization
is not exactly what classical least squares
does. The mathematics of classical least
squares adjusts the curves, one to the other,
so that the sum of the differences between
them squared is a minimum. It does that by
calculating a slope as the single coefficient
by which to multiply the entire curve (in this
case the 10 torr spectrum) and by adding
some constant value to the result. However,
because of the nonlinear response of the
instrument and the fact that the polynomials
describing the absorbance seem to be
1006 1008 1010 1012 1014 1016 1018 1020 1022
WAVE NUMBER (CM"1)
Figure 8-12. Match of Water Absorbance
at 1014.5 cm"1.
8-14
-------
TR-4423-99-03
different for different wave numbers, no such
process can really match the curves.
All the above analysis describes what
error would, be made if the analysis for
concentration were done at a single wave
number using a single reference. However,
the classical least squares analysis uses a
range of wave numbers for the calculation. In
the remainder of this Analysis section, the
classical least-squares technique is applied to
this data to determine the actual error
involved with this procedure in light of the
nonlinearities discussed above.
To explore the effect of a reference
spectrum whose concentration-path length
product is not at the concentration-path
length product of the field spectrum, a
methane spectrum calculated for 6 ppm of
methane at 295 K was used as a "field"
spectrum. The spectra used as references
were all at 295 K, but the concentrations
were allowed to vary from 1.5 ppm to
10 ppm. The results for these calculations
are shown in Figures 8-13 and 8-14.
Figure 8-13 is a plot of the analyzed
concentrations of methane over the wave
number range 2915-2929 cm"1. This region
was chosen for this analysis because there
are two methane lines that are not strongly
impacted by the interfering species water. In
Figure 8-14, the analysis region has been
expanded to cover the region from 2900 to
3000 cm'1. These plots clearly indicate that
the best accuracy is at the higher resolution,
and also that the smaller analysis region
seems to also have better accuracy. This
must indicate that the least-squares
technique is less efficient at matching the
two spectra when the analysis region is
large.
To explore the effect of water as an
interfering species, a "field" spectrum of
methane and water was calculated from
•HITRAN and then analyzed by classical least
squares. The field spectrum used a
concentration of 6 ppm for methane and a
partial pressure of water of 1 5 torr, all at a
temperature of 295 K. The partial pressure of
the spectra used as water references was
allowed to range from 10 to 20 torr at
295 K. Figure 8-15 shows the results from
classical least-squares analysis for methane
for the two wave number regions
2915-2929 cm'1 and 2900-3000 cm'1. The
data points for the two regions have been
shifted slightly for clarity. These results
indicate that the methane concentration is
not strongly impacted by the presence of
water. There does seem to be a bias of a
few percent for each region from the true
value, and the magnitude of the error bars is
larger for the larger region. It is not clear why
the small but definite biases in these graphs
are present. A possible reason is that in the
presence of water, because of its high
concentration-path length product, the
resulting absorption spectrum is not simply a
linear combination of the absorbances from
methane and water.
8-15
-------
TR-4423-99-03
FIELD SPECTRUM IS FIXED AT 6 PPM
O
Z
O
O
Q
UJ
6.8
6.4
6.0
< 5.6
5.2
0 2 4 6 8 10
REFERENCE SPECTRUM CONC (PPM)
Figure 8-13. Analysis Results for Methane from 2915 to 2929 cm'1.
12
FIELD SPECTRUM CONCENTRATION FIXED AT 6 PPM
7.8
2
Q.
£L_
O
z
O
O
Q
OJ
<
<
6.6
5.4
4.2
0 2 4 6 8 10
REFERENCE SPECTRUM CONC (PPM)
Figure 8-14. Analysis Results for Methane from 2900 to 3000 cm"1.
12
8-16
-------
..
TECHm^mm
TR-4423-99-03
Field spectrum Is 6 ppm CH« plusl 5 torr water
i.»
s-
o
J
T
PARTIAL PRESSURE OF WATER REFERENCE (TORR)
Figure 8-15. Methane Analysis Allowing the
Water Reference Concentration to Vary.
Some further study has shown that as
the resolution gets poorer, the errors for the
above calculations also get worse (data not
shown). The reason for water as an
interfering species to not strongly impact the
methane analysis, although somewhat
surprising, is clear. The mathematical
procedure of classical least squares adjusts
the spectra so that for the individual
components most of the variability of the
absorbance in the field spectrum is
accounted for. It makes that adjustment by
minimizing the sum of the squares of the
residuals. But, in the case of water—just as
with methane, the calculated concentration
is not the correct value unless the water
reference has the same partial pressure and
was taken at the same temperature as the
water in the field spectrum. Nonetheless,
because the residuals have been minimized,
classical least squares accounts for most of
the variability in the absorbance of the water
and also minimizes the effect of water on the
analysis of methane.
8.5 Discussion
The calculated spectra have been
analyzed to determine the magnitude of the
error when a linear function is assumed for
the response of the FT-IR instrument. From
Figure 8-2 it is seen that for a measured
absorbance the concentration is
overestimated when the concentration-path
length product of the field spectrum is less
than that of the reference spectrum.
Conversely, the concentration is
underestimated when the concentration-path
length product of the field spectrum is high in
comparison with the reference. It is also
shown here that the magnitude of the error
is larger with poorer resolution.
At present there seems to be no
simple correction that can be applied to the
calculated concentration-path length product
to account for the error. In the cases
presented here, the spectra could be
calculated from the HITRAN database, but
the number of gases available in HITRAN is
quite limited to the predominant atmospheric
species. What must be made available is
either a set of references for each gas that
encompasses a large range of
concentration-path length products or a set
of high-resolution spectra that can be
modified through the mathematics shown
here to account for the nonlinear response.
Then the analysis should proceed by using a
polynomial fit to the absorbance versus
concentration.
8-17
-------
TR-4423-99-03
Even with a reasonable estimate of
the maximum concentration-path length
product that can be used with some
assurance that the errors will not be very
large, the implied maximum allowable
concentrations in terms of parts per million
over the 207-m path are fairly small. For
example, Table 8-1 shows that at a
resolution of 4 cm'1 the maximum allowable
concentration would not really encompass
the methane concentration variability
normally seen in the atmosphere. While the
higher resolutions imply higher maximum
values, measurements at coal mines might
have high unexpected errors that are not
reported at all by the classical least-squares
technique. The criterion used to arrive at the
values in this paper was that the ratio of the
quadratic term to the linear term should be
less than 0.1. It is felt that this is not a
stringent criterion, and that implies that
higher reported values of methane, even at
normal atmospheric concentrations, probably
have some unexpected and unreported error
associated with them. The magnitude of
such errors is probably unknown to the
experimenter.
The results for ammonia are similar to
those of methane except that at the
967-cm"1 peak there does not seem to be as
much effect due to changing resolution.
Water presents an entirely different
problem to the analysis of FT-IR data. The
absolute value of the concentration of water
is rarely, if ever, calculated, and the
important concern seems to be whether the
absorbance due to water is adequately
accounted for. This evaluation indicates that
analyzing for an actual value for the
concentration of water may be difficult but
that this may not make much difference
since the variability of the absorbance due to
water seems to be accounted for almost
entirely. Figures 8-15 and 8-16 tend to
corroborate these assumptions. Figure 8-16
plots the value of the linear regression slope
when the dependent variable is a water
spectrum at a partial pressure of 1 5 torr and
a temperature of 275 K. The independent
variables were a set of water spectra whose
partial pressures were all 1 5 torr but whose
temperatures varied from 255 to 295 K. The
expected value of all the slopes was 1.00.
This curve implies that the temperature
difference plays a major role in the error of
the analysis. If, for example, the calculations
are repeated for a set of independent
variables, all at the same temperature but at
changing partial pressure, the regression
slopes are all within a few percent of the
expected values.
Partial pressure Is fixed at 15 torr for all spectra
Field spectrum at 275 K , analyze from 1008 cm "' to 1019 cm''
255 260 265 270 275 280 285 290 295
TEMPERATURE OF REFERENCE SPECTRA (K)
Figure 8-16. Plot of Regression Slopes Vs.
Temperature.
8-18
-------
TR-4423-99-03
Figure 8-17 is a plot of the
difference of two spectra. One is the
original field spectrum where the partial
pressure of water is 15 torr at 275 K.
The reference spectrum was at 1 5 torr
but at a temperature of 255 K. To obtain
the plot in Figure 8-17, the difference
was found between the field spectrum
and the reference spectrum to which the
regression results had been applied.
These results show that the difference is
less than 10% of the original, thereby
accounting for at least most of the
absorbance due to water. Figure 8-17
also shows a number of other curious
results. The two spectra were aligned at
the 1014.5-cm"1 line, but the difference
clearly shows that the reference
spectrum was somewhat broader than
the field spectrum because of the "W"
shape of the curve. The line at 1017 cm"1
clearly shows that these two spectra
were not properly aligned, although they
were at 1014.5 cm'1. Atthe 1010.7-crrV1
line, the difference indicates both a
misalignment and a difference in the
widths of the two lines. The discussion of
this chapter does not speculate on why
Field spectrum at 27S K
reference spectrum at 255 K regression results applied
o
til
t. 0.001
1010 1012 1014
WAVE NUMBER (CM'1)
Figure 8-17. Difference After Regression
Coefficients Have Been Applied.
that happens, but most workers in the field of
open-path FT-IR measurements have seen this
occur on many occasions.
8.6 Conclusions and Recommendations
The work that has been carried out here
has been restricted to molecules that have fairly
narrow absorption features, and broadband
features have yet to be studied. It is likely that
whenever the instrument line function (or slit
function) is broad in comparison with the
absorption feature, the results presented here
will be noticeable. Because the response of the
FT-IR instrument is inherently nonlinear but the
most commonly used analysis technique
assumes it to be linear, errors of an unknown
magnitude can occur in the data. These errors
occur for two primary reasons: First, the
reference spectra that are commonly used by
workers with the FT-IR instrument have not been
taken at the same concentration-path length
product or at the same temperature as existed
during the field spectra acquisition phase.
Second, the differences in the temperatures at
which the reference and the field spectra were
acquired seem to be more important than was at
first thought. This is clearly true for water.
From this work, the conclusions that can
be drawn are as follows.
• Errors of unknown magnitude occur in
the FT-IR data whenever the reference
spectrum of the target gas does not
have the same concentration-path
length product as the field spectrum.
There is probably at least a 10% error
8-19
-------
TR-4423-99-03
whenever the reference and the
field spectrum differ in
concentration-path length product
by a factor of 2.
• Differences in temperature cause
some further error.
• In all the cases studied here,
higher resolution indicated lower
predicted errors.
• Water, when used as an
interfering species, does not
strongly impact the analysis, even
when the difference in
concentration-path length product
is large. It is anticipated that this
is true for all interfering species.
• The analysis for water directly is
limited by the same difficulty as
analysis for any other target gas.
• It is essentially impossible to
determine the absolute error in
concentration calculated for any
one field spectrum. This is
because the magnitude of the
error depends on the magnitude of
the difference in the
concentration-path length product
of the reference and the field
spectra.
Although this may seem to be a
formidable problem for the analysis of
FT-IR data when the response is assumed
to be linear, there are some ways to
overcome it. The recommendations are
as follows.
• The combination of high resolution and
boxcar apodization (or unapodized
spectra) seems to create the most linear
response. Because it is likely that at
present few reference spectra using
boxcar apodization exist, they must be
manufactured.
• A new mathematical analysis approach
that accounts for the nonlinear response
directly during the analysis should be
developed.
• Future databases like the NIST database
should incorporate high-resolution
spectra, along with the capability to
create apodized, lower resolution spectra
that account for the inherent nonlinearity
created by the instrument line function.
8.7 References
Filler, A.S. 1964. Apodization and Interpolation
in Fourier-Transform Spectroscopy. J. Opt. Soc.
Am. 54:762-767.
Happ, H., and L. Genzel. 1961. Interfernz-
Modulation Mit Monochromatischen Millimeter-
wellen. Infrared Phys. 1:39-48.
Norton, R.H., and R. Beer. 1 976. New Apodizing
Functions for Fourier spectrometry. J. Opt. Soc.
Am. 66:259-264.
Kauppinen, J.K., D. J. Moffatt, D.G. Cameron,
and H.H. Mantsch. 1981. Noise in Fourier Self-
Deconvolution. Appl. Opt. 20:1866-1879.
The use of high resolution
(0.25 cm'1) makes the errors
smaller and manageable.
Marshall, A.G. and FiR. Verdun. 1990. Fourier
Transforms in NMR, Optical, and Mass
Spectrometry, Elsevier, Amsterdam.
8-20
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Ropertz, A. 1997. Kalibrierung Eines
FT-IR La ng weg a bsorpt i ons-
spektrometeres in Verbindung Mit Einer
Einstelbaren I nf ra rot-m u Iti-
reflexionsgaszelle Und Validerung Der
Ergebnisse Wahrend Einer Messkampagne
Bei Einer Raffinerie. Diplomatarbeit im
Fachbereich Maschienen und
Vefahrenstechnik an der Fachhochschule
Dusseldorf, Matrikel-Nr 240415,
Dusseldorf.
Russwurm, G.M. 1996. Long-Path Open-Path
Fourier Transform Infrared Method Monitoring of
Atmospheric Gases. Compendium of Methods
for the Determination of Toxic Organic
Compounds in Ambient Air—Compendium
Method TO-16, EPA/625/R-96/010b,
U.S. Environmental Protection Agency, Research
Triangle Park, NC.
Rothman, L.S., R.R. Gamache,
A. Goldman, R.A. Toth, H.M. Pickett,
R.L. Poynter, J.M. Flaud, C. Camy-Peyret,
A. Barbe, N. Hussen, C.P. Rinsland, and
M.A.H. Smith. 1987. The HITRAN
Database: 1986 Edition. Appl. Opt.
26:4058-4096.
8-21
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Chapter 9
The Technique of Classical Least Squares
SUMMARY
This chapter can be considered a tutorial on the use of classical least squares
analysis as applied to the FT-IR data. The following specific points are addressed.
• Least squares analysis for one dependent and one independent variable or
simply regression analysis
• Development of the least squares techniques in matrix terms
• Using more than one reference gas
• Expansion of the technique to include the quadratic terms
• Discussion of the errors as calculated by this technique
9.1 Introduction and Overview
At the time of this writing the
preferred technique for data analysis of the
FT-IR spectra is the method of least squares.
In order for this technique to be used, a set
of reference spectra must be available to the
operator. These spectra .are acquired by
using pure samples of gas under controlled
conditions of pressure and temperature. They
are generally acquired with the gas in an
enclosed cell in a laboratory. Once the
absolute pressure of the target gas in the cell
is adjusted, the cell is backfilled to a total
pressure of one atmosphere by using an
nonabsorbing gas such as nitrogen, and the
spectrum is acquired. In order to accurately
analyze a so-called field spectrum there has
to be one reference spectrum for each gas
whose absorbance is contained in the field
spectrum.
This chapter describes in some detail
the process of the analysis itself, and this
description is by necessity somewhat
mathematical. Section 9.2 of this chapter
considers the case where there is one gas in
the field spectrum and only one gas is used
as a reference. The result of this is to derive
the general expressions for the linear least-
squares fit, or what is generally referred to
as linear regression. Section 9.3 introduces
matrix terminology and describes how the
analysis is generalized to several gases.
Section 9.4 describes those changes in the
matrix terminology that are necessary to
include a quadratic term in the equations so
that a nonlinear response can be accounted
for.
9.2 Least Squares Analysis for One Gas
The least squares technique has been
developed for many years and is amply
9-1
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described in many texts (Sokolnikoff and
Redheffer 1966; Draper and Smith 1966).
As applied here, it consists of trying to fit the
absorbance of a reference spectrum to the
absorbance measured in a field spectrum in
some so-called best way. The assumption is
that at each wave number of the spectra
there is a linear relation between the field
spectrum absorbance and the absorbance of
the reference spectrum. This assumption
arises naturally from Beer's law, which
implies that there is a linear relation between
the absorbance and the concentration-path
length product from which the spectrum was
obtained. Mathematically, this linear relation
is written as A = aCL, where CL is the
concentration-path length product and the
constant of proportionality is a, the
absorption coefficient of the gas. This implies
that for a fixed path length L the absorbance
is a linear function of the concentration C.
Thus at each wave number there is a linear
relation between the absorbance of the field
spectrum and the absorbance of the
reference spectrum. If the absorbance of the
field spectrum is considered to be the
dependent variable Y and the absorbance of
the reference the independent variable X,
then at each wave number a relation of the
form Y = mX + b should exist. The problem
then becomes a mathematical one of
determining the slope m and the intercept b.
As an illustration, consider the situation
where there is a single gas in the field
spectrum, and therefore only one gas is
necessary in the reference set. If the
instrument is operating at a resolution of
0.5 cm'1, then there is a data point at every
0.25 cm"1. A partial tabular listing of the
absorbance data looks like that given in
Table 9-1 below.
The data in this table shows that the
baseline for both the field spectrum and the
reference spectrum is at an absorbance (abs)
of 0.001 and that an absorbance peak exists
at 1000.75 cm'1. If a graph of these
absorbances is plotted with abs (field) along
Table 9-1. Partial Listing of Spectral Absorbance (abs) Data
Wave Number abs (field) abs (reference)
1000.00
1000.25
1000.50
1000.75
1001.00
1001.50
1001.75
0.001
0.050
0.085
0.100
0.090
0.055
0.030
0.001
0.010
0.017
0.020
0.018
0.011
0.006
9-2
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TECHmlmm
TR-4423-99-03
the Y-axis (dependent variable) and the abs
(reference) along the X-axis (independent
variable), then the linear relation becomes
apparent. In the absence of noise in the
spectra, the intercept should be 0 according
to Beer's law, but because of noise it is not,
and the individual data points do not lie
precisely on a straight line.
The question then becomes what is
the "best" straight line that can be fit to the
data points. The classical least squares
technique defines what is meant by the term
best, in that it requires that the sum of the
squares of the residuals be a minimum. Once
the slope and the intercept are determined,
then a Y value can be calculated for any
point X from Y = rnX + b. The X values are
chosen to coincide with the actual data
points along the X-axis, and then the
difference between the calculated Yand the
actual 7data value is found. This difference
is the residual. The individual residuals are
squared and then summed, and the best fit is
found when this sum is a minimum.
This procedure gives rise to the term
least squares. The minimization process is
completely transparent to the user, and he
does not have to make small adjustments to
the line and recalculate the sum of the
residuals squared and then select the one
slope and intercept that gives a minimum
result. The process does that automatically
because the equations used already make the
sum a minimum.
The situation is shown schematically
in Figure 9-1. The original data points are
residual {
0.02
ABSORBANCE (REFERENCE)
Figure 9-1. Least Squares Fit of a Data Set.
The squares represent actual data but do
not fall on the regression line.
shown as squares in the figure along with
the best fit line. The residual at one data
point (0.04,0.045) is also depicted.
As a demonstration of how the usual
least squares equations for this simplified
case arise, consider the following. Suppose
that a field spectrum has been acquired and
that the analysis region covers a range of
discrete data points (total N) along the wave
number axis. The reference spectrum has
the same number N oi data points along the
wave number axis. A plot similar to that in
Figure 9-1 is made, and the problem is to
determine the slope m and the intercept b for
the best fit straight line between the two
sets of spectral data. Let the equation of the
best fit line be given as y = mX+b and let the
original data points in the field spectrum be
at (Xj , Yj. At each data point (X-t , Yj,
calculate a new y from the equation such
thaty, = mXj + b. Then form the residuals at
each point such that /?, = Y, - yf = Yt -
(mXj + b). The individual residuals are then
squared and summed over all the data points.
This leads to the expression
9-3
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where the sum is taken over all the data
points from 1 to N. In order to minimize S,
the derivative of S with respect to both m
and b must be found and each set equal to 0.
The derivatives are each given below.
(9-2)
dm
and
This expression for b can be substituted into
Equation 9-3, which can then be solved for m
to get
(9-7)
It should be noted that in Equation 9-6 the
terms
c&
(9~3)
and
Equations 9-2 and 9-3 are a set of
simultaneous equations that can be solved
for m the slope and b the intercept. These
expressions can be rewritten as
m
and
(9-4)
(9-5)
The term ££ is equal to Nb, where N is the
total number of data points, so Equation 9-4
can be solved for b as
N
are just the average values of the X's and the
Fs, so Equation 9-5 becomes
(9-8)
Equations 9-6, 9-7, and 9-8 are the
usual equations that are used for doing a
linear regression between two data sets. As
applied to the spectral data from the FT-IR,
the X's in these equations are the
absorbances at the various wave numbers for
the reference spectrum, and the Fs are the
absorbances of the field spectrum.
As a numerical example, the data in
Table 9-1 can be used. There are a total of
seven data points, so N = 7. There are really
9-4
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TR-4423-99-03
only four quantities that have to be
calculated. They are the sum of the X's, the
sum of the Fs, the sum of Byproducts and
the sum of the X's squared. From the data in
Table 9-1, these quantities are: £X = 0.083,
£y= 0.411, £*y = 0.006351, and OT2 =
0.001271. Substituting these values into
Equation 9-7, the slope is obtained as
m =
0.006351-(0083)7(0411)
= 5.151
The intercept can be calculated next from
Equation 9-8. From the above data the
intercept is
N
0.411 (5.15l)(0.083)
= -0.002367
When the results of this calculation
are applied to the original data to determine
the atmospheric concentration of the gas,
the concentration product of the reference is
multiplied by the slope and then divided by
the actual path length used to acquire the
field spectrum. So if the reference
concentration-path length product is
20 ppm-m and the actual path length used
was 200 m, then the atmospheric
concentration is 20*5.15/200 = 515 ppb.
9.3 Matrices
The technique outlined above is
limited to a single gas in the field spectrum
and therefore uses a single reference.
Continuing on to the more realistic case of
several gases and several interfering species
is a tedious if not impossible task in the
method described above, and some other
method of describing the process has to be
found. Fortunately, there is such a method,
and it involves the use of matrices. Thus a
short tutorial session on the description and
manipulation of matrices is presented next.
Many excellent texts (Hohn 1964; Belman
1970) cover the mathematics of matrices,
and the interested reader should consult
them for more in-depth descriptions of the
use of matrices.
9.3.1 Matrix Types
A matrix is simply an array of
numbers. The array can have i rows and j
columns. If the number of rows / equals the
number of columnsy, the matrix is said to be
square. The convention used in this tutorial
will be to designate a matrix by an italicized
bold letter. A square matrix A that has 3
rows and 3 columns is shown below
A =
a
n
where the elements of the matrix are
designated by the subscripts ij. The element
a,, is the element in the first row and the
first column, while the element a32 is the
9-5
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MAIWl
..
;=•••;:=••= =
TR-4423-99-03
element in the third row and the second
column. The numerical elements of a matrix
will always be enclosed by the square
brackets as shown. A matrix can have only
1 row as A = [<2,, a,2 an • • • a{j ] or it can
have only 1 column as
a
11
a
21
a
31
a,-
In these cases the matrices are called either
a row vector or a column vector. A general
matrix of / rows andy columns can be written
as A = [a,y] or just simply as A. There are
other matrices that are necessary for this
work, and they will be introduced at the
appropriate time.
Matrices arise naturally in
mathematics from the study of the solutions
to simultaneous equations, and they
represent a concise way to manipulate the
coefficients of the equations. For a pair of
simultaneous equations
aQX
b0X
= c
there are a number of matrices that can be
written to describe these equations. The
coefficient matrix is shown below as the
[2x2] matrix
c =
a0 a,
and the augmented matrix shown below as
the [2x3] matrix
A =
9.3.2 Some Matrix Properties
Matrices have a number of
mathematical properties that allow them to
be used for obtaining the solutions of
algebraic equations. They can be added and
subtracted from one another so that if A = [
a{j ] and B = [by ], then A ± B = [a&. ± bv ]. A
matrix A can be multiplied by a scalar k,
(simply a number) such that if A = [a:j ], then
kA = [ka^]. These properties are
demonstrated with actual numbers below. If
A =
2 1
5 12
and
B =
then
4 9
3 8
6 16'
8 20
and
A-B =
-2 -2
2 4
9-6
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TR-4423-99-03
Also, for multiplication by a scalar, say k =
3, then
~6 21"
15 36_
Division of a matrix by a scalar is also
possible.
C =
#22^2! 021^12 + ^22^22
Multiplication of one matrix by
another is allowed, but it is not possible to
divide one matrix by another. Multiplication
of one matrix by another follows certain
mathematical rules, and these are described
in the next section.
9.3.3 Multiplication of Matrices
The description of matrix
multiplication begins with a discussion of
how to multiply two square matrices
together. Suppose that two matrices, A and
B, are each [2x2] matrices and they are to be
multiplied as C — AB. Then if
A =
a
n
a
l2
and
B =
n n
b2l b22
The first thing to note here is that each of
the elements of the product matrix is made
up of a sum of products of the original matrix
elements. Each of the product elements is
found by multiplying a row element of A with
a corresponding column element of the
matrix B and then summing the individual
terms. So, the elements of row 1 of the
matrix A are multiplied by the elements of
column 1 of the matrix B, and then the
individual terms are summed to get the
element (1,1) of the product matrix C. The
element (1,2) of the product matrix C is
found by using the elements from row 1 of
the matrix A and the elements from column 2
of the matrix B. Thus the subscripts of the
product matrix elements provide the
instructions of which row and which column
to use from the original matrices. The
numerical examples above for the matrices A
and B can be used to demonstrate this
multiplication. Thus
then the product C = AB is given by
9-7
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TR-4423-99-03
then the result is a [2x2] matrix C such that
"2 7"
5 12
"8+21 18+56"
20+36 45+96
"4 9"
3 8
"29 74"
56 141
i
"4 9"
3 8
"2 7"
5 12
However, an important point about
matrix multiplication is that it is not
commutative. That is, the product AB does
not equal the product BA. This is clearly
shown in the example below (again using the
same matrices as above).
Cf = BA =
8+45 28+108] f53 136'
6+40 21+96 = 46 117
Matrices need not be square in order
to multiply them together. For example, a
matrix with 3 rows and 2 columns can be
multiplied by a matrix that has 2 rows and 3
columns. An example is shown below.
Suppose that
A =
an al2 al3
a2l a22 a23
and
B =
\\ \2
b2\ b22
'31
'32
\ A I + G\2b2\
2\b\ 1 + a22b2\
3\ °2\b\2
If the product BA is found, then the result is
a [3x3] matrix. Thus the order of
multiplication is again important, and one
generally speaks of either pre-multiplying one
matrix by another or post-multiplying one
matrix by another. For the product AB, one
says that A pre-multiplies B, while for the
product BA the matrix A post-multiplies the
matrix B. In general a matrix of order (i,f)
(one that has / rows and/ columns) can pre-
multiply a matrix of order (&,/) only if j = k.
This gives rise to a matrix of order (/,/) or a
matrix with / rows and / columns.
To solve the matrix equations that are
used for the least squares analysis of FT-IR
data, several further definitions are required.
They include the identity matrix, the
transpose of a matrix, cofactors of matrices
or submatrices, and the inverse of a matrix.
Also required is a discussion of the
determinant of a matrix. Rather than provide
a purely mathematical definition of the
determinant, several examples are used,
which provide the information about them
that is required for the present discussion.
9.3.4 The Identity Matrix
The identity matrix/is simply a matrix
that has all ones along the principal diagonal
of the matrix and zeroes in all other
9-8
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TR-4423-99-03
elements. Thus a [3x3] identity matrix is
written as
1 0 0
0 1 0
0 0 1
The principal diagonal of a matrix is the
diagonal going from the upper left element to
the lower right element. The usefulness of
this matrix is explained below.
9.3.5 The Transpose of a Matrix
The transpose of a matrix A is written
as AT and is that matrix formed by
interchanging the rows and the columns of
the matrix A. So if the matrix A is a [3x3]
matrix written as
A =
-------
TECHmdl^m
TR-4423-99-03
The determinant of a [2x2] matrix is
found by multiplying the elements of the
principal diagonal together and subtracting
from that product the result of multiplying
the elements of the secondary diagonal. The
secondary diagonal of a matrix is that
diagonal running from the upper right to the
lower left of the matrix. Thus if the [2x2]
matrix is given by
A =
#n #12
42\ "22
the determinant is given by the expression
det(A) = aua22 ~ 3i2a2i- A numerical
example of this is given below. If the matrix
A is
A =
1 4
8 3
then the determinant of the matrix A is
detW) = (7K3) - (4)(8) = -11.
In order to find the determinant of a
larger, say [3x3], square matrix, the problem
must always be reduced to one of finding the
appropriate [2x2] matrices by using the rules
to be discussed. To obtain the proper [2x2]
matrices from the original [3x3] matrix, the
elements of the top row are each used in
turn. The row and the column that element
is in is then eliminated from the original
matrix. The [2x2] matrix that remains is the
one that has to be used. To complicate
matters a little, the [2x2] must be multiplied
by the matrix element whose row and
column were eliminated. So, if the [3x3]
matrix is given by
A =
flf
31
#
33
then the determinant is given by
det(/l) -
It is important to note the change in
sign from a plus to a minus in the second
term in the determinant. The first term of the
determinant is formed by starting with the
element [1,1], then crossing out the first row
and the first column and then finding the
determinant of the [2x2] cofactor of the
element [1,1]. The second term is found by
starting with the negative of the element
[1 ,2], then crossing out the first row and the
second column and using the determinant of
the cofactor of the element [1,2]. The third
term is found by starting with the element
[1 ,3] and then crossing out the first row and
the third column to get the determinant of
the [2x2] cofactor of the element [1,3].
Whether the sign in front of any particular
term is .positive or negative is found by
actually using the expression (-1)l+; where
the / and the j are the element subscripts.
Thus for the first term the element subscripts
are 1 , 1 and 1 + 1 =2; therefore (-1 )2 = 1 ,
For the second term, however, the / and the
j subscripts total 3 and (-1)3 = -1. The
subscripts for the third term again yield a
+ 1 multiplier. A numerical example of
9-10
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TR-4423-99-03
calculating the determinant for a [3x3] matrix
is given below. Let the matrix A be given by
the original matrix. Thus if the matrix A is
given by
3 9 1
675
12 2 8
The determinant for this matrix is
found following the rules above as
det(/l)=3[(7)(8)-(5)(2)]-
= 3(56- 10]- 9[48- 60]+ 1[12- 84]
= 138+108-72
-174
In general the determinant is found by
using all the elements along the top row as
described above and then continuing down to
the [2x2] matrix level. This procedure
becomes very cumbersome very quickly, and
for a [4x4] matrix the determinant has four
terms that each multiply a [3x3] matrix.
Each of these [3x3] matrices have a three-
term determinant, so that for a [4x4] matrix
there are 1 2 terms to calculate to obtain the
determinant.
9.3.7 Cofactors of Matrices
A cofactor of the [i,j] element of a
matrix is the determinant of the matrix that
remains after the fth row and/th column are
removed from the original matrix. Just as for
the determinant, each cofactor has to be
multiplied by the term (-"\Y+J. There can be
as many cofactors as there are elements in
A =
and the row and the column that contain the
element a,, is eliminated from the matrix, the
cofactor that remains is the determinant of
the [2x2] matrix Z)n, given by
a22 a23
a32 033
Or, the cofactor of the element [1,1] is
det(Du) = a22a^ - a23a}2.
By using the same procedure, the
cofactor of the element a22 is given by
det(.D22) and is seen to be
det(£>22) = det
a,
a,
13
a.
31
a
33.
where again the -1 multiplier is a plus
because (-1)2+2 = +1. These cofactors are
important for the discussion of the inverse of
a matrix that follows below.
9.3.8 The Inverse of a Matrix
Division of one matrix by another is
not allowed, but there is a process that is
similar to a division, and it is called inversion.
The inverse of a matrix A is simply written as
A"1. The principal property of the inverse is
9-11
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TR-4423-99-03
that the result of multiplying a matrix by its
inverse yields the identity matrix. That is,
given the matrix A and its inverse A'1
=04-')04) =
det(X)
Thus for the [2x2] matrix
There are two very important
properties that a matrix must have in order
for an inverse even to exist. First, the matrix
must be square; it must have as many rows
as it has columns. Second, the determinant
of the matrix cannot be equal to zero. In a
very loose sense, this merely implies that
dividing by zero is not allowed. Nonsquare
matrices must first be made into a square
matrix before the inverse can be found. This
can be accomplished by simply multiplying a
matrix by its transform (explained below).
Since this chapter is meant to be a
simplified discussion of matrices and how
they are applied to the classical least squares
analysis of FT-IR data, a definition, without
proof, and a numerical example of finding the
inverse will be sufficient.
In order to find the inverse of a
matrix, one first has to find the determinant
of the matrix as defined above. Then for
each element of the matrix, the cofactor of
that element of the original matrix has to be
found. The transform of the matrix formed by
the cofactor matrix must then be found by
interchanging the rows and the columns. If
the cofactor matrix is given by C, then the
transform is given by CT, and the inverse A"1
of the [2x2] matrix A is then given by
A =
an al2
a2l a22
the cofactor matrix is seen to be
a.
c =
'22 "21
-an an
The transform of this matrix is given by
CT =
a22 -an
-a
2l
and the inverse of the matrix A is finally
found as
1
det(/4)
a22 -al2
-a2l au
For a numerical example, let the
matrix A be
A =
4 9
-2 -5
The cofactor matrix is given by
-5 2
-9 4
9-12
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TR-4423-99-03
and the transform of the cofactor matrix is
CT =
-5 -9
2 4
The determinant of the matrix A is
easily found to be -2. Thus the inverse of the
matrix A is given by
"-5
~^2
2
.-2
-9"
_2
4
^2.
2.5
_ i
4.5"
-2
/*-' =
From here it is an easy matter to show that
this last matrix is indeed the inverse of A
simply by multiplying A and A"1 together to
get the identity matrix. Thus
AA'l =
"4 9"
-2 -5
"10-9 18-18"
-5+5 -9+10
"2.5 4.5"
-1 -2
"1 0"
0 1
At this point all the tools that are
required to continue processing the FT-IR
spectra data are available in matrix form.
9.4 Matrices and Algebraic Equations
The utility of matrices can easily be
demonstrated by considering the solution for
a set of simultaneous equations. As an
illustration, consider the following set of
equations
cX+dY = k{
To solve these equations for X and Y, the
.first equation can be solved for Xto get
X
kn-bY
a
This can be substituted into the second
equation to get
ckn-cbY
•+dY= k,
a
which when solved for /yields
ak, - ckn
io
ad-cb
Then by using the expression for Y and
solving for X, it is seen that
X =
ad- cb
To solve these equations by using
matrices, the equations are first written in
matrix form so that
'a b
c d_
' X
Y
This expression is seen to be a column
matrix that is multiplied by the coefficient
matrix, and that product is equal to the
column matrix of the constant terms. It can
9-13
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.'«.;r./ = .:r =
TR-4423-99-03
be rewritten in purely matrix format as CV =
K, where the C represents the coefficient
matrix, the V represents the variable column
matrix, and the K represents the column
matrix of the constants. To solve this for the
variable matrix, the coefficient matrix must
be removed from the left-hand side of the
equation. This is easily accomplished by
multiplying both sides of the equation by the
inverse of the coefficient matrix C"1 to get
C'CY = C[K. Then, after noting that a
matrix times its inverse is just the identity
matrix /, the final expression for the variable
matrix is obtained as V = C{K. Thus in order
to solve this equation for the X and the Y, the
inverse of the coefficient matrix must be
found. In reviewing the rules for finding the
inverse of a matrix given in Section 9.3.8, it
is seen that in order to find the inverse of the
coefficient matrix, one has to obtain its
determinant and then form the transpose of
the cofactor matrix. The determinant of the
coefficient matrix is just the term ad - be.
The cofactor matrix is found to be
d -C
-b a
The transpose of this is
d -b
-c a
and the inverse of the coefficient matrix is
just this transpose divided by the
determinant, or
C"1 =
1
ad -be
d -b
-c a
Now the final matrix expression becomes
'X
Y
1
ad -be
' d -b
-c a
"*0~
A
By multiplying out the matrix terms on the
right-hand side of this equation, the final
result is obtained as
' X'
Y
1
ad -be
dk0 -bk{
-ck0 + akl
The X term is the upper element of the
matrix divided by the determinant, and the Y
term is the lower element of the matrix
divided by the determinant. These
expressions are seen to be identical to the
expressions derived above by the algebraic
substitution method.
9.5 Least Squares and Matrices
The next step in this discussion is to
show that the matrix technique allows the
same equations for the regression analysis,
which was initially presented, to be derived.
Note that in that discussion a linear relation
was assumed between the absorbance of the
field spectrum and the absorbance of the
reference spectrum so that at each particular
data point (or wave number) an expression of
the form Y = mX + b could be used. In terms
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of the spectra, the Y represents the
absorbance of the field spectrum as a
function of wave number. Therefore, the
matrix that represents this absorbance has
one element for each data point over the
range of the analysis. It is represented by a
column matrix given by
a
N
The FT-IR usually acquires data at a rate so
that there are two data points per resolution
unit. Thus if the instrument is operating at a
resolution of 1 cm"1 there is one data point
every half wave number. It is best, for
statistical reasons, to use about 80 data
points in the analysis, so the matrix above
would have 80 elements and N = 80, and
the wave number range for the analysis
would cover 40 wave numbers at 1-cm'1
resolution.
In the case of the FT-IR, the variables
that are to be calculated are actually the
slope m and the intercept b. Therefore, the
variable matrix Vis given as
The matrix that is used for the
absorbance of the reference spectrum is a
two-column matrix that will also have Nrows
to match the absorbance of the field
spectrum matrix. This matrix is represented
by AR and is given by
m
This matrix has one column that is all
1 's because of the intercept term b that
arises from the linear fit. The aR's are the
absorbances of the reference spectrum at
the individual data points. They must be
chosen to be at the same wave numbers as
the data in the field spectrum, and there
must be an equal number of data points Win
each matrix. The fundamental matrix
equation that has to be solved is then AF =
AKV + e. The e is a matrix that describes the
errors in the data. Without the error term all
the data would fall on a straight line, and the
least squares process has essentially no
meaning. The e matrix is the matrix that
represents the residuals, and that can be
solved for and then squared to get the sum
of the residuals squared. This gives rise to
the expressions below.
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STS = (AF-ARV}T(AF-ARV)
= ATFAF-ATFARV-(ARV)T AF-
(ARV)TARV
Although it will not be carried out
here, when this expression is differentiated
with respect to V and set equal to zero, and
after making use of the fact that
(AB)T = BTAT
twice the primary matrix equation that must
be solved is obtained. That is,
The terms in the variable matrix V, namely
the intercept b and the slope m, are the terms
that have to be found and are the best
estimates of the slope and the intercept. In
order to solve for the b and the m, the matrix
AR must be removed from the right-hand side
of the equation. The way to do that is, just
as before, to pre-multiply both sides by the
inverse of the matrix AR. But there is a
problem here because only square matrices
have inverses, and the matrix AR is decidedly
not square. It has at least 80 rows but only
2 columns. So the first step is to make the
matrix AR square by multiplying it by its
transpose
At this point the fundamental matrix equation
that needs to be solved is
(9-9)
This is, in reality, a fairly simple equation and
comprises only two spectra, the measured
absorbance spectrum AF and the reference
spectrum AR. The following discussion
describes how these two matrices must be
manipulated to derive the expressions used
for normal linear regression calculations.
The matrix that represents the
reference spectrum AR requires the most
manipulation, and although that chore may
seem formidable, it is seen that the task
quickly becomes fairly simple. The first step
is to multiply the AR matrix by its transpose in
order to get a square matrix. The transpose
of AR is given by
1 1
• • • 1
• • • a
R(N-\)
and it has to multiply the AR matrix in the
following way
1 °R\
1 QB->
11... 1 1
J«l aRl * * « *«AM) aKN
t •
• •
• •
Now, utilizing the rules set out above
about the multiplication of matrices, it is
seen that this product will result in a [2x2]
matrix. Before writing down the result, it is
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i 'L-J -.Ai • r
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instructive to first contemplate the individual
elements in the product matrix.
• For the element [1,1 ] it is seen that the
first row elements of the transpose
matrix must multiply the first column
elements of the original matrix and then
be summed. But these elements are
just all 1 's and when summed yield the
number N, the total number of data
points.
• To obtain the element [1,2] the first
row elements of the transpose matrix
must multiply the second column
elements of the original. But this just
turns into the sum of the absorbances
of the individual data points from the
reference spectrum.
• The element [2,1 ] of the product matrix
is again the sum of the individual
absorbances because it is found by
multiplying the elements of row 2 of
the transpose by the elements of
column 1 of the original (all 1 's).
• The fourth and final element of the
product matrix (element [2,2]) is found
by multiplying the elements from row 2
of the transpose by the elements of
column 2 of the original and summing.
These individual terms are seen to be
the squares of the absorbances at the
individual data points, so the element
[2,2] becomes the sum of these
squares.
The result of multiplying the matrix AR by its
transpose becomes
I an
Next, the inverse of this matrix has to be
found, and this is done in three steps. The
first is to find the cofactor matrix, the second
it to take the transpose of that, and the third
is to divide the individual elements by the
determinant of the original matrix. The
cofactor matrix is
IK)3
N
Because the elements [1,2] and [2,1] are
identical, the transpose of this matrix is the
same as the original. The determinant of the
original matrix is found to be
The inverse that is required here is just the
cofactor transpose divided by the
determinant, so that
(9-10)
The next step is to multiply the matrix
that represents the absorbance in the field
spectrum by the transpose of the reference
spectrum matrix, that is, to find the product
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This product is
far =
1 1 • t . '1
am aR2 * • » flfl(AM)
"F\
aF2
t
*
*
Here again, a little inspection is
helpful. The result of this product will be a
column matrix with only two rows. The first
element is made by multiplying the first row
of the transformed reference matrix by the
elements of the field spectrum matrix. But
that is just the sum of the absorbances at
the individual data points. The second row is
obtained by multiplying the second row of
the transformed reference matrix by the
elements of the field spectrum matrix. This is
again a sum, but now the terms to be
summed are the products of the two
absorbances such that each individual term
has the form
It should be clear now why there is
the requirement that the number of data
points in the field spectrum must be the
same as the number of data points in the
reference spectrum. If they were not, then
this last matrix multiplication could not be
done. At any rate, this product is given by
The final step in obtaining the variable matrix
is then multiplying the two matrices from
Equations 9-10 and 9-11 together.
Remember here though that the order of
multiplication is important. When this final
product is performed, the result is
v = -
y
.LI aRiaFi\
or
v' =
When these results for the intercept b (the
element [1,1] of V) and the slope m (the
element [2,1] of V) are compared to the
results derived from an algebraic standpoint,
it is seen that the expressions are the same.
9.6 Expansion to Many Gases
Once the expressions for the slope
and the intercept are obtained as above, it is
fairly simple to see how to expand this
solution to analyze for several gases
simultaneously or to analyze for one gas in
the presence of several interfering species.
The fundamental matrix equation stays the
same. That is, the expression
always stays the same, but the individual
(9-11) matrices V and AR have to change to
incorporate more information. In most cases
the problem is formulated a bit differently
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than was used above, in that the intercepts
are actually ignored. When several gases are
to be analyzed for, the problem is usually
stated by considering the final field
absorption spectrum to be a linear
combination of the individual reference
absorbance spectra. The mathematical
statement is that
and the problem now becomes one of
determining the individual mf terms. These
nij's are the coefficients for the individual
references. In the mathematical equation,
they determine the amount of each of the
individual references to use to achieve the
final result of matching the field spectrum.
Thus the expanded AR reference
matrix changes from a two-column matrix,
with the first column being 1 's, to a matrix
with N columns, but there are no 1 's. That
is,
a
n
a
22
Here there are j gases and N absorbance
values for each gas. Typically, there are
perhaps six or seven gases that are analyzed
for simultaneously, but there can be many
more, and there are cases where as many as
30 have been targeted. The final maximum
number of gases that can be used is
determined by how large a matrix is allowed
by the computer and the algorithm being
used. The final variable matrix V is then a
one-column matrix withy rows that represent
the m's as given above. That is
m,
mj
It is now easy to see how to expand
the least squares technique even further to
account for a quadratic fit such as is
indicated by the development in Chapter 8.
In that case the AR matrix needs to contain
terms that are
absorbances, or
the 'squares of the
a
Ri
and for each addition column in the reference
matrix, there has to be one additional m in
the variable matrix that needs to be
determined.
Calculating anything but the simple
case that is presented above is not really
possible, nor would it be overly instructive.
However, it is of interest that the absorbance
due to water actually contributes to the
continuum, and that makes up the baseline
as seen in the single beam spectrum. The
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water concentration can and does change in
time rather dramatically, and therefore there
are changes in the baseline. If the water
absorbance is measured from the baseline to
a peak, an error will occur because of the
continuum, which is already at a lower
transmission than 100% by a few percent.
The work in Chapter 8 indicates that the
absorbance in the water continuum actually
rises as the square of the partial pressure of
water. This seems to indicate that a square
term ought to be included in the reference
matrix for the water. At the present time
none of these considerations have been
tested with spectra to determine whether the
analysis results are better than the current
methods. Also, only two software packages
that include that term (the Nicolet Omnic
software [Madison, Wl] and the MIDAC
AutoQuant software [Irvine, CA]) seem to be
available at the time of this writing.
9.7 Least Squares Errors
Once the coefficients for the
individual gaseous components have been
determined from the least squares technique,
the uncertainties in these coefficients must
be examined if the uncertainties in the
concentrations are to be understood. The
overall derivation of the expressions for the
errors and a thorough examination of the
errors can be quite involved, and an in-depth
discussion is felt to be beyond the scope of
this work. The interested reader is directed
to two excellent references (Draper and
Smith 1966; Bevington 1969) for an in-depth
analysis of these questions.
However, it is important to note here
that the errors calculated by statistical
techniques are associated with only the least
squares technique, and they are not
indicative of the overall error in the FT-IR
data. The expressions for determining the
errors are derived from a study of the
residuals or the analysis of variance. These
errors are related to the amount of the
variance in the original field spectrum that is
explained by the variance in the sum of the
individual reference spectra, and these errors
have more to do with how well the sum of
the reference spectra match the original field
spectrum rather than any absolute error.
While these errors are important to
the overall discussion of the FT-IR data, they
do not comprise the entire picture of the
errors. The errors generally reported by the
least squares technique do not take into
account the actual magnitude of the real
errors in the data because they do not
account for several major contributors to the
error. These unreported errors are errors like
the nonlinear response error produced by the
apodization function or the temperature
effect on the reference spectra, as described
in Chapter 8 of this document. They also do
not include any errors in the reference
spectra themselves.
Any study of these unreported errors
shows that they can be quite large when
compared to the errors calculated from the
least squares technique. Because of this, it
is felt that no claim for accuracy better than
about ±30% can be made for the FT-IR
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data, regardless of what the error
calculations of the least squares technique
produce.
9.8 References
Belman, R. Introduction to Matrix Analysis
2nd ed. McGraw Hill Book Company, 1970.
Bevington, P.R. Data Reduction and Error
Analysis for the Physical Sciences. McGraw
Hill Book Company, 1969.
Draper, N.R. and H. Smith. Applied
Regression Analysis. John Wiley & Sons Inc,
1966
Hohn, F. E. Elementary Matrix Algebra 2nd ed.
The Macmillan Company, New York, 1964.
Sokolnikoff, I.S., and R.M. Redheffer. 1966.
Mathematics of Physics and Modern
Engineering. McGraw-Hill Book Company,
New York.
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Chapter 10
Quality Assurance and Quality Control
SUMMARY
The topics and specific points of emphasis discussed in this chapter include
the following.
• The need for a quality assurance (QA) project plan
• QA project plan categories and relevant EPA documents
• A general format for a 1 6-point QA project plan
• A discussion of specific quality assurance and quality control
(QA/QC) issues related to FT-IR long-path, open-path monitoring
• Portions of an approved QA project plan
• A case study presenting QA data collected over a two and one-half
month period
• Recommendations of procedures to be included in a QA program
10.1 Introduction and Overview
For open-path FT-IR spectrometry to
become an accepted method for
environmental monitoring, QA procedures
must be established. While QA issues have
been addressed (Kricks et al. 1992;
Russwurm 1992a,b; Weber et al. 1992;
Kagann et al. 1994), there is currently no
consensus regarding the proper QA
procedures required to validate open-path
FT-IR data. In fact, there is very little
information in the literature that addresses
the quality of the data generated by FT-IR
long-path, open-path systems. For example,
when error bars are given, they are often
merely stated, and no discussion of how they
were derived is supplied. As the FT-IR long-
path technique begins to be used for routine
monitoring, this approach will not be
satisfactory, and a more extensive QA plan
must be developed.
The development of and adherence to
a QA project plan requires the operator to
consider exactly how the data generated by
an FT-IR long-path, open-path monitoring
program will be obtained, processed,
interpreted, and used. When implemented
properly, the QA plan will alert the operator
if the instrument is not functioning properly
or is generating erroneous data, and it will
contain recommendations for the corrective
action to be taken. The various levels of QA
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project plan designs apply to programs
ranging from research and development
programs to routine monitoring programs that
must produce legally defensible data. This
chapter covers some of the points that will
have to be addressed for any QA program.
The general points that must be
addressed for any QA program are given in
this chapter. These points are drawn from
specific documents that address QA
requirements for data obtained for the U.S.
Environmental Protection Agency. Points of
emphasis discussed in these documents
include the following: project description,
organization, and responsibilities; QA
objectives; site selection and sampling
procedures; sample and data custody;
calibration procedures and frequency;
analytical procedures; data reduction,
validation, and reporting; internal quality
control checks; performance and systems
audits; preventive maintenance; calculation
of data quality indicators; corrective action;
quality control reports to management; and
references.
These, and other, items are addressed
with respect to FT-IR long-path, open-path
monitoring in this chapter. In addition,
portions of the QA project plan for a 1989
Superfund Innovative Technology Evaluation
study in Delaware are presented as an
example for use in FT-IR long-path, open-path
monitoring. Also, a case study involving the
acquisition of QA data over a two and one-
half month period is presented in Section
10.3, and recommendations for procedures
to be included in a QA program are given in
Section 10.4.
10.2 Project Plan Categories
The U.S. Environmental Protection
Agency has published a document that
defines four different categories of QA
project plans, as described in Section 10.2.1.
The program with the least requirements is a
research and development program (Category
IV), whereas a program that produces data
by routinely monitoring the atmosphere
(Category I) has the most. When considering
programs that are specifically designed to
obtain data for the U.S. Environmental
Protection Agency, it is convenient to refer
to two documents that describe QA project
plans: (1) Preparing Perfect Project Plans: A
Pocket Guide for the Preparation of Quality
Assurance Project Plans and (2) Preparation
Aids for the Development of RREL Quality
Assurance Plans (U.S. Environmental
Protection Agency 1989, 1991). Actually,
there are four parts to the second document,
one for each of the four categories, and each
has its own document number.
Some of the features of the items
that need to be addressed in the Category I
project plans are covered in Sections 10.2.1
and 10.2.2. It is intended that these
sections be a paraphrasing of the two
documents listed above. People who have to
deal with these issues must obtain a copy of
the documents and follow the guidance given
there. To give some specificity to the
various points of a QA project plan, the QA
project plan used for a recent program
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conducted by EPA is used as an example.
The program entailed taking data with an
FT-IR open-path monitor in an industrial
complex and comparing that data to data
obtained by a canister technique according to
method TO-14 (Russwurm and McClenny
1 990). Funding was allocated for 10 days of
measurements with the FT-IR instrument in
the field.
10.2.1
Category Definitions
• Category I projects are those that are
designed so that their results can be
used directly, without additional
support for compliance or other
litigation. As such, they must be able
to withstand legal challenge and
therefore have the most rigorous and
detailed requirements. These projects
are critical to the goals of the U.S.
Environmental Protection Agency.
• Category II projects are those whose
data complement other projects.
When combined with the output from
other projects, these data can be
used for rule making or policy making.
• Category III projects are those
producing data that allow the
evaluation and selection of basic
options for use in feasibility studies.
• Category IV projects are those that
are associated with research and
development projects. The results are
used to assess the basic or underlying
assumptions or suppositions of other
work. Because of the nature of these
projects, they have the minimum
number of items that need to be
addressed in a QA program.
These categories are intended to be
fairly general and broad, and any project
must fit into one of the four. The number of
items that must be addressed for each of the
categories is 16, 13, 12, and 6 for
Categories I through IV, respectively. The
project described above for acquisition of
data for comparison purposes and referred to
as an example in Sections 10.2.2.1 through
10.2.2.16 was considered to be a research
program, and therefore it fell into
Category IV.
10.2.2 Category I Points to Be Addressed
The 16 items that must be addressed
for the QA project plan in this category are
listed below.
1. Project description
2. Project organization and
responsibilities
3. QA objectives
4. Site selection and sampling
procedures
5. Sample custody
6. Calibration procedures and
frequency
7. Analytical procedures
8. Data reduction, validation, and
reporting
9. Internal quality control checks
10. Performance and systems audits
11. Preventive maintenance
12. Calculation of data quality indicators
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13. Corrective action
14. Quality control reports to
management
1 5. References
16. Other items
These 16 items are discussed briefly below.
10.2.2.1 Project Description
The most important feature of the
project description is that a person who is
unfamiliar with the project, but is familiar
with the technology, must be able to
understand this section.
For the example project, the following
items were included in this section.
• An in-depth discussion of the
comparison program. The primary
aspect of this was to relate in detail
how the data would be taken. The
FT-IR instrument is a long-path
monitor, and the canister technique is
a point monitor. Thus, it was decided
to transport the canister along the
path while the FT-IR monitor was
acquiring data. Topics that had to be
included in the QA project plan were
the number of traversals along the
path and the number of scans the
FT-IR spectrometer would make.
• A brief description of the FT-IR
technique and the canister technique.
The techniques were described, and
appropriate documents for each
technique were referenced.
10.2.2.2 Project Organization and
Responsibilities
This section must describe the
relationships among all of the people
connected with the project, including the QA
manager, and give their responsibilities. It
should be noted that, somewhere in the
organization conducting the program, there
should be an autonomous QA representative.
Most organizations have this function
removed from the technical staff and under
the jurisdiction of an administrative manager.
The primary function of this person is to act
as final arbiter for any disputes about the QA
aspects of the program. Therefore, he
should not be administratively connected
with the technical program.
For the project being outlined as an
example, the management and administrative
staff consisted of U.S. Environmental
Protection Agency staff and staff from two
contractors. The following descriptions were
therefore included in this section.
• All the principal people involved and
their duties
• The relationship of one person to the
other concerning decision-making
responsibilities
• The lines of communication among
the project personnel
All lines of communication among the various
project personnel, including any sub-
contractors, must be described. If no
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subcontractors are used, it is sufficient to
simply state that fact.
10.2.2.3 QA Objectives
This section of the QA project plan
must cover items such as detection limits,
precision, accuracy, completeness of the
data, representativeness of the data, and
comparability of the data. There must be a
discussion of the impact of not meeting
these objectives and how these indicators
will affect the legal defensibility of the data.
Inadequately addressing these items is
probably the most frequent cause of the
rejection of a QA project plan.
Three items—detection limits,
precision, and accuracy—must be numerically
defined as QA objectives. Completeness of
the data defines what percentage of the total
number of possible data points that are
available under the sampling schedule are
expected to be captured.
Representativeness of the data implies how
well the acquired data account for the
variability of the real situation.
Representativeness of the data concerns
itself with sampling. Comparability of the
data indicates how well the data can be
compared to that taken with other
instrumentation.
specific definitions were required. At the
present time there are no generally accepted
definitions for these quantities for FT-IR
open-path monitors.
For the completeness of the data, the
following procedure was used. A 10-h
working day was assumed, and 2 h were
allocated for setup and warm-up time of the
instrument. The data-taking period was
assumed to be 0.5 h for each spectrum.
Therefore, it was anticipated that 16 spectra
a day would be taken. During the study, it
was noted that the concentration of the
gases being monitored was changing at a
much higher rate than could be
accommodated by the 0.5 h allocated to
each data spectrum. Therefore, the
sampling schedule was altered to account for
the change. It should be noted that this is
certainly an appropriate response to changing
conditions. The QA plan is a guide for
subsequent operations and not something
that is unchangeable. All changes must be
recorded, and the rationale for the change
must be presented.
A large section of the plan concerned
itself with the representativeness and
comparability of the data. The reason that
the canisters had to be transported along the
path was precisely to satisfy the
requirements of these two items.
A portion of the example field program
(Russwurm and McClenny 1990) was
designed to determine how to best make
measurements of the detection limits, the
accuracy, and the precision. Therefore, no
10.2.2.4 Site Selection and Sampling
Procedures
In addition to a physical description of
the site, the rationale for selecting any
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individual site must be presented. This
discussion must address how the site will
allow the data objectives to be met.
The sampling portion of this section
must address the scientific and regulatory (if
any) objectives that the sampling protocol
allows. It must also address how any
calibration samples are to be obtained and
delivered to the system. In the case of the
FT-IR system, if a gas sample cell is to be
used, then its preparation and use must be
addressed in this section.
Site selection and sampling
procedures played an important role in the
example study. Several months before the
field portion of the example study, a search
for suitable sites was started. The general
area of the study had been selected, but the
individual sites and FT-IR paths needed to be
chosen. Therefore, this section of the
example QA plan contained the following
descriptions for the site selection process
and sampling procedures.
• Background information on site
selection. During a number of trips to
the general area, various land owners
were contacted, and several sites
were selected as usable for the study.
• Predominant requirements for the site.
Proximity to the source, an
unobstructed path length of up to
300 m, a path that could be used to
transport the canister while the FT-IR
monitor was taking data, and a site
that was safe for the operators.
• Procedure for using a QA gas cell. A
description of using a short cell filled
with a high concentration of gas for
calibration purposes was described
here. The use of this cell was also
intended for determining the precision
of the instrument.
10.2.2.5 Sample Custody
This section must present complete
sample custody procedures and personnel
responsibilities in handling samples. Because
the FT-IR data are stored on disk, all
procedures for ensuring the integrity of the
data on the disk and the legal defensibility of
those procedures must be addressed.
For the example program, no sample
custody procedures were required because it
was a research program.
70.2.2.6 Calibration Procedures and
Frequency
The FT-IR open-path monitor is not
calibrated in the classical sense. That is, a
sample of known concentration is not
presented to the instrument for
measurement. During FT-IR sampling, the
absorbance values in all the spectra obtained
at various wave numbers for the specific
gases are always compared to the
absorbance values of the reference spectra.
These reference spectra are made with pure
samples of the gas. Production of reference
spectra is a formidable task, and few
laboratories are equipped for such an
undertaking. Because of this, only a limited
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number of spectral libraries that can be used
for quantitative analysis exist.
Although measurements of the
precision can be made by using a short cell
filled with a pure sample of the gas, this is
not routinely done at the present time. There
is currently no agreed-upon procedure for the
use of such a cell.
The project being used as an example
did not require that the system be calibrated.
However, a written procedure for using a
short cell to make precision measurements
was part of the QA plan.
7 0.2.2.7 Analytical Procedures
For the most part, unless other
techniques are to be used along with the
FT-IR system, there is nothing to address in
this section. The analytical procedures that
are to be used to determine the
concentrations of any short-cell gas mixtures
would have to be addressed here.
In the QA project plan being used as
an example, the procedures for preparing the
short cell and the gas mixtures were given
here. The cells are generally filled with a
pure gas sample and then backfilled with
nitrogen so that the total pressure is 1 atm.
All the apparatus used for this procedure was
described in this section.
This section also contained a
description of the procedure to be used for
the analysis of the canister samples. This
was a brief description, but it referenced the
TO-14 procedure manual. The entire QA
procedure for that portion of the effort did
not have to be presented in the plan, but it
had to be referenced. If one had not been
available, then it would have had to be
written and given in this section.
10.2.2.8 Data Reduction, Validation, and
Reporting
The data reduction procedures must
be discussed in this section. This includes
the least-squares regression analysis, or
other multicomponent analysis method, if it
is to be used. All statistical methodology
that is used as an aid to data interpretation
must be described here. This section can
also include sample calculations. All
procedures to be used for flagging the data
and removing outliers from the data set must
be stated in this section. The flow of data
and the procedures that will be used to
transfer the data from where it is generated
to the end user must also be described.
The QA project plan being used for
discussion purposes included an analysis of
the spectral data with a classical least
squares algorithm. The actual process of
recording the interferogram, performing the
Fourier transform, and the least-squares
analysis was not discussed in detail. The
published papers that describe these
techniques were referenced. The process of
selecting the wave number range for analysis
was discussed, and the wave number
regions that were used were listed in this
section of the QA project plan.
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The TO-14 procedure for data
reduction also was referenced, but the actual
details were not presented in the plan.
The major portion of this section dealt
with the comparison of the data which was
to be done by regression techniques. At
various stages in the program, two canister
samples were taken simultaneously, and the
comparison procedure for these data was
discussed.
Validation of the data was described
as the process of reviewing the study
logbooks to make sure that no unwanted
contamination of the samples had occurred.
For example, one sample was invalidated
because an automobile had followed the
person transporting the canister along the
path.
10.2.2.9 Internal Quality Control Checks
This section is designed to determine
what internal QC checks are to be made. It
must also cover why these checks are
necessary and how they will help to achieve
the data quality objectives. For example, this
section would describe the use of control
charts that show the peak-to-peak readings
of the single-beam spectrum at various path
lengths and with varying amounts of water
vapor.
At the time of the example study,
there were no requirements for internal QC
measurements written into the plan. A
portion of the study was designed as an
attempt to develop procedures for making
these measurements.
10.2.2.10 Performance and System Audits
System audits are generally done
before any data are taken. They are
designed to answer questions about the
proposed procedures and sampling protocols
to be used in the program. The performance
audits are designed to determine whether the
instrument is operating as it was described in
the other sections of the study's QA project
plan. Both of these audits are generally done
by people who are not associated with the
daily operation of the instrument.
There were no provisions for either
system or performance audits for the study
being used as an example.
Although it is easy to envision the
system audit for the FT-IR instrument, the
performance audit of the instrument would
be much more difficult to do at this time.
This is usually done by using the instrument
to measure a known concentration of gas
and determining the response. There has
been no systematic development of a
procedure for doing this for the FT-IR
systems to date. Currently, not all
commercially available systems have
provisions for putting a short cell in the
beam.
10.2.2.11 Preventive Maintenance
This section requires a description of
the preventive maintenance procedures and
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the schedule on which they will be
performed. The time involved in performing
preventive maintenance will affect the total
amount of data that can be taken, and this
must be accounted for in the description of
the completeness requirements.
In the example QA project plan, no
preventive maintenance schedule was given
because the study was a short-term intensive
program. Over the 10-day field program, no
maintenance of the instrument was required.
10.2.2.12 Calculation of Data Quality
Indicators
This section must contain detailed
procedures that are to be used for
determining the data quality. It must include
all the statistical routines that are to be used.
Items that must be addressed are precision,
accuracy, outliers, etc.
Currently, no generally accepted
definitions for precision and accuracy are
available for the FT-IR open-path technique.
10.2.2.73 Correc tive A c tion
The corrective action portion of the
QA project plan is a set of contingency plans
that try to address "what if" questions.
These corrective action plans serve as a
check for the general tendency to want to
perform quick fixes of equipment to get as
much data as possible. This is certainly the
case with short-term field programs, but it is
generally better to take the instrument off
line and repair or adjust it properly. The
corrective action plans should describe how
this is to be done and specifically what
criteria will be used to make the judgement
as to when to discontinue data collection and
shut down the instrument for repair. This
section was not a requirement for the
example QA project plan.
10.2.2.14 Quality Control Reports to
Management
This section must state what reports
will be transmitted to whom and when they
will be transmitted. There should be a
description of the contents of each report,
and all the QA/QC data that must be
included in each report should be stated in
this section of the QA project plan.
The QA project plan for the example
study did not address this requirement
because there was no consistent QA data
generated in the program.
10.2.2.15 References
When references related to the
present program are available, they should be
included in the QA project plan. For
example, as mentioned in Sections 10.2.2.1
and 10.2.2.7, appropriate documents were
referenced for the canister technique used in
the example QA project plan.
10.2.2.16 Other Items
The QA project plan contains
information that the principal investigator will
need at various points of the program.
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Because of this, it is somewhat personalized,
and this section can include any other items
that are considered important to the program.
There were no other items included in
the QA project plan for the example study.
10.3 Case Study: QA Data Collected
Over Two and One-Half Months at a
Semipermanent Field Site
The study described here was
designed to evaluate the stability of a long-
path FT-IR system and to determine the
precision and accuracy of the concentration
measurements (Thompson et al. 1994). The
following criteria were used to assess the
stability of the instrument: electronic noise,
the magnitude of the. return signal, the RMS
baseline noise, and the repeatability of the
position and full width at half height (FWHH)
of selected absorption bands. Ambient
concentrations of CH4, N20, and CO were
measured to test the use of these data for
determining the precision and accuracy of
the FT-IR open-path monitor. Measurements
were made daily over two and one-half
months, from November 1993 to mid-
January 1994.
Spectral data were acquired by using
a monostatic FT-IR monitor. Each spectrum
consisted of 64 co-averaged scans recorded
at a nominal 1-cm"1 resolution. Triangular
apodization was used. The collection of
each spectrum required approximately
5 minutes. A spectrum was taken every
15 minutes. Single-beam spectra were
typically, acquired over a 7- to 8-h time
period. Absorption spectra were created by
ratioing the single-beam spectra to a
synthetic background spectrum generated
from a 2048-scan single-beam spectrum
recorded over the 414-m path. This
background spectrum was recorded at the
beginning of the experiment and was used
throughout the study. The data were
analyzed by using a CLS software package
and reference spectra from a commercial
library.
The site is located near I-40, one of
the main traffic arteries for the Research
Triangle Park, NC, area. The instrument was
kept in a climate-controlled shed, which is
heated during the winter months. The total
path length was 414 m, and it extended over
an open, grassy field and a small parking
area with very limited traffic. The beam path
rose from about 1.8 m to 1 2.8 m above the
ground as it was directed from the FT-IR
spectrometer to the retroreflector array,
which was mounted on a tower.
The instrumental electronic noise was
measured each morning before the detector
was cooled with liquid nitrogen. This signal
typically ranged between 600 and 620
counts with the instrument in the single-
beam mode. Shortly after the detector was
cooled, the instrument was aligned and the
maximum return signal was recorded. The
return signal was recorded again (without
realignment) around noon to check the
stability of the signal. On clear days the
single-beam return signal ranged from
10,500 to 13,500 counts. (See Figure 10-1.)
Certain atmospheric conditions caused the
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14,000 -
|^
3 10,000 -
to
•-000'
Z 4,000-
oc
2,000 -
0
4 ,
Data of Measurement
Figure 10-1. Return Signal Magnitude of the
FT-IR Monitor Measured Daily at 0700 (A)
and 1200 (•). (The data points have been
connected by lines for the convenience of
the reader and not to indicate continuous
data.)
I
M
Date of Measurement
.
yf yf-
Figure 10-2. The RMS Baseline Noise
Measured Between 980 and 1020 cm 1 (•),
2480 and 2520 cm'1 (•), and 4380 and
4420 cm"1 (A). (The data points have been
connected by lines for the convenience of
the reader and not to indicate continuous
data.)
return signal to vary from day to day. For
example, the return signal dropped by
20-30% during fog. On some mornings,
when the humidity was close to or below the
dew point, condensation or ice formed on the
retroreflector, resulting in a lower return
signal in the early morning measurement. As
the condensation evaporated, an increase in
return signal counts was measured. To
remedy the problem of condensation, a heat
lamp was mounted on the tower and directed
at the retroreflector. After the heat lamp
was installed on December 10, the noon and
early morning return signals were nearly the
same. The use of the heat lamp did not
cause an increase in noise or detected IR
signal.
The RMS baseline noise measured
over 26 days is illustrated in Figure 10-2.
The baseline noise was determined by
collecting two back-to-back, 64-scan, co-
added spectra. One spectrum was ratioed
against the other to obtain an absorption
spectrum. The RMS noise (in absorbance
units) was calculated over three spectral
regions: 980-1020, 2480-2520, and
4380-4420 cm"1. During operations when
condensation did not form on the
retroreflector, the baseline noise was on
average approximately 2 x 10'4 for the 980-
1020-cm"1 region, 2.5 x 10"4 for the
2480-2520-cm"1 region, and 9 x 10"4 for
the 4380-4420-cm"1 region. In these
measurements, the 980-1020-cm'1 region
included water vapor bands. For a true
measurement of instrument performance that
is not influenced by temporal changes in
water vapor concentration, it is
recommended that the region from 968 to
1008 cm"1 be used. During measurement
periods when condensation formed on the
retroreflector, the baseline noise for these
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regions increased to 9.7 x 10'4,5.5 x 10"4,
and 2.9 x 10"3, respectively.
The wave number stability of the
instrument was determined by monitoring the
peak position and the FWHH of the water
vapor singlet at 1014.2 cm'1. Band positions
typical of data collected at the beginning, in
the middle, and near the end of the study are
depicted in Figure 10-3. No shift in the
frequency was observed during this time
period. Also, no shifts were observed in the
1-cm"1 spectra collected under a variety of
weather conditions, including rain, freezing
rain, sleet, snow, and low (single-digit)
temperatures. To determine if the water
vapor singlet at 1014.2 cm"1 broadened, a
spectrum collected at the beginning of the
experiment was subtracted from a spectrum
in the middle and end of the experiment. No
broadening was evident during the middle of
the experiment; however, a slight broadening
for some of the spectra at the end of the
o
I
o
M
a
1010 1015 1020
Wavenumbers (cm '1)
Figure 10-3. Repeatability of the Position of
the Water Vapor Singlet at 1014.2 cm'1
Measured on (A) November 10, 1993, (B)
December 22, 1993, and (C) January 4,
1994.
experiment was observed. The FWHH of the
water vapor singlet in spectra taken during
different atmospheric conditions was also
examined. When a clear day spectrum was
subtracted from any of these spectra, no
broadening was evident. It should be noted
that short wavelengths (higher wave
numbers) will be more sensitive to spectral
shifts and changes in resolution. The HDO
doublet centered at 2720 cm'1, the CO band
at 2169 cm"1, or other water vapor bands in
the higher wave number region can also be
used to test for shifts and changes in
resolution.
The feasibility of using ambient gases
for accuracy and precision measurements
was also investigated. Ambient
concentrations of N20, CH4, and CO were
measured on a daily basis. Each morning
between 071 5 and 0930 the concentrations
of these gases increased, then steadily
decreased during the remainder of the day.
However, concentrations of N2O and CH4
remained constant, approximately 250 ppb
and 1.7 ppm, respectively. To determine
whether the increases in concentration
during the first 3 h of operation were due to
an instrument effect or to the proximity of
the site near a major highway, data were
collected continuously for 36 h.
Data were collected from
November 17 at 0730 until 1730 on
November 18. The CH4 concentration data
exhibited scatter during an early morning fog
episode and decreased steadily during the
day. (See Figure 10-4A.) A step in the CH4
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concentration measurement was observed
when the liquid nitrogen in the detector was
depleted at approximately 2345 on
November 1 7. The CH4 concentration value
was 1.70 ppm just before the liquid nitrogen
was depleted, increased to 1.9 ppm after
liquid nitrogen was refurbished, and remained
10% higher compared to the previous levels.
The concentration data for CO showed a
similar, stepped increase.
c
o
O
07:12 12:12 17:19 22:15 03:30 08:30 13:30 11:30
09:42 14:40 19:45 01:00 06:00 11:00 IfcOO
Time
Figure 10-4. Measurement of (A) Ambient
Methane Concentration and (B) Single-Beam
Intensity at 987 cm'1 on November 17 and
18, 1993.
The CH4 concentration data exhibited
irregular behavior during a 6-h period shortly
after the detector Dewar was refilled with
liquid nitrogen. To determine if the
instrument was operating properly during this
time period, the single-beam intensity at
987 cm"1 was measured from archived
spectra. The single-beam spectra had a
lower intensity during the fog episode, then
leveled off until the detector ran out of
coolant. (See Figure 10-4B.) After this
sudden .drop, the single-beam intensity
returned to its original reading and remained
relatively constant throughout the remainder
of the experiment. This indicates that the
instrument was working properly during the
episode of high measured CH4 levels.
One other observation during this time
period concerned the effect of water vapor
concentration on CIS analysis for CH4. On
November 17 a cold front moved through the
area in the late evening, and the water vapor
pressure dropped rapidly. Because the water
vapor spectrum is used as an interfering
species in the CLS concentration analysis for
CH4, the sudden change in water vapor
pressure could have had an effect on the CH4
concentration measurements. The relative
concentration of water vapor along the path
was determined by measuring the peak area
of the absorption band at 1014.2 cm'1.
Likewise, the relative concentration of CH4
was determined by measuring the peak area
of the absorption band at 2998.8 cm'1. This
peak was chosen because the water vapor
bands do not interfere with it. However, it
was later brought to our attention that this
CH4 band actually overlapped nearly exactly
with a water vapor band (W.F. Herget, ETC,
personal communication). This might explain
the dip in the peak area measured at
2998.8 cm"1 during the time that the water
vapor concentration was decreasing rapidly.
Therefore, this band is not a good choice for
this type of data analysis; the CH4 bands at
2916.8 and 2927 cm"1 do not overlap with
water vapor and should be used instead. As
shown in Figure 10-5, the relative water
vapor concentration decreased rapidly when
the front moved through the area. The
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relative CH4 concentration increased during
this period. Similar trends were observed
between plots of the CH4 peak area and CH4
concentrations determined by the CLS
concentration analysis. This indicates that
the change in water vapor concentration did
not greatly affect the CLS analysis for CH4,
and the fluctuations in the CH4
concentrations were real.
a
< 0.10
(Q
I,
I.
A
07:12 12:12 17:13 22:15 03:30 00:30 13:30 18:30
09:42 14:40 19:49 01:00 09:00 11.-00 16:00
Time
Figure 10-5. Peak Area of 2998.8-cm1
Absorption Band of CH4 (A) and the
1014.2-cm'1 Absorption Band of Water
Vapor (B) Measured on November 17 and
18, 1993.
The data collected in this study
indicate that for this particular FT-IR monitor
the return signal and baseline noise are
repeatable and are instrumentally stable over
extended periods, but are subject to
variations due to weather conditions. The
peak positions and the FWHHs of the water
vapor singlet at 1014.2 cm"1 were repeatable
from day to day and were not affected by
rain, freezing rain, snow, or single-digit
temperatures. The variability in the
concentrations of CH4 limits its use in
instrument stability studies and for accuracy
and precision determinations. A step in the
concentration measurements associated with
the depletion and refurbishment of detector
coolant is not yet understood. Future
experiments with a QA cell and surrogate
standards are planned to further investigate
this effect.
10.4 Recommendations for Tests to be
Included in a QA Program for FT-IR
Long-Path Monitors
We are currently evaluating and
developing procedures to determine the
quality of data taken with FT-IR monitors.
The following is an outline of criteria that we
have used in a preliminary QA program to
verify the performance of an FT-IR long-path
system. Development of a QA plan for FT-IR
monitoring should include, but not
necessarily be limited to, these types of
measurements. These tests are designed to
determine that the instrument is operating
properly and producing good data. Some of
these issues were discussed in Chapter 3 for
the initial verification of instrument
performance, but can be used for routine QA
procedures as well. Other criteria for
development of a QA plan, such as siting
criteria or data chain-of-custody, should be
addressed as warranted, but are not
discussed here. These procedures were
developed for a research and development
program, but factors relevant to routine
monitoring programs were also taken into
consideration. Bear in mind that two
separate issues must be addressed in a QA
plan. One is whether or not the instrument
is working properly. The other issue is if the
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method used for quantitative analysis is
producing the correct results.
analysis of a target gas to give an estimate
of detection limits.
10.4.1 Noise Measurements
Measurements of two types of noise
can be routinely taken, instrumental
electronic noise and random baseline noise.
Electronic noise is recorded before the
detector Dewar is filled with liquid nitrogen.
This small signal is indicative of the
electronic noise of the system with no
detector signal. This should remain relatively
constant and typically contributes less than
0.25% of the total return signal. If some
electrical component of the system is
producing spurious noise, it will become
apparent from this measurement.
Random baseline noise is measured by
recording back-to-back spectra after the
detector has been filled with liquid nitrogen.
One spectrum is then ratioed to the other
and the absorption spectrum is calculated.
The result is a spectrum of the random
system noise. The RMS or peak-to-peak
noise in absorbance units can then be
calculated from these spectra. These
spectra should be acquired by using the
instrumental parameters to be used during
the analytical measurements. The baseline
noise measurements should be taken in a
spectral region that is devoid of absorption
due to water vapor or other atmospheric
gases. If not, changes in water vapor
concentration over the measurement time
will influence the magnitude of the noise
calculations. Noise measurements can also
be taken over the spectral region chosen for
For the baseline noise measurement it
is best to record these two spectra back to
back, as passage of time between the two
spectra, might also include changes in
atmospheric conditions or concentrations of
species in the path. Spectra taken at longer
time intervals during the study can be ratioed
in this manner to determine baseline stability
or systematic noise.
10.4.2 Stability of Instrument
Several aspects related to the stability
of the instruments can be measured. One is
the repeatability of the noise measurements
described above. These noise measurements
should be taken daily and recorded on a
control chart to alert the operator of any
gross changes or trends in the deterioration
of the baseline noise.
Another measurement to be taken
daily, or several times during the day, is the
return intensity. This can be measured either
as the single-beam intensity at a selected
wave number region or the magnitude of the
interferogram. At this time, the position of
the zero peak difference of the interferogram
should also be recorded, and the single-beam
spectrum should be examined for evidence of
system nonlinearity (see Chapter 3,
Section 3.4). The single-beam intensity
should be measured in different wave
number regions to determine if the source
characteristics have changed or the
interferometer alignment has been altered.
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• •
-.•'•:• •=••==
f=7?± ~^=
_-.i •
TR-4423-99-03
The high wave number (short wavelength)
portion of the spectrum will be most
sensitive to interferometer misalignment and
will show a decrease in intensity relative to
the other wave number regions if changes
have occurred.
In addition to being dependent on the
instrument's performance, the return
intensity also depends on atmospheric
conditions. For example, fog has a
deleterious effect on the return signal. Thus,
the atmospheric conditions must be noted
when the measurement is taken. As with
the noise measurements, the return intensity
should also be plotted daily on a control
chart. A decrease in return intensity could
be related to a drop in the source intensity,
misalignment of the external optics,
misalignment of the interferometer optics,
deterioration of the system optics, or a loss
in the detector Dewar hold time.
The positions of selected absorption
bands should also be recorded. In long-path
measurements the water vapor singlet at
1014.2 cm"1 works well for this purpose.
The FWHH of this band can also be
measured to determine the repeatability of
the resolution of the system. The
subtraction technique described by
Russwurm (1992b) can be used to detect
small frequency shifts or subtle changes in
the instrument resolution. If the resolution of
the system is deteriorating, and the band
becomes broader than a spectrum recorded
previously, the subtraction result will appear
as an "M". Shifts in frequency will produce
a derivative shape in the subtraction result.
Note that the FWHH measurement and the
spectral subtractions should be done on an
absorption spectrum, and not on a single-
beam spectrum or transmission spectrum.
As mentioned previously, bands in
higher wave number regions actually may
work better for this test, as they will be
more sensitive to spectral shifts and changes
in resolution. In addition to the water vapor
bands centered at 1014.2 cm'1, the HDO
bands centered at 2920 cm"1 can be used for
this test.
All of the above measurements should
be recorded on at least a daily basis and
compared to existing data to establish that
the instrument is performing properly.
10.4.3 Accuracy and Precision
The determination of accuracy and
precision are not as straightforward as the
tests used to determine if the instrument is
performing properly. The concentrations of
ambient gases, such as CH4 or N20, can be
used to a certain extent for these purposes.
This approach has the advantage that certain
gases are always present in open-path
spectra and no changes have to be made to
the instrumental configuration to measure
these gases. If the ambient concentrations
of these gases are assumed to be constant,
precision measurements can be made. For
example, we have measured the
concentration of N2O continuously over a
five-day period in the late spring to be within
±3.5% of the mean value. On the other
hand, as discussed in Section 10.3, we have
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seen CH4 concentrations increase by a factor
of 2.5 in a short time during measurements
taken in the late fall. Therefore, care must
be taken to account for possible emission
sources if ambient gases are used for QA
purposes. Ambient gases can also be used
to test for frequency shifts or changes in
resolution as described above. The use of
ambient gases for QA purposes can be used
to estimate the precision of the
measurement, but this approach does not
really address the accuracy of the method.
The alternative approach to using
ambient gases for QA data is to insert a
short gas cell that contains surrogate
standards into the beam. This has the
disadvantage of an attenuated IR beam due
to the transmitting and reflecting properties
of the windows used in the cell. Thus, the
performance of the instrument is somewhat
degraded. However, this approach does
have the advantage of having a known
quantity of target gas in the path. Assuming
this quantity is accurately known and it
remains constant, accuracy and precision
measurements can be made with a short cell
technique. To date, however, no universally
applicable technique using a short cell has
been developed.
As discussed in Chapter 3, stray light
in the monostatic configuration and
background blackbody radiation in the
bistatic configuration can affect the
quantitative results. The signal due to stray
light or background radiation must be
subtracted from the sample spectrum prior to
quantitative analysis. The stray light in the
spectrometer of a monostatic instrument can
be measured by blocking the return beam
with some type of opaque and nonreflective
material. In our experience the signal due to
stray light has been relatively constant,
provided no components of the system are
changed. The background blackbody
radiation of a bistatic system can be
measured with the IR source off. This
response will vary for different sites and can
also change throughout the day. Therefore,
this signal must be recorded on a more
frequent basis. It is not obvious at this point,
however, that simple subtraction adequately
compensates for the effects of stray light or
background radiation linearly over a range of
absorption values. Thus, the accuracy of the
system might be affected.
In addition to determining the
accuracy and precision of the instrument, the
accuracy and precision of the method used
for quantitative analysis must also be
determined. In most cases, an automated
software package, such as one that uses the
CLS algorithm, is used to determine the
concentrations of the target gases. These
procedures can be checked manually by
comparing the sample spectra to spectra of
reference gases with a known concentration.
Interactive subtraction procedures that yield
a scaling factor for the reference spectrum
can be used to check the concentration
measured by the CLS software. In addition,
the reference spectra can be scaled to the
desired concentration and then added to the
sample spectrum. When the composite
spectrum is then analyzed, the measured
concentration should reflect the amount of
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reference gas added. Care must be taken in
choosing the spectral regions used to analyze
for each target compound. For example, the
optimum region for analysis does not always
encompass the entire absorption envelope.
Possible interfering species must also be
accounted for in the analysis method.
The operator should also be aware
that any time a concentration spike appears
that cannot be immediately attributed to a
known source, the actual spectral data
should be examined to verify the presence of
the compound in question and its
concentration. This can be done by first
subtracting the appropriate absorption
spectra of any interfering species from the
sample spectrum. The signature and
absorbance values of the resultant spectrum
should then be compared to the reference
spectrum for proper features and intensities.
Also, any time that the concentrations of the
target compounds seem to correlate with
changes in water vapor concentration, the
spectra of the target compounds should be
examined to verify that the changes in
concentration are real. If the concentrations
of the target compounds exhibit either
positive or negative inflections with respect
to changes in water vapor concentration, the
analysis method should be altered to alleviate
the problem.
Ultimately, if the instrument is
operating properly and a suitable analysis
method is developed, the accuracy of the
FT-IR technique will be determined by the
accuracy of the reference spectra. To date,
no way of validating or certifying these
reference spectra exists.
10.4.4 Completeness and
Representativeness of Data
These requirements will vary with
specific monitoring applications. Care must
be taken to ensure that data points are
acquired frequently enough to account for
the variability of the target gas
concentration. Failure to do this will make it
difficult to discern between real changes in
the target gas concentration and possible
variability in the FT-IR measurements.
10.4.5 Comparability of the Data
If possible, the FT-IR data should be
initially compared to an established method.
This can be difficult because the FT-IR
produces a path-averaged concentration,
whereas most established methods use some
type of point monitor. As discussed in
Section 1 0.2.2, some of the FT-IR data have
been compared to the canister method. In a
current study, we are comparing ozone
measurements recorded with the FT-IR
monitor to those taken with personal
sampling devices and to hourly averages
from the state ozone monitoring program.
Although not exact, these comparisons can
give the operator an idea if the FT-IR
measurements are within generally accepted
values. If not, corrective action should be
taken.
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10.4.6 Ancillary Measurements
The type of ancillary measurements
required will vary, depending on the type of
study being conducted. For any long-path,
open-path measurements, the ambient
temperature, water vapor concentration,
ambient pressure, and wind velocity should
be recorded. The operator should also be
aware of the effect of changes in altitude on
ambient pressure. If the instrument is
housed in an enclosed environment, the
temperature of that environment should also
be recorded. We have also found it useful to
record the temperature inside the
spectrometer itself, especially in cold
weather situations.
10.4.7 Documentation
As with any analytical methodology,
a log of instrument usage, downtime, and
repairs, as well as notes regarding unusual
observations, should be maintained. These
notes can prove invaluable for analyzing data
that appear to be abnormal. Records should
be kept that are appropriate for the type of
study being conducted. For example,
requirements for a research and development
project may be different from those required
for legally defensible data.
10.5 References
Kagann, R.H., J.G. Jolly, D.S. Shoop,
M.R. Hankins, and J.M. Jackson. 1994.
Validation of Open-Path FTIR Data at
Treatment, Storage, and Disposal Facilities.
SP-89 Optical Sensing for Environmental
Monitoring, Air & Waste Management
Association, Pittsburgh, PA, pp. 437-442.
Kricks, R.J., Scotto, R.L., Pritchett, T.H.,
Russwurm, G.M., Kagann, R.H., and
Mickunas, D.B. 1992. Quality Assurance
Issues Concerning the Operation of Open-
Path FTIR Spectrometers. Proceedings of
Optical Remote Sensing. Applications to
Environmental and Industrial Safety
Problems, SP-81, Air & Waste Management
Association, Pittsburgh, PA, pp. 224-231.
Russwurm, G.M. 1992a. Quality
Assurance, Water Vapor, and the Analysis of
FTIR Data. Proceedings of the 85th Annual
Meeting and Exhibition of the Air & Waste
Management Association. Air & Waste
Management Association, Pittsburgh, PA, pp.
92-73.03.
Russwurm, G.M. 1992b. Quality Assurance
and the Effects of Spectral Shifts and
Interfering Species in FT-IR Analysis.
Proceedings of Optical Remote Sensing.
Applications to Environmental and Industrial
Safety Problems, SP-81, Air & Waste
Management Association. Pittsburgh, PA,
pp. 105-111.
Russwurm, G.M. and W.A. McClenny 1 990.
A Comparison of FTIR Open Path Ambient
Data with Method TO-14 Canister Data.
Proceedings of the 1990 U.S. EPA/A&WMA
International Symposium on the
Measurement of Toxic and Related Air
Pollutants. Air & Waste Management
Association, Pittsburgh, PA, pp. 248-253.
Thompson, E.L, Jr., J.W. Childers, and G.M.
Russwurm. 1994. Development of Quality
Assurance Procedures in Open-Path FT-IR
Monitoring. Proceedings of the 1994 U.S.
EPA/A&WMA International Symposium on
Measurement of Toxic and Related Air
Pollutants. Air & Waste Management
Association, Pittsburgh, PA, pp. 529-534.
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U.S. Environmental Protection Agency.
1989. Preparing Perfect Project Plans: A
Pocket Guide for the Preparation of Quality
Assurance Project Plans. EPA/600/9-
89/087. Available from Guy F. Simes,
Quality Assurance Manager, U.S.
Environmental Protection Agency, Risk
Reduction Engineering Laboratory, Cincinnati;
OH 45268.
U.S. Environmental Protection Agency.
1991. Preparation Aids for the Development
of RREL Quality Assurance Plans (Category I
Project Plans). EPA/600/8-91/003.
Available from Guy F. Simes, Quality
Assurance Manager, U.S. Environmental
Protection Agency, Risk Reduction
Engineering Laboratory, Cincinnati, Ohio
45268.
Weber, K., H.J. van de Wiel, A.C.F. Junker,
and C. de LaRiva, C. 1992. Definition and
Determination of Performance Characteristics
of Air Quality Measuring Methods as Given
by the International Organization for
Standardization (ISO) - Applicability to
Optical Remote Sensing. Proceedings of
Optical Remote Sensing. Applications to
Environmental and Industrial Safety
Problems, SP-81, Air & Waste Management
Association, Pittsburgh, PA, pp. 30-42.
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Chapter 11
Glossary of Terms for
FT-IR Open-Path Remote Sensing
11.1 Introduction and Overview
This chapter contains a glossary of
terms for remote sensing, with an emphasis
on those terms relevant to FT-IR long-path,
open-path monitoring. When possible,
definitions of terms have been drawn from
authoritative texts or manuscripts in the
fields of remote sensing, air pollution
monitoring, spectroscopy, optics, and
analytical chemistry. In some cases, general
definitions have been augmented or
streamlined to be more specific to long-path,
open-path monitoring applications. These
definitions were intended to remain
scientifically rigorous and still be generally
applicable to a variety of FT-IR open-path
remote-sensing issues.
11.2 Terms
Absorbance: The negative logarithm of the
transmission. A = -ln(///0), where / is the
transmitted intensity of the light and 70 is the
incident intensity. Generally, the logarithm to
the base 10 is used, although the quantity /
really diminishes exponentially with A
(Pfeiffer and Liebhafsky 1951). If the term
"fractional transmission" is used for the ratio
///0, then the implication is that the
instrument's slit function (see "Instrument
function") is accounted for (Penner 1959).
Active system: A system that radiates
energy to the surrounding environment (for
example, a radio transmitter).
Apodization: A mathematical transformation
carried out on data received from an
interferometer to alter the instrument's
response function. There are various types
of transformation; the most common are
boxcar, triangular, Happ-Genzel, and Beer-
Norton functions.
Average concentration: For FT-IR or
differential absorption spectroscopy systems,
this quantity is the result of dividing the
integrated concentration (the quantity that is
measured) by the path length used for the
measurement. It has units of parts per
million, parts per billion, micrograms per
cubic meter, etc. (McClenny and Russwurm
1978).
Background spectrum: 1. With all other
conditions being equal, that spectrum taken
in the absence of the particular absorbing
species of interest. 2. Strictly, that radiant
intensity incident on the front plane of the
absorbing medium. 3. A spectrum obtained
from the ambient black body radiation
entering the system. This background must
be considered in FT-IR systems, in which the
IR beam is not modulated before it is
transmitted along the path. For FT-IR
systems that do not use a separate source of
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infrared energy, the background is the source
of infrared energy.
Band pass filter: A filtering device that
allows the transmission of only a specific
band of energies. It can be wide band or
narrow band.
Bandwidth: The width of a spectral feature
as recorded by a spectroscopic instrument.
This width is listed as the full width at the
half maximum of the feature or as the half
width at the half maximum of the spectral
feature. This is also referred to as the line
width (Lengyel 1971).
Beer's law: Beer's law states that the
intensity of a monochromatic plane wave
incident on an absorbing medium of constant
thickness diminishes exponentially with the
number of absorbers in the beam. Strictly
speaking, Beer's law holds only if the
following conditions are met: (1) perfectly
monochromatic radiation, (2) no scattering,
(3) a beam that is strictly collimated,
(4) negligible pressure-broadening effects
(Pfeiffer and Liebhafsky 1951; Lothian
1963). For an excellent discussion of the
derivation of Beer's law, see Penner (1959).
Bistatic system: A system in which the
receiver is some distance from the
transmitter. This term is actually taken from
the field of radar technology. For remote
sensing, this implies that the light source and
the detector are separated and are at the
ends of the monitoring path.
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Broad band system: Any system that admits
a broad range of energies into its signal-
processing section. Alternatively, a system
that has a flat response to a large range of
energies.
Closed path: The optical path over which
the beam travels in a sensor that is entirely
enclosed. This is the case when White cells
or Harriot cells are used with the system.
Cooler: A device into which the detector is
placed for maintaining it at a low
temperature in an IR system. At a low
temperature, the detector provides the high
sensitivity that is required for the IR system.
The two primary types of coolers are a liquid
nitrogen Dewar and a closed-cycle Stirling
cycle refrigerator.
COSPEC: An acronym for "correlation
spectrometer." This is a misnomer for the
type of instrument implied. It is really an
instrument that uses a diffraction grating
either in the active, bistatic or the passive
mode. This instrument is more correctly
included in the class of instruments using
differential absorption spectroscopy
techniques. It is used primarily to measure
sulfur dioxide and nitrogen oxide.
DIAL: An acronym for "differential
absorption lidar." This system uses two
pulsed frequencies from the same laser or
from different lasers to measure the
concentration of gas over a path. The two
laser lines are at different positions within
the absorption feature. The difference of the
amount of light backscattered at these two
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wavelengths is the quantity used for the
measurement.
DOAS: An acronym for differential optical
absorption spectroscopy. A technique
whereby, in principle, any known difference
in absorbance is used to determine the
concentration of a gas. Generally, the
absorption difference is taken between the
spectral line center and the wing.
Electromagnetic spectrum: The total of all
possible frequencies of electromagnetic
radiation. Different sources may emit over
different frequency regions. All
electromagnetic waves travel at the same
speed in free space (Halliday and Resnick
1974).
Fingerprint region: The region of the
absorption spectrum of a molecule that
essentially allows its unequivocal
identification. This region covers the wave
number range from 650 to 1300 cm'1
(Willard et al. 1974).
Flux: The number or mass of particles or
molecules that pass through a given unit area
of surface per unit of time (Calvert 1990).
Fourier transform: A mathematical transform
that allows an aperiodic function to be
expressed as an integral sum over a
continuous range of frequencies (Champeney
1973). The Fourier transform of the
interferogram produced by the Michelson
interferometer in an FT-IR is the intensity as
a function of frequency.
FT-IR: An abbreviation for "Fourier transform
infrared." A spectroscopic instrument using
the infrared portion of the electromagnetic
spectrum. The working component of this
system is a Michelson interferometer. To
obtain the absorption spectrum as a function
of frequency, a Fourier transform of the
output of the interferometer must be
performed. For a brief overview of the FT-IR,
see the publication by Nicolet (Nicolet
Analytical Instruments 1986). For an in-
depth description of the FT-IR, see Griffiths
and deHaseth (1986).
GASPEC: An acronym for "gas filter
correlation spectrometer." The earliest of
these devices was described by Luft in
1943, and they have been used in various
configurations ever since. The primary
feature of these devices is a pair of gas cells.
One cell contains a carefully selected
quantity of the target gas and the other a
gas that is spectroscopically inactive. The
difference in spectral transmittance of the
two cells is an indicator of the concentration
of the target gas in the atmosphere (Ward
and Zwick 1975).
Infrared spectrum: That portion of the
electromagnetic spectrum that spans the
region from about 10 cm"1 to about
12,500 cm'1. It is divided (Willard et al.
1974) into (1) the near-infrared region (from
12,500 to 4000 cm'1), (2) the mid-infrared
region (from 4000 to 650 cm'1), and (3) the
far-infrared region (from 650 to 10 cm'1).
Instrument function: The function
superimposed on the absorption line shape
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by the instrument. This is sometimes
referred to as the slit function, a term taken
from instruments that use slits to obtain
resolution.
Intensity: The radiant power per unit solid
angle. When the term "spectral intensity" is
used, the units are watts per steradian per
nanometer. In most spectroscopic literature,
the term "intensity" is used to describe the
power in a collimated beam of light in terms
of power per unit area per unit wavelength.
However, in the general literature, this
definition is more often used for the term
"irradiance," or "normal irradiance" (Calvert
1990; Stone 1963).
Interference: The physical effects of
superimposing two or more light waves. The
principle of superposition states that the total
• amplitude of the electromagnetic disturbance
at a point is the vector sum of the individual
electromagnetic components incident there.
For a two-component system of collinear
beams of the same amplitude, the
mathematical description of the result of
addition is given by I(p) = 2/0(1 + cos/4/),
where 70 is the intensity of either beam, and
A is the phase difference of the two
components. The cosine term is called the
"interference term" (Halliday and Resnick
1974; Stone 1963). See also "Spectral
Interference."
Interferogram: The effects of interference
that are detected and recorded by an
interferometer; the output of an FT-IR and
the primary data that is collected and stored
(Stone 1963; Griffiths and deHaseth 1986).
Interferometer: Any of several kinds of
instruments used to produce interference
effects. The Michelson interferometer used
in FT-IR instruments is the most famous of a
class of interferometers that produce
interference by the division of an amplitude
(Tolansky 1962).
Irradiance: Radiant power per unit projected
area of a specified surface. This has units of
watts per square centimeter. The term
"spectral irradiance" is used to describe the
irradiance as a function of wavelength. It
has units of watts per square centimeter per
nanometer (Calvert 1990).
Laser: An acronym for the term "light
amplification by stimulated emission of
radiation". A source of light that is highly
coherent, both spatially and temporally
(Lengyel 1971).
LIDAR: An acronym for the term "light
detection and ranging" (Calvert 1990). A
technique for (1) detecting the presence of
gases and aerosols by measuring the
backscattered portion of a laser beam and
(2) determining the range of these gases and
aerosols by electronically gating the detected
signal and performing a calculation based on
the speed of light (about 30 cm/ns).
Light: Strictly, light is defined as that portion
of the electromagnetic spectrum that causes
the sensation of vision. It extends from about
25,000 cm'1 to about 14,300 cm'1 (Halliday
and Resnick 1 974).
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Light scattering: The redirection of light
waves due to interaction with molecules or
aerosols. If the size of the body causing the
scattering is small compared to the
wavelength of the incident radiation, the
scattering is termed "Raleigh scattering." If
the size is large compared to the wavelength,
the scattering is termed "Mie scattering."
Scattering by molecules is generally Raleigh
scattering, and scattering by aerosols is Mie
scattering. As light travels through a
medium, two physical processes diminish the
intensity in the forward direction - scattering
and absorption. The sum of these two
effects is called extinction (van de Hulst
1981).
Long-path monitoring: This is a monitoring
technique that uses an extended, open path.
LIDAR systems can make measurements
over a path length of a few kilometers.
DOAS systems can make measurements of
ozone over a path of up to 2 km. The FT-IR
systems customarily use paths with length
less than 1 km.
Minimum detection limit: The minimum
concentration of a compound that can be
detected by an instrument with a given
statistical probability. Usually the detection
limit is given as 3 times the standard
deviation of the noise in the system. In this
case, the minimum concentration can be
detected with a probability of 99.7% (Calvert
1990; Long and Winefordner 1983).
Monitoring path: The actual path in space
over which the pollutant concentration is
measured and averaged.
Monitoring path length: The length of the
monitoring path in the atmosphere over
which the average pollutant concentration
mea-surement is determined (U.S.
Environmental Protection Agency 1994).
Monostatic system: A system with the
source and the receiver at the same end of
the path. For FT-IR systems and for DOAS
systems, the beam is generally returned by a
retroreflector. For LIDAR systems, the
backscattered portion of the laser beam is
measured directly.
Open-ended system: A system in which the
remote sensor uses light reflected from
targets of opportunity (walls, trees, etc.) or
skylight as a source.
Open-path analyzer: An automated analytical
instrument that is used for a method of
measuring the average atmospheric pollutant
concentration in situ along one or more
monitoring paths that are 5 m or more in
length (U.S. Environmental Protection
Agency 1994).
Open-path monitoring: Remote sensing over
a path that is completely open to the
atmosphere. Thus, the concentration of a
particular gas in the beam path can be
changed by winds and diffusion. The open
path is the most frequently used in remote
sensing.
Optical remote sensing: A generic term used
to describe any of a number of optical
measurement techniques that measure some
quantity or constituent of the atmosphere.
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These techniques include DIAL, DOAS,
FT-IR, GASPEC, LIDAR, etc. One thing that
is common to all the techniques is that no
sample must be collected.
Parts per million meters: The unit term for
the quantity that is measured by many
remote sensors. It is the unit associated
with the quantity path-integrated
concentration. It is a possible unit of choice
for reporting data from remote sensors
because it is independent of the path length.
Passive system: Any system that does not
radiate energy to its surroundings.
Path-averaged concentration: The result of
dividing the path-integrated concentration by
the path length. Path-averaged
concentration gives the average value of the
concentration along the path (McClenny and
Russwurm'1978).
Path-integrated concentration: The quantity
that is measured by a remote sensor over a
long path. It has units of concentration times
length.
Plume: The gaseous and aerosol effluents
emitted from a chimney or other source and
the volume of space they occupy. The shape
of a plume and the concentration of
pollutants within it are very sensitive to
meteorological conditions (Calvert 1990).
Point analyzer: An automated analytical
method that measures pollutant
concentration in an ambient air sample
extracted from the atmosphere at a specific
inlet probe point (proposed changes [U.S.
Environmental Protection Agency 1994]).
Probe: The actual inlet where an air sample
is extracted from the atmosphere for delivery
to a sampler or point analyzer (proposed
changes [U.S. Environmental Protection
Agency 1994]).
Radiometry: The measurement of various
quantities such as intensity associated with
radiant energy (Calvert 1990). This is in
contrast to the term photometry, which
assumes the spectral sensitivity of the
human eye as the detector (Walsh 1965).
Real-time system: Any monitoring system
that acquires and records data at a rate that
is comparable to the rate at which the
concentration is changing.
Reference spectra: Spectra of the
absorbance versus wave number for a pure
sample of a set of gases. The spectra are
obtained under controlled conditions of
pressure and temperature and with known
concentrations. For most instruments, the
pure sample is pressure-broadened with
nitrogen so that the spectra are
representative of atmospherically broadened
lines. These spectra are used for obtaining
the unknown concentrations of gases in
ambient air samples.
Resolution: The minimum separation that
two spectral features can have and still, in
some manner, be distinguished from one
another. A commonly used requirement for
two spectral features to be considered just
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resolved is the Raleigh criterion. This states
that two features are just resolved when the
maximum intensity of one falls at the first
minimum of the other (Jenkins and White
1950; Tolansky 1962). This definition of
resolution and the Raleigh criterion are also
valid for the FT-IR, although there is another
definition in common use for this technique.
This definition states that the minimum
separation in wave numbers of two spectral
features that can be resolved is the
reciprocal of the maximum optical path
difference (in centimeters) of the two
interferometer mirrors employed (Griffiths
and deHaseth 1986; Nicolet 1986).
Retroreflector: The CIE (Commission
Internationale de I'Eclairage) defines
retroreflection as "radiation returned in
directions close to the direction from which
it came, this property being maintained over
wide variations of the direction of the
incident radiation." Retroreflector devices
come in a variety of forms and have many
uses. The one commonly described by
workers in remote sensing uses total internal
reflection from three mutually perpendicular
surfaces. This kind of retroreflector is
usually called a corner cube or prismatic
retroreflector (Rennilson 1980).
several lasers that also are used as sources
for DIAL and LIDAR instruments.
Spectral intensity: See "Intensity."
Spectral interference: When the absorbance
features from two or more gases cover the
same wave number regions, the gases are
said to exhibit spectral interference. Water
vapor produces the strongest spectral
interference for infrared spectroscopic
instruments that take atmospheric data.
Synthetic background: A spectrum that is
made from a field spectrum by choosing
points along the baseline and connecting
them with a high-order polynomial or short,
straight lines. The synthetic background is
then used to find the absorbance spectrum.
Truncation: The act of stopping a process
before it is complete. In FT-IR
spectrometers, the theoretically infinite scale
of the interferogram is truncated by the finite
movement of the interferometer mirror.
Unistatic system: A system that has the
source and the receiver at the same place;
now more commonly referred to as a
monostatic system.
Slit function: See "Instrument function."
Source: The device that supplies the
electromagnetic energy for the various
instruments used to measure atmospheric
gases. These generally are a Nernst glower
or globar for the infrared region or a xenon
arc lamp for the ultraviolet region. There are
Wave number: The number of waves per
centimeter. This term has units of reciprocal
centimeters (cm'1).
11.3 References
Calvert, J.G.
Atmospheric
1990. Glossary of
Chemistry Terms
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(recommendations 1990). PureAppl. Chem.
62 (111:2167-2219.
Champeney, D.C. 1973. Fourier Transforms
and Their Physical Applications. Academic
Press, London.
Griffiths, P.R., and J.A. deHaseth. 1986.
Fourier Transform Infrared Spectrometry.
John Wiley and Sons, New York.
Halliday, D., and R. Resnick. 1974.
Fundamentals of Physics. Wiley and Sons,
New York.
Jenkins, F.A., and H.E. White. 1950.
Fundamentals of Optics. McGraw-Hill, New
York.
Long, G.L., and J.D. Winefordner. 1983.
Limit of Detection: A Closer Look at the
IUPAC Definition. Anal. Chem. 55(7): 712A-
724A.
Lothian, G.F. 1963. Beer's Law and Its Use
in Analysis. Analyst 88:678.
Lengyel, B.A. 1971. Lasers, 2nd Ed. Wiley-
Interscience, New York.
Luft, K.F. 1943. Uber Eine Neue Methode
der Registrierenden Gas Analyze Mit Hilfe der
Absorption Ultraroter Stahlen Ohne Spektrale
Zerlegung. J. Tech. Phys. 24:97.
McClenny, W.A., and G.M. Russwurm.
1978. Laser-Based Long Path Monitoring of
Ambient Gases - Analysis of Two Systems.
A tmos. Environ. 1 2:1443.
Nicolet Analytical Instruments. 1986. FT-IR
Theory. Nicolet Analytical Instruments,
Madison, Wl.
Penner, S.S. 1959. Quantitative Molecular
Spectroscopy and Gas Emissivities. Addison-
Wesley, Reading, MA.
Pfeiffer, H.G., and H.A. Liebhafsky. 1951.
The Origins of Beer's Law. J. Chem. Educ.
28:123-125.
Rennilson, J.J.
Measurements:
19:1234.
1980. Retroreflection
A Review. Appl. Opt.
Stone, J.M. 1963. Radiation and Optics.
McGraw-Hill, New York.
Tolansky, S. 1962. An Introduction to
Interferometry. John Wiley and Sons, New
York.
U.S. Environmental Protection Agency.
1994. Ambient air quality surveillance siting
criteria for open path analyzers (proposed
rule). Fed. Reg. 59(1 59):42541-42552.
van de Hulst, H.C. 1981. Light Scattering
by Small Particles. Dover Publications, New
York.
Walsh, J.W.T. 1965. Photometry. Dover
Publications, New York.
Ward, T.V., and H.H. Zwick. 1975. Gas
Cell Correlation Spectrometer: GASPEC.
Appl. Opt. 14:2896.
Willard, H.H., L.L. Merritt, and J.A. Dean.
1974. Instrumental Methods of Analysis,
5th Ed. D. Van Nostrand, Princeton, NJ.
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Chapter 12
Bibliography
12.1 Introduction and Overview
This chapter contains a bibliography
of journal articles, books, and conference
proceedings that address FT-IR long-path
monitoring, as well as general references that
present discussions of the basic principles of
FT-IR spectrometry. This is not a reference
section for literature cited in the text of this
guidance document, but is a general
bibliography. References in this document are
listed at the end of the chapter in which they.
are cited.
This bibliography is by no means
exhaustive, but is intended to give a broad
overview of the available literature in the
FT-IR long-path discipline. During the initial
phase of this overview, a computer-assisted
on-line literature search was conducted for
citations listed in Chemical Abstracts through
September 29, 1992. A subsequent on-line
search was conducted for citations listed in
Chemical Abstracts from 1 992 through July
22, 1 994. These literature searches focused
on, but were not limited to, current
publications regarding FT-IR long-path, open-
path monitoring, in keeping with the
emphasis of this document. For this latest
edition, a literature search of the documents
available through NTIS in Springfield, VA,
was conducted through 1998. Other
citations were gleaned from the reference
sections of articles on file. Several early
citations are also given to provide an
important, historical perspective into long-
path IR monitoring in environmental analysis.
Only articles that are on file in our laboratory
are listed in the bibliography. This
bibliography will continue to be updated as
revisions to this document are made.
Several of the more recent citations
are from conference proceedings, which may
limit their general availability. They are
included to give the reader access to current
research in the field that has in many cases
not yet appeared in the peer-reviewed
literature. Also, inclusion of the conference
proceedings provides the reader with
pertinent information regarding conferences
and meetings that typically address FT-IR
long-path or remote-sensing issues.
12.2 Publications
Amoto, I. 1988. Remote Sensing: A Distant
View of Chemistry. Anal. Chem.
60(23): 1339A-1344A.
Anderson, R.J., and P.R. Griffiths. 1975.
Errors in Absorbance Measurements in
Infrared Fourier Transform Spectrometry
Because of Limited Instrument Resolution.
Anal. Chem. 47(14):2339-2347.
Andreas, E.L., J.R. Gosz, and C.N. Dahm.
1992. Can Long-Path FTIR Spectroscopy
Yield Gas Flux Measurements Through a
Variance Technique? Atmos. Environ.
26A(2):225-233.
Bangalore, A.S., G.W. Small, R.J. Combs,
R.B. Knapp, R.T. Kroutil, C.A. Traynor, and
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J.D. Ko. 1997. Automated Detection of
Trichloroethylene by Fourier Transform
Infrared Remote Sensing Measurements.
Anal. Chem. 26:118-129.
Barnes, H.W., Jr., W.F. Herget, and
R. Rollins. 1974. Remote Sensing of Sulfur
Dioxide in Power Plant Plumes Using
Ultraviolet Absorption and Infrared Emission
Spectroscopy. Analytical Methods Applied to
Air Pollution Measurements (R.K. Stevens
and W.F. Herget, Eds.), Ann Arbor Science,
Ann Arbor, Ml, pp. 245-266.
Barnett, R.W., and B.T. Smith. 1994.
Modeling Background Temperatures in
Passive Infrared Remote Sensing. SP-89
Optical Sensing for Environmental
Monitoring, Air & Waste Management
Association, Pittsburgh, PA, pp. 293-304.
Batterman, S.A., C. Peng, and P. Milne.
1994. Sequential Extractive Sampling of
Indoor Air Contaminants Using FT-IR
Spectroscopy. SP-89 Optical Sensing for
Environmental Monitoring, Air & Waste
Management Association, Pittsburgh, PA,
pp. 242-254.
Beer, A. 1852. Ann. Physik 86:78.
Beer, R. 1992. Remote Sensing by Fourier
Transform Spectrometry, John Wiley and
Sons, New York.
Beil, A., R. Daum, R. Harig, and G. Matz.
1998. Remote Sensing of Atmospheric
Pollution by Passive FTIR Spectrometry. Proc.
SP/£3493:32-43.
Bell, R.J. 1972. Introductory Fourier
Transform Spectroscopy, Academic Press,
New York.
Bennett, C.L. 1994. FTIR Measurements of
Thermal Infrared Sky Radiance and
Transmission. Department of Energy Report
UCRL-117864.
Bhattacharyya, R., and L.A. Todd. 1995.
Two Dimensional Mapping of Air
Contaminant Movement Using a
Tomographic System. Proceedings of the
SP/E Specialty Conference Optical Sensing
for Environmental and Process Monitoring,
McClean, VA, International Society for
Optical Engineering, Bellingham, WA.
Biermann, H.W., E.G. Tuazon, A.M. Winer,
T.J. Wellington, and J.N. Pitts, Jr. 1988.
Simultaneous Absolute Measurements of
Gaseous Nitrogen Species in Urban Ambient
Air by Long Pathlength Infrared and
Ultraviolet-Visible Spectroscopy. Atmos.
Environ. 22(8): 1 545-1 554.
Bishop, G.A., J.R. Starkey, A. Ihlenfeldt,
W.J. Williams, and D.H. Stedman. 1989. IR
Long-Path Photometry: A Remote Sensing
Tool for Automobile Emissions. Anal. Chem.
61(10):671A-677A.
Bishop, G.A., and D.H. Stedman. 1990. On-
Road Carbon Monoxide Emission
Measurement Comparisons for the 1988-
1989 Colorado Oxy-Fuels Program. Environ.
Sci. Technol. 24(6):843-847.
Bishop, G.A., D.H. Stedman, and T. Jessop.
1992. Infrared Emission and Remote
Sensing. J. Air Waste Manage. Assoc.
42(5):695-697.
Bittner, H., T. Eisenmann, H. Mosebach,
M. Erhard, and M. Resch. 1994.
Measurements of Diffuse Emissions of
Volatile Organic Compounds by High
Resolution FTIR Remote Sensing. SP-89
Optical Sensing for Environmental
Monitoring, Air & Waste Management
Association, Pittsburgh, PA, pp. 443-454.
Blumenstock,T., H. Fischer, A. Friedle, F.
Hase, and P. Thomas. 1997. Column
Amounts of CIONO2 HCI, HN03 and HFfrom
Ground Based FTIR Measurements Made
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near Kiruna, Sweden in Late Winter 1994.
J. Atmos. Chem. 26 (3):311-321.
Brandon, R.W., S.D. Garbis, and
R.H. Kagann. 1992. Quantitative Gas
Standards for the Calibration of Open Path
Optical Sensors. SP-81 Optical Remote
Sensing. Applications to Environmental and
Industrial Safety Problems, Air & Waste
Management Association, Pittsburgh, PA,
pp. 434-445.
Briz, S., A.J. De Castro, J. Melendez,
J. Meneses, J.M. Aranda, and F. Lopez.
1997. Proc. SP/E3106:159-170.
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D.S. Lavery. 1982. Matrix Representations
and Criteria for Selecting Analytical
Wavelengths for Multicomponent
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54(9):1472-1479.
Byrd, L.A.B. 1994. Ambient Air Monitoring
Siting Criteria for Open Path Analyzers
Measuring Nitrogen Dioxide, Ozone, and
Sulfur Dioxide. SP-89 Optical Sensing for
Environmental Monitoring, Air & Waste
Management Association, Pittsburgh, PA,
pp. 349-357.
Calvert, J.G. 1990. Glossary of Atmospheric
Chemistry Terms (recommendations 1990).
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Cantu, A., G. Pophal, S. Hall, and C.T. Laush
1998. Unique Application of an Extractive
FTIR Ambient Air Monitoring System for the
Simultaneous Detection of Multiple ppb Level
VOC's. Appl. Phys. B. Lasers Opt. 67
(4):493-496.
Carlson, R.C., A.F. Hayden, and W.B. Telfair.
1 988. Remote Observation of Effluents from
Small Building Smokestacks Using FT-IR
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4959.
Carter, R.E., Jr., D.D. Lane, G.A. Marotz,
M.J. Thomas, and J.L. Hudson. 1992. A
Method of Interconversion Between Point
and Path-Averaged Ambient Air VOC
Concentrations, Using Wind Data. SP-8J
Optical Remote Sensing. Applications to
Environmental and Industrial Safety
Problems, Air & Waste Management
Association, Pittsburgh, PA, pp. 529-540.
Carter, R.E., Jr., D.D. Lane, G.A. Marotz,
C.T. Chaffin, T.L. Marshall, M. Tucker,
M.R. Witkowski, R.M. Hammaker,
W.G. Fateley, M.J. Thomas, and
J.L. Hudson. 1993. A Method of Predicting
Point and Path-Averaged Ambient Air VOC
Concentrations, Using Meteorological Data.
J. Air Waste Manage. Assoc. 43:480-488.
Carter, R.E., Jr., M.J. Thomas, G.A. Marotz,
D.D. Lane, and J.L. Hudson. 1992.
Compound Detection and Concentration
Estimation by Open-Path Fourier Transform
Infrared Spectrometry and Canisters Under
Controlled Field Conditions. Environ. Sci.
Technol. 26(111:2175-2181.
Carter, R.O., III, N.E. Lindsay, and
D. Beduhn. 1990. A Solution to Baseline
Uncertainty Due to MCT Detector
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44(71:1147-1151.
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M.D. Tucker, M. Hammaker, and W.G.
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Sensing of Volatile Organic Compounds
Emitted near Ground Level. Proceedings of
the 86th Annual Meeting and Exhibition, Air &
Waste Management Association, Pittsburgh,
PA.
Chaffin, C.T., Jr., W.G. Fateley,
M.D. Tucker, and R.M. Hammaker. 1 994. An
Alternative Sampling Technique for Fourier
Transform Infrared (FT-IR) Remote Sensing of
Fugitive Emissions from Industrial Sites.
SP-89 Optical Sensing for Environmental
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Monitoring, Air & Waste Management
Association, Pittsburgh, PA, pp. 814-825.
Chaffin, C.T., T.L. Marshall, R.J. Combs,
R.B. Knapp, R.T. Kroutil, W.G. Fately, and
R.M. Hammaker. 1995. Passive Fourier
Transform (FTIR) Monitoring of S02 in
Plumes: A Comparison of Remote Passive
Spectra of an Actual Emission Spectra
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2365:303-313.
Champeney, D.C. 1973. Fourier Transforms
and Their Physical Applications. Academic
Press, London.
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Long Path Open Air FTIR Technique for Air in
the State of Kentucky. Proc. SPIE 2365:
347-358.
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Measurement of Traffic Generated Carbon
Monoxide. J. Air Pollut. Control Assoc.
33(3):220-222.
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Measurement of the Taiwan Ambient Trace
Gas Concentration by Kilometer-Path Length
Fourier-Transform Infrared Spectroscopy.
Anal. Sci. 10(1): 193-201.
Chang, S.-Y., and T.-L. Tso. 1994. Field
Applications of Long Infrared Absorption in
Taiwan. SP-89 Optical Sensing for
Environmental Monitoring, Air & Waste
Management Association, Pittsburgh, PA,
pp. 157-181.
Childers, J.W. 1993. Resolution
Considerations in Long-Path, Open-Path FT-IR
Spectrometry. Paper 93-RA-121.05,
Proceedings of the 86th Annual Meeting and
Exhibition, Air & Waste Management
Association, Pittsburgh, PA.
Childers, J.W., and E.L. Thompson, Jr. 1 994.
Resolution Requirements in Long-Path FT-IR
Spectrometry. SP-89 Optical Sensing for
Environmental Monitoring, Air & Waste
Management Association, Pittsburgh, PA,
pp. 38-46.
Childers, J.W., G.M. Russwurm, and
E.L. Thompson, Jr. 1996. Instrumental
Parameters and Their Effect on Open-Path
FT-IR Data. Proceedings of the 89th Annual
Meeting & Exhibition of the Air & Waste
Management Association. Paper 96-MP5.07,
Air & Waste Management Association.
Pittsburgh, PA.
Childers, J.W., G.M. Russwurm, and
E.L. Thompson. 1997. QA/QC Issues in
OP/FTIR Monitoring. Proceedings of the
1997 Annual Meeting AWMA, Air & Waste
Management Association, Pittsburgh, PA.
Childers L.O. 1996. USEPA QA Auditor Is
Scheduled for a Visit. What Can I Expect?
Proceedings of the 1995 Specialty
Conference In San Francisco, Air & Waste
Management Association, Pittsburgh, PA.
Chu, P.M., G.C. Rhoderick, W.J. Lafferty,
F. R. Guenther,and S.J. Wetzel. 1997.
Quantitative Infrared Data Base of Hazardous
Air Pollutants. Proceedings of the 89th
Annual Meeting of A WMA in Nashville, Tenn.
Air & Waste Management Association,
Pittsburgh, PA.
Chughtai, A.R., and D.M. Smith. 1 991. Long
Optical Path Cell for Photochemical Kinetics
in Heterogeneous Systems of Low
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1207.
Clark, J.M. 1994. Mercury Cadmium
Telluride Cryocooled Detector Performance
Parameters for FTIR Spectroscopy. SP-89
Optical Sensing for Environmental
Monitoring, Air & Waste Management
Association, Pittsburgh, PA, pp. 591-606.
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Collins, J.D., and L.A. Todd. 1992.
Evaluation of Infrared Optical Remote
Sensing Equipment in an Exposure Chamber.
SP-81 Optical Remote Sensing. Applications
to Environmental and Industrial Safety
Problems, Air & Waste Management
Association, Pittsburgh, PA, pp. 351-355.
Cronin, J.T. 1992. Stack-Gas Monitoring
Using FT-IR Spectroscopy. Spectroscopy
7(5):33-39.
Dando, N.R., T.O. Montgomery,
L.A. Schneider, and J.E. Gibb. 1994.
Applications of Open-Path FTIR Spectroscopy
for Characterizing Fugitive Emissions at Metal
Production Plants. SP-89 Optical Sensing for
Environmental Monitoring, Air & Waste
Management Association, Pittsburgh, PA,
pp. 123-133.
Demirgian, J.C., and M.D. Erickson. 1990.
The Potential of Continuous Emission
Monitoring of Hazardous Waste Incinerators
Using Fourier Transform Infrared
Spectroscopy. Waste Manage. 10:227.
Demirgian, J.C., C.L. Hammer, and
R.T. Kroutil. 1992. The Potential of Passive-
Remote Fourier Transform Infrared
Spectroscopy to Detect Organic Emissions
Under the Clean Air Act. SP-81 Optical
Remote Sensing. Applications to
Environmental and Industrial Safety
Problems, Air & Waste Management
Association, Pittsburgh, PA, pp. 464-476.
Demirgian, J.C., C. Hammer, E. Hwang, and
Z. Mao. 1994. Advances in Passive-Remote
and Extractive Fourier Transform Infrared
Systems. SP-89 Optical Sensing for
Environmental Monitoring, Air & Waste
Management Association, Pittsburgh, PA,
pp. 780-790.
Douard, M., J. Zentzius-Reitz, T. Lamp.
A. Ropertz, and K. Weber. 1997. Quality
Assurance Procedures and Measurements for
Open Path FTIR Spectroscopy. Proc. SPIE
3107:114-125.
Dowling, J.A. 1994. A Review of the Naval
Research Laboratory Program of Long-Path
Air Measurements Using Lasers and FT-IR.
SP-89 Optical Sensing for Environmental
Monitoring, Air & Waste Management
Association, Pittsburgh, PA, pp. 145-156.
Draves, J.A., J.P. LaCosse, D.M. Hull, and
R.L. Spellicy. 1992. A Comparison of Open
Path Fourier Transform Infrared Spectrometry
with Conventional Ambient Air Monitoring
Methods. SP-81 Optical Remote Sensing.
Applications to Environmental and Industrial
Safety Problems, Air & Waste Management
Association, Pittsburgh, PA, pp. 252-265.
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S.P. Levine, A.J. Gadgil, M.L.Fischer, and
W.W. Nazaroff. 1995. Measurement of
Tracer Gas Distributions Using an Open Path
Coupled with Computed Topography.
Proceedings of Specialty SPIE Conference in
McClean, Va. International Society for
Optical Engineering, Bellingham, WA.
Dubois, A.E. , J.W. Engle, P.L. McKane, and
S.H. Perry. 1996. Open Path FTIR Quality
Assurance Data: Demonstration of
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AWMA Specialty Conference in San
Francisco. Air & Waste Management
Association, Pittsburgh, PA.
Edney, E.O., J.W. Spence, and P.L. Hanst.
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Industrial Zone Using Remote Sensors.
Proceedings of SPIE/AWMA Specialty
Conference in San Francisco. Air & Waste
Management Association, Pittsburgh, PA.
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Eisenmann, T., H. Mosebach, H. Bittner,
M. Resch, R. Haus, and K. Schafer. 1993.
Selected Applications of Remote Sensing
Measurements with the Double Pendulum
Interferometer in Germany with Special
Consideration of Quality Assurance Aspects.
Paper 93-FA-165.01, Proceedings of the
86th Annual Meeting and Exhibition, Air &
Waste Management Association, Pittsburgh,
PA.
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1994. Remote Sensing FTIR-System for
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1996. Uncertainity Estimate for Open Path
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SP-89 Optical Sensing for Environmental
Monitoring, Air & Waste Management
Association, Pittsburgh, PA, pp. 281-292.
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Temperature Reference Spectra. SP-89
Optical Sensing for Environmental
Monitoring, Air & Waste Management
Association, Pittsburgh, PA, pp. 266-280.
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R.C. Noonan. 1976. Atmospheric Oxidation
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Techno/. 10(1):58-67.
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for Environmental Monitoring, Air & Waste
Management Association, Pittsburgh, PA, pp.
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Symposium on the Measurement of Toxic
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Quantitative Analysis of Gases. SP-81
Optical Remote Sensing. Applications to
Environmental and Industrial Safety
Problems, Air & Waste Management
Association, Pittsburgh, PA, pp. 490-510.
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Hanst, P.L., and B.W. Gay, Jr. 1977.
Photochemical Reactions Among
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