EPA-600/2-77-154
August 1977
f*"
Environmental Protection Technology Series
OF GASEOUS POLLUTANTS
LIBEA3Y
U. S. EWROIiltWAl PROTECTION
N. J. oaai?
U.S. Environmental Protection Agency
Research Triangle Park, North 27711
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U S Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields
The nine series are:
1 Environmental Health Effects Research
2 Environmental Protection Technology
3 Ecological Research
4 Environmental Monitoring
5 Socioeconomic Environmental Studies
6 Scientific and Technical Assessment Reports (STAR)
7 Interagency Energy-Environment Research and Development
8 ' Special" Reports
9 Miscellaneous Reports
This report has been assigned to the ECOLOGICAL RESEARCH series This series
describes research on the effects of pollution on humans, plant and animal spe-
cies, and materials Problems are assessed for their long- and short-term influ-
ences Investigations include formation, transport, and pathway studies to deter-
mine the fate of pollutants and their effects This work provides the technical basis
for setting standards to minimize undesirable changes in living organisms in the
aquatic, terrestrial, and atmospheric environments
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/2-77-154
August 1977
APPLICATION OF A FABRY-PEROT INTERFEROMETRY
TO REMOTE SENSING OF POLLUTANTS GASEOUS
by
Wm. Hayden Smith and Robert A. King
Princeton University Observatory
Princeton, New Jersey 08540
Contract No. 68-02-0327
Grant No. 800805
Project Officer
William F. Herget
Emissions Measurement and Characterization Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27707
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OR RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
LIB
:>RARY
u. s. LNVIKL;.,..'.. , ^
N. J. (W817
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DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Agency, and approved for publica-
tion. Approval does not signify that the contents necessarily reflect the
views and policies of the U.S. Environmental Protection Agency, nor does
mention of trade names or commercial products constitute endorsement or
recommendation for use.
n
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ABSTRACT
A method for the remote sensing of molecular species via the rotation-
al Raman effect was developed. The method uses the properties of a scann-
ing Fabry-Perot interferometer to multiplex the spectra in a manner speci-
fic for a given species. Furthermore, the method allows the "in principle"
U
sensitivity of remote pollutants to be increased by as much as 10 over the
vibrational Raman effect. To achieve this goal, a scheme was developed for
the rejection of the Raman spectra of the abundant background gases, Np and
0 . This was accomplished efficiently and with little loss of the Raman
scattered light from the pollutant species. Laboratory measurements were
conducted to demonstrate the method for a few specific cases; results
were encouraging. In addition to the light rejection scheme actually
used, a radically new technique utilizing the polarization properties
of the Raman scattered light was also developed.
This report is submitted in fulfillment of Grant Number R-8oo805
and Contract Number 68-02-0327 by Princeton University under the sponsor-
ship of the Environmental Protection Agency. Laboratory work was completed
as of March 15, 1975.
Ill
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CONTENTS
Abstract iii
Figures vi
Tables viii
1. Introduction 1
2. The Fabry-Perot Interferometer 8
3. Experimental Configurations 21
J+. Multiplexing Rotational Raman , ... 43
5. Fabry-Per">t Interferometers in Reflection 81
6. Polarization Rejection Filter 115
Appendices
A. Basic Equations 127
B. Component Specifications 132
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FIGURES
Number Page
2.1 Fabry-Perot Interferometer, Ray Tracing. '
2o2 The Airy Function ^ '
1 ?
2.3 Single Passed Fabry-Perot Interferometer I0
2.4 Scan of the 10 Micron PZT Stacks ^
2.5 Linearity of the High Voltage Amplifier "
3.1 Overview of the Apparatus
3.2 Electronics 23
71
3.3 Photomultiplier Tube Dark Count Rate
29
3-4 Laser Cavity Extension
3.5 Laser Line Profiles 33
3.6 The Gas Cell 34
3.7 Gas Fill System 36
OQ
3.8 Vacuum Distillation System
40
3-9 'Plate Spacing Measurements
49
4.1 Rotational Raman Stick Spectra
U.2 Fabry-Perot Resonances
cc
4.3 Plot of Normalized Stokes-antiStokes Fringe Separation
Versus the Relative Order of the Interferometer
65
U.U Carbon Dioxide UB Resonance
U.5 Double Passed Fabry-Perot Interferometer
CO
k.6 Nitric Oxide 2B Resonance
k.7 Nitric Oxide 8B/3 Resonance
k.8 Methane at the hE Resonance
U.9 Methane off the UB Resonance
VI
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Number Page
QO
5.1 Mixtures of CO and Nitrogen
5.2 The Rejection Apparatus 87
5-3 Fraction of Reflected Light vs. Degree of Alignment 88
5.^ Fraction of Reflected Light vs. Etalon Surface Figure 91
vs. Incident Line Width
5.5 Calibration Scan of FPI in Reflection 94
5.6a Rejection of CO Rayleigh Light 97
b Rejection of CO Rayleigh Light 98
c Rejection of CO Rayleigh Light 98
5.?a Rejection of N? Rayleigh Light 100
b Rejection of N_ Rayleigh Light
5.8 Rejection of N Raman 101
5.9a CO Calibration 107
b Np Raman with and without Rejection
c 1.5% 0 in Np with N? Raman Rejection
5.10a 0 Calibration 1°9
b I.h% 00 in N0
c ?60 Torr Np
5.11 Og Calibration ]11
a l.U% 0 in Xenon, no Rayleigh Rejection
b 1.^% 0 in Xenon, Rayleigh Rejected
6.1 Elements of the Polarization Rejection Filter 116
6.2 Configurations of the Birefringent Filter 126
VII
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TABLES
Number Page
3.1 Laser Lines and Line Strengths 3]
3.2 Ketling and Boiling Points of the Oxides of Nitrogen 35
4.1 Molecular Data 45
U.2 Resonance Displacements due to Distortion Effects 53
U.3 Fractional Orders for C0? SB Plate Spacing Measurement 58
1*.U Fractional Orders for C0? ^B Plate Spacing Measurement 62
5.1 Coincidences Between Np Raman Lines and C00 82
5.2 Fabry-Perot Comb
5-3 Summary of the Rejection Measurements -112
6.1 Polarization Rejection Filter Attenuation of N Raman 122
6.2 Polarization Filter Passing Oxyger. Raman -123
6.3 Comparison of Fabry-Ferot and Polarization Rejection Kechfr.isms 124
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SECTION 1
INTRODUCTION
1.1 Early Interferometry
In approaching spectroscopic instrumentation, the historical choice
and conconEitar.t agony has "been that of the trade-off "between resolution
and throughput. Traditionally this has "been viewed from the single line
stance with subsequent thought "being directed to criteria for the resolu-
tion of quasi-monochromatic lines and to single line or band transmission
functions. Indeed, simultaneous transmission of several lines served
only to confuse the interpretation of the spectrum and was considered a
handicap rather than a. useful effect. This parochial view was quite
evident with regards the Fabry-Perot interferometer whose multiple order
transmission function necessitated the use of 'order sorters' or blocking
filters to remove radiation falling to either side of the order of
interest, with the problem becoming especially acute at higher resolving
powers and with grating spectrometers often used as prefilters because
of their tunability. In their paper of 1897, Fabry and Perot value
their new instrument as useful in the determination of the spacing between
tvo parallel surfaces, giving only brief mention to its value as a
spectroscopic tool.
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Additional, and perhaps more severe, problems plagued early Fabry-
Ferot interferometers. The high absorption silver coatings and poor
surface figure of the etalons limited the transmission, resolution, and
contrast of the instrument, vhile mechanical and thermal instabilities
limited the patience of the experimenter. Grating spectrometers, al-
though lacking the throughput of the Fabry-Perot, were generally reliable
and displaced interferometric methods.
1.2 Current Interferometry
Advances in optics, including low-loss dielectric coatings, etalons
with surface figures to X/200 over a two-inch aperture, piezoelectric
translators, and electronic temperature controllers eliminated many of
the difficulties associated with earlier Fabry-Perct interferometers.
Accompanying these technical advances were new conceptual techniques.
In the infrared the Michelson interferometer was multiplexed as a Fourier
transform spectrometer giving improved signal-to-noise ratios, while
2
more recently, Barrett and Meyers demonstrated in the laboratory that
the Fabry-Perot interferometer could multiplex rotational Raman lines
from linear molecules without the disadvantage of having to perform an
inverse Fourier transform to extract the useful data in this case, the
rotational constants of the molecule under study.
Used in the multiplexed mode, the Fabry-Perot interferometer passes
simultaneously several spectral lines in which the observer is interested
without transmitting the unwanted radiation which falls between the lines.
-------
With its already high throughput and entendue enhanced by mutiplexing,
the Fabry-Perot interferometer becomes a sensitive detector for a
restricted class of applications where the spectra involved are periodic
or near periodic in wavenumber. One of these, proposed recently by
Smith, is a method for the remote detection of gaseous atmospheric
pollutants using laser excited backscattered rotational Raman light
from the molecule of interest.
1-3 Multiplexed Fabry-Perot Interferometers
The following work will show, using mixtures of carbon dioxide
in air, that the single passed Fabry-Perot interferometer is generally
incapable of discriminating the minority component scattering from a
gas mixture in those concentrations typical for atmospheric pollutants
because of coincidences between the comb of the Fabry-Perot inter-
ferometer which has been set for a particular pollutant molecule, and
certain rotational Raman lines of N? or another high concentration back-
ground gas that niay be present. The degree of contamination will go
roughly proportional to
1-R
1+R
vhere R is the reflectivity of the Fabry-Perot etalons and cannot be
made arbitrarily small by increasing the reflectivity towards unity,
because the accompanying loss of signal would require prohibitively
long integration times.
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Section IV will examine the complex interferogram produced by
the atmospheric pollutant NO vhen multiplexed through the Fabry-Perot
interferometer and demonstrate that the normal 1*B and 2B resonances are
not the optimum ones to be utilized when searching for the rotational
Raman scattering from NO because of the blurring of the features of
the interferogram by contamination from other rotational Raman lines
of the NO molecule not in resonance with the comb of the Fabry-Perot
interferometer. It will be shown that instead, an 8B/3 resonance should
be used to sharpen the Raman peaks produced in the transmitted inter-
ferogram, thus forming a feature which is more visible than those at
the 2B resonance due to higher photon count rates and a clearly defined
position. This chapter will also examine how the rotational constants
of the molecule under observation affect the width of the transmitted
interferogram resonance and how data on NO implies that resonances
with B values differing by 0.05 cm (with B average 1.7 cm ) and
contaminated by background scattering from AJ = ±2 u ,? and TT ,^
transitions can be distinguished if the approximate form of the
resonance is known beforehand. Nitric oxide is a difficult case
because of its doublet ground state. Other molecules-not suffering
the background resulting from the effects of this split state have
observable hot bands at temperatures sufficiently high to give them
1^
significant populations.
The results of this work give impetus to the study of multiplexed
Fabry-Perot interferometers in the remote sampling of atmospheric
pollutants, but the laboratory study of a two component gas system
does not simulate field conditions closely enough to yet define
-------
whether or not the remote sampling of NO (or another pollutant) is
possible by this method. Certainly, the severe background contamination
from Np and 0_ rotational Raman scattering and from Rayleigh scattering
can be removed, and presumably those molecules with concentrations
on the order of the pollutant to be detected will be attenuated by the
mismatch of the periodicities of their spectra with the comb of the
Fabry-Perot interferometer. How other background sources will affect
the level of detection is not clear and remains to be demonstrated for
particular situations in the field. A view of remote sampling techniques
not including the multiplexed Fabry-Perot interferometer is given in
the work by Kildal.5
In addition to use in the problem of pollution detection, the
rejection techniques should prove useful in the analysis of spectra
having - close lying B values (such as hot bands) and perhaps
also in flame spectra where there are contaminating influences. Chapter
6 presents a different approach to the rejection of periodic spectra and
background Raman scattering with the use of a crystal polarization filter.
This may prove a more efficient and easily handled field technique than
that of the rejection Fabry-Perot interferometer.
Apart from the remote sensing problem, a search was made using
the multiplexed Fabry-Perot interferometer and the rejection intefero-
meter for the pure rotational Raman scattering from methane. Although
this process is forbidden to first order because of symmetry, the
zero point energy of the vibrational modes distorts this symmetry
giving rise to a small pure rotational Raman scattering cross-section.
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The Raman scattering was not observed, and the results show that the
differential cross-section for Raman scattering with the scattered
and incident polarisations parallel must be a factor k x 10 down from
methane Rayleigh scattering for the same geometry, i.e.,
D (e = 0) < k x 10 a _ (6=0)
Ram Ray
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References
1. C. Fabry and A. Perot, Ann. Chi;n. et Phys. 12, 459 (1897)
2. J. J. Barrett and S. A. Meyers, J.O.S.A. 6l, 1246 (1971).
3. W. H. Smith, Opto-electronics 4, l6l (1972).
4. J. J. Barrett and A. B. Harvey, J.O.S.A. 6.5, 392 (1-975).
5. H. Kildal and R. L. Byer, Proc. IEEE 5£, 1644 (1971).
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SECTION 2
THE FABRY-PEROT INTERFEROMETER
^l An Introduction to the Fabry-Perot
In 1897, Fabry and Perot developed an interferometer consisting of
two plane parallel partially silvered mirrors with separation t. Monochromatic
light incident upon their instrument is multiply reflected (figure 2.1) by
the coatings and in interfering with itself gives rise to a transmitted inten-
sity dependent upon the plate spacing, the reflectivity of the plates, and the
2
incident wave-vector's angle to the mirror's normal. Born and Wolfe show
this to be the Airy Function A (x), v/here
IT2
A(x) = g-£ (2.1)
1+R -2R cos O
cos 0
0 = the angle of Incidence
k = incident wavenumber
p. = index of refraction of the medium between the etalons
R = reflection coefficient
T = transmission coefficient
L = absorption coefficient = 1-R-T
= incident light intensity
-------
This function is periodic with transmission maxima occuring when the phase
satisfies
4> =r inrukt cos 0 = 27m (2.2)
rind transmission minima vhen
$ = 470.1k t cos 0.= 27r(n+l/2) (2.3)
vh?re n is an integer giving the order of the interferometer.
If the phase be changed by altering the plate separation, a series of
fringes will be generated (figure 2.2) whose period is one half of the in-
cident wavelength. Similarily for a fixed plate spacing, non-collimated
light transmitted by the Fabry-Perot will form a series of circular fringes
vhen brought into focus with a lens (figure 2.1) as the phase has an angular
o.^p^naence through cos 8 and the angle of incidence. Fringes represent
successive orders of the interferometer, akin to orders of a spectrometer.
It follows that light collimated within the spectral bandwidth of the inter-
ferometer gives a uniform illumination to the plates.
The Airy function description of the Fabry-Perot interferometer was de-
Teloped assuming the ideal situation of mirrors with infinite extent, no
absorption losses, perfect surface figure, and in parallel alignment. Fabry
and Porot had some difficulty in approaching these ideals, but recent techni-
ccl advances noted in the introduction have radically improved this situation.
Deviations from predictions based on a simplified use of the Airy equation
remain critical in certain applications which will be discussed in later
chapters as the situation warrants.
-------
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2.2 Bandpass, Transmission, and Lineshapes
As noted in the introduction, a compromise must be made between resolu-
tion and throughput. A brief discussion is therefore given as to how para-
i:vtors relating to the above problem were determined for the interferometer
experiments.
Figure 2.3 illustrates one common experimental configuration for the
Fr.bry-Perot, with a radiation source of small but finite extent, an input
collimating lens LI, the Fabry-Perot, an out put lens L2, and an output pin-
hole which in this example is the limiting aperture of the system. If the
pinhole subtends the angle 2cc frOm the lens L2, then the wavenumber equiva-
lent bandpass of this aperture is
7 = 1/2 ka2cm"1
P
K = l/\ cm"1 (2.U)
The transmission through the system of an arbitrary spectrum J (k) will be the
convolution of this spectrum with the Airy function A (k) for the interfero-
meter and the rectangular aperture profile given above.
T = A*P*J (2-5)
The line-shape of A*P is close to Lorentzian because:
(a) the Airy function can be considered as the convolution of a
Dirac comb with a Lorentzian profile and thus for finesses
commonly used an individual order is nearly Lorentzian.
(b) the high count rates allowed a small pinhole with correspond-
ingly small half width in comparison to that of the Fabry-
Perot. (Typically a pinhole of radius 150 microns was used
with a lens of focal length 15 cm. Applying equation .?.';
12
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7'a = Airy half width
7 = Pinhole half width
7 . = Spectrum half width
J
The resultant half width of A*P is
The spectrum J (k) consists of rotational Raman lines whose shapes is
dominated by the line shape of the laser used to provide the scattering photon
flux. The laser profile was far from the Gaussian profile expected and had
a width twice that of the norm for this type of Argon ion laser. Consequently
the spectrum J (k) did not have a simple mathematical form. Chabbal has
calculated the half widths produced by the convolution of several functions
including Gaussians with Lorentzians so that a crude estimate of the expected
line width could be made in spite of the pathological shape of the laser line.
Experimental measurements of the widths of J and A*P will be given in the
following chapters.
lj
Hirschberg and Wouters show that the maximum transmission for a single
line incident upon the Fabry-Perot can be written as
(f = fineGse) (2.7)
where £ is an overlap factor between .3 and .5 depending upon the exact form
of t':.s co:A'olrtion integrol, and j is the line width generated by J*A.
14
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2.3 The Practical Fabry-Perot Intorf."romotor
Critical components of the Burleigh Fabry-Porot interferometer used in
these experiments were constructed of invar to minimize thermal effects. These
components included the etalon mounting rings as well as the spacers and
differential screw assemblies. In addition, components were paired one
against the other so that the net motion of the etalon spacing was different-
ial as the temperature varied.
Fine adjustment of the etalons was provided by differential screws having
a resolution of 10 inches per revolution, and final alignment was performed
o
using piezoelectric translators. The PZT's (three spaced at intervals of 120
about the etalons) could be adjusted independently to align the mirrors and
then with a common control moved simultaneously to scan the Fabry-Perot.
The PZT's were provided with slope trims to compensate for varying rates of
expansion with applied voltage. The maximum range of a PZT scan was 20-25
o
orders of 51^5 A light for the 10 micron stacks and approximately 3 orders for
the 1 micron stacks.
A graph of applied voltage versus PZT expansion is shown in figure 2.b
for the 10 micron elements, with fiducial markings being provided by the 51^5
o
A Argon laser line. Although highly nonlinear when viewed over the entire
range, a scan was reproducible provided that 2-3 minutes were allowed at the
beginning of each expansion for the elements to relax after the rapid drop
back from full extension. In addition, since fiducial markings were provided
by the laser line, it was necessary to be concerned with nolinearity only
within the range of a single order. The apparent change in spacing between
successive orders near the center of the scan did not amount to more than '«\',.
15
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To see what fraction of the nonlinearity originated in the high voltage
amplifier that drove the PZT's, a plot of the voltage applied to the PZT
elements against the input ramp voltage to the amplifier was made. The
graph is given in figure 2.5. Coefficients a and a determined from a
least squares fit to a straight line are
a = U379.^2 ± 5.9 Volts
a = 573.91 - 1.2 Volts
where the voltage to the PZT's = (afl + a.. n)/10, and n is a number proportion-
al to the input amplifier voltage. (The errors reflect the 95% confidence
level). The maximum deviation from linear is less than 0.2% and the conclus-
ion is that the nonlinearity in the scan of figure 2.1+ is due to the PZT
elements themselves.
The ceramic material from which the PZT elements were fabricated was
additionally the source of most of the thermal drift in the interferometer.
For work involving short sampling intervals, the temperature scanning was
quite negligible with the electronics stepping through an order in 2-5 minutes
while the Fabry-Perot v:ould typically drift one order in 10-15 hours. For
very long scans of 200-300 orders, fiducial markings provided by the R.%yleigh
scattered laser light from the gas sample proved a reliable method to account
for absolute plate spacings. At any particular time, it was possible to give
a
the absolute etalon separation to within 100 A and better, depending upon the
the finesse and resolution used, and in spite of temperature drifts and non-
linear effects.
?»^ Fabry-Fcrot Etnlons and Coatings
The etalons used were 2 inches in diameter with surface figures of X/'rCO
in the visible. The surfaces facing away from the Fabry-Perot cavity were
18
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wedded by 30 minutes of arc and antireflection coated to eliminate tVie effects
of first surface contribution to scattered light into the photomultiplier
tube. 'Hie etalons were mounted into invar rings by the manufacturer which
were then set into the interferometer proper using nylon screws. The:
counting procedure used vas such as to not degrade the surface figure of the
0
etalons whose r.m.s. deviation (for a matched pair) was on the order of 25 A.
The grinding process for the etalons resulted in a spherical defect (again
o
less than 25 A) which could be seen by illuminating the Fabry-Perot with
collimated light. Any strains introduced in mounting the etalons were visible
as a breakdown of this symmetry in the intensity of the transmitted light.
Multilayer dielectric coatings were used on the etalons with specificat-
ions given in the materials appendix. These coatings are discussed in detail
in reference 2.5 and will not be mentioned further other than to note that
thejr are low loss (absorption coefficient^-0.05$) with low scatter and good
surface figure. Soft coatings were used and care was required because they
are hygroscopic to a slight degree and also sensitive to abrasion. No
substantial deterioration was noted; however, over the period of a year.
19
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References
1. C. Fabry and A. Perot, Ann. Chira. et Phys. 12, 459 (1897).
2. M. Born and E. Wolf, Principles of Optics (Pergamon Press,
New York, 1959), p. 323-329-
3. R. Chabbal, Revue d'Optique 37, 49,336,501,608 (1958);
R. Chabbal, J. des Rech. du C.N.R.S. 2u, 138 (Paris, France,
1953) - ~~~
4. J. G. Hirschberg and A. Wouters, MIAPHOOP-68.10 (Dept. of
Physics, Univ. of Miami).
5. H. A. MacLeod, Thin Film Optical Filters (American-Elsevier
Pub. Co., Inc., New York,
20
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SECTION 3
THE EXPERIMENTAL CONFIGURATIONS
3.1 Introduction
A schematic view of a. single passed Fabry-Perot is given in figure 3.1.
A gas cell containing the mixture to be studied was placed at the intra-cavity
focus of an Argon ion laser operating with approximately UO watts of circulat-
o o
ing power in the 51^5 A or k&80 A line. An f/3 lens looking along the direction
of the incident laser polarization to minimize Rayleigh scattered light (rot-
tational Raman is completely depolarized with p = 3A) collected the
JKam
scattered radiation, collimated it, and directed it through the Fabry-Perot
interferometer. The light transmitted by the interferometer was focused by
an output lens onto a pinhole and from there to the photomultiplier tube.
Photon counting techniques were used with maximum counting rates for Raman light
being on the order of 100 kHz.
Details of the apparatus will now be discussed along with the gas purifi-
cation system and the plate spacing determination procedure. When applicable,
test data or calibration results will be presented.
3.2 Control Electronics
A drawing of the Fabry-Perot controller and data recording system is
shown in figure 3.2 along with the associated waveform that it generates to
drivo the FT.T elements. The control logic has the flexibility of variable
stop .Ure for the PL'T's (Av), data integration tiir.e (T ), and upper and lower
21
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limits V and V . to the voltage on the driving stacks. The output voltage
max
from the D/A in the controller was multiplied by a factor 100 with a high
voltage amplifier and was used to drive the FZT elements in common to scan
the interferometer.
Having stepped the Fabry- Perot with a voltage increment A v, the logic
would enable the gate from the FMT preamplifier to the digital counting
circuits where photon counting was performed. After a time T , the gate was
disabled, and the information from the scalar along with a number proportional
to the voltage on the PZT stacks wa,s written onto magnetic tape. The process was
repeated until the upper limit of the ramp was reached at which time the cycle
repeated or terminated depending upon the settings on the controller.
As well as writing onto magnetic tape, the controller could simultaneously
plot the data on a chart recorder with a digitally stepped x-axis, or could
display it on an oscilloscope. This latter function (with "C set to 0.01 sec.)
and the ramp set to scan over one free spectral range was useful for dynamic
alignment of the Fabry-Perot interferometer since the effects of altering the
various parameters of the system became visible in real time in terms of an
alteration in the finesse of the Fabry-Perot fringes being displayed. With
dynamic alignment, it was also possible to count fringes moving by on the
oscilloscope screen as the fine differential screws were adjusted by hand.
In this fashion, by piecing together a number of 10-20 order scans done by
the PZT elements with each successive scan beginning where the former finished
(the difference being set by turning the fine adjustment screws), it was
possible to scan over a few hundred orders without losing track of the
absolute plate separation.
24
-------
The pro-amplifier coble from the PMT was kept as short as possible to
minimize transmission problems with tlie low level PMT pulses. The pre-amp-
2
lifier hod a rectangular wave-form with a full width of ?50 nanoseconds, and
count rates being less than 200 kHz avoided any saturation problems.
3.3 The Piiotoip.ultip3.ier Tube
A Centronic bialkali photornultiplier tube was used because of its high
sensitivity and extremely low dark current. When count rate was plotted
versus PMT voltage for a vhite light source of constant illumination, a plateau
was reached in the neighborhood of 1.2 KV. This is the region of greatest
stability. Operation at lower voltage gave abnormally low count rates for
low incident light intensities in comparison to normally expected count rates
at higher light levels. This had the effect of making the Fabry-Perot fringes
appear to have a much higher contrast than would normally be expected. An
explanation is that the weaker pulses in the pulse height distribution from
the PMT were not being sufficiently amplified by the low gain of the tube to
reach the threshold set by the discriminator on the pre-amplifier. Lowering
the discriminator setting had the effect of sending the pre-amplifier into
oscillation, and consequently the tube and discriminator were not operated
in this low voltage region.
Plotting the PMT voltage as a function of the ratio £ , defined by
e = 0//IT
where
G = experimentally determined standard deviation for N
N «* the number of photons/sec, counted by the system for
a given FMT voltage.
yielded statistics approaching what would be considered normal fluxuat.ions at
25
-------
those voltngos (1.2 KV) corresponding to the plateau discussed in the above
paragraph. Hi (/.her or lower voltages give increasingly poor statistics.
Fluxuations or drift in the intensity of the source account for e not approach-
ing unity, with £ . being on the order of 1.1-1.2.
Figure 3-3 gives a plot of the number of dark counts per second (sample
time was 50 seconds) against discriminator setting on the pre-amplifier. At
settings greater than 2 (gain equal to ~ 3 x 10 ), there is an extremely slow
decrease in count rate with increased level of discrimination, and with the
FMT shut off, this rate drops to zero. It was unlikely that any of these
counts were generated in the PMT dynode string as cleaning in an ultrasonic
bath removed any residue which might have contributed to leakage current and
noise pulses. The cathode was held at ground to avoid envelope generated
noise in the anode grounded situation, and the tube was kept in its housing
at all times to prevent exposure to room light and the resulting higher dark
count rates. Characteristics of the tube can be found in the materials index.
The above considerations give the optimum operating voltage for the tube
as 1.1-1.2 kV with the discriminator set to two. The PMT dark count rate
under these circumstances was approximately 6 per second.
3.14. The Laser
An Argon ion laser was modified so as to run in the intra-cavity mode
(figure 3«^). To this end, the output coupling mirror was removed and re-
e
placed with a dielectric mirror Ml, of reflectivity 99.99^ at 14880 A and a
radius of curvature equal to 25 cm. A lens LI, of focal length 12 cm, was
placed between this mirror and the plasma tube such that its focal point fell
approximately at the center of curvature of the mirror Ml. Laser resonator
26
-------
t
q
ro
o
CO
o
<
\-
CO
CO
* K 2
\- O <
_j a: UJ
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o
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IO ^J- IO CM
(08S/SN010Hd ) 1NPI03
27
-------
theory ' gives that this configuration will be stable and that the diameter
of the beam at any point in the cavity can be found from:
T.S ' <3a>
(3.2)
l/2b = .U^/A (3_3)
where
R is the radius of curvature of mirror KL (25 cm)
R2 is twice the focal length of the lens (2x12 cm)
d is the separation between the lens-and the mirror (^37 cm)
WQ is the radius of the beam at its waist
W is the radius of the beam at a distance R from the waist.
The parameters given above for this experiment yield a beam waist of 130
microns and a beam diameter at the mirror Ml of .3 mm.
The circulating power in the cavity was estimated by using the fact that
with the 5$ output coupling mirror in place; the laser gave 2 watts of power
o o
at 51^5 A and at 1*880 A. This implies that power levels in the cavity will
be on the order of Uo watts, assuming that losses with the extended cavity do
not exceed 5$. The losses due to the lens are minimized by having it ground
from laser quality material (low loss, low scatter, nnd good surface figure)
and then having anti-reflection coatings with R less than .25% deposited on
the surfaces. In addition, a single element lens rather than n cemented
28
-------
o
o
."o
C.
C
o
'w
C
a
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c
o
'(/)
O)
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-------
achromat was used to avoid absorption in the bonding material with the change
in focus with different laser lines compensated for by an adjustment of the
Fabry-Perot input lens on an x-y translation stage. The cavity was so stable
as to lase over a wide range of positions for the lens LI.
The losses at the gas cell inserted into the cavity at the position of
the beam waist were minimized by using entrance ports of laser quality materi-
al set at Brewster's angle to the incident radiation. For small angular
variations about Brewster's angle, the reflection coefficient varies by less
o
than 0.1 percent (forA6~_3 ) and as a consequence, slight misalignments of
the cell were not critical. Because the windows were at Brewster's angle,
they did not have the effect of single-nvoding the laser.
The only other losses in the cavity were the end mirror with R =0.9999 as
stated previously, and scattering and absorption from dust and gas in the path
of the beam. When dust became a problem, the system could be enclosed in a
plexiglass cover.
It's not unreasonable to assume therefore that the losses in the cavity
were less than U-5% and circulating powers of 30-^0 watts likely.
The lens LI was adjustable along the length of the cavity so that its
focus could be made approximately coincident with the center of curvature of
the mirror, while the mirror itself was mounted in an orientation stage to
provide angular alignment. The cavity could be tuned by rotating either
mirror Ml or else the Littrow prism, and was stable at the wavelengths listed
in table 3.1 listed below.
30
-------
Table 3.1. LASER LINES AND LINE STRENGTHS
o
Wavelength (A) Relative Power Level5
51^5.319 ^.0
5017.160 0.5
U965oO?3 1.2
U879.860 3.2
U76U.862 l.O
1*579.3^6 0.3
The wavelengths were taken from sources 3.6 and 3«7 end the power levels
U
from the Spectra Physics handbook. As scattering has a v dependence and the
o
E'T is more sensitive in the blue, the U880 A line was used in preference
o
over the 51^5 A line.
The laser linewidth was measured using a Coherent Radiation spectrum
analyzer with the beam profile (in wave-numbers) shown in figure 3«5 and its
full width at half maximum being 0C25 cm Since the light used to perform
this measurement was scattered from an etalon inserted into the cavity at
Brewster's angle, line was not narrowed due to single-moding effects.
The broad line width of the laser used for these experiments caused
severe problems in some measurements. These will be discussed in later
chapters.
31
-------
3.5 The Gos Cell
The gas cell is diagrammed in figure 3.6. Brewster's angle windows
minimized light loss through reflection and were given a non-parallel
orientation relative to one another so that the net spatial displacement of
the beam in traversing the cell would be zero. The Wood's horn arrangement
effectively trapped back-scattered light by dissipating its energy in success-
ive reflections from the blackened interior. The baffling on the input and
output arms for the laser eliminated light scattered from the Brewster angle
windows on the gas cell and on the plasma tube, and also glow from the laser
cathode and plasma discharge that was not confined to the beam axis. The set
of baffles on the viewing window removed scattered and diffracted light from
the baffles on the arms. All windows were of laser quality so as not to distort
the wave-fronts, and in addition had low scratch and dig specifications to
minimize scattering. A final extension or baffle covered the distance from
the viewing port to the Fabry-Perot collecting lens to shield the system from
outside radiation.
The gas cell was filled through a Hoke valve with a Swagelok coupling that
mated either a 1/V diameter glass tube from the vacuum distillation system or
a 1/V' diameter piece of stainless steel tubing when samples were taken directly
from the gas bottle withoxit distillation. (The gas sample was in either case
pre-filtered with a millipore filter to remove particulate matter that might
contribute to Mie scattering). Figure 3.7 shows the gas fill system for the
case of direct filling from the bottle. Pressures were measured using a
Bourdon guage in which the gas is not exposed to face plates or other con-
taminating surfaces. The guage could be read to 0.5 Torr of pressure.
32
-------
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O
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if)
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it
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A1ISN31NI
33
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-------
When filling the cell, the entire system includin;1; the regulator on the
gas bottle was evacuated and filled with the sample. This was repen tor! two
or three times to flusr, out the apparatus before the final fill was done.
During t .is procedure, the valve or; the gas cell was opened and closed
several times to free any pockets of air that may have been trapped in the
mecnanism of the valve. T.'.is was particularly important wnen dealing witn
nitric oxide. Pressures in the cell were kept at a few Torr above atmosphere
so that gases on the outside could not be drawn in through a slow leak. (No
leaks could be found upon testing with the He leak detector. Out-gassing was
minimal).
3.6 Preparation of "itric Oxide
Beinr; highly reactive, NO will quickly getter oxygen from the air or
surface of the container in which it is being held to form an equilibrium
system with its other oxides including N?0, N0_, NpO. , a.id NO. The proper-
o
ties of these compounds are briefly outlined in table 3-2 below.
Table 3.2 MELTING AND BOILING POINTS OF THE OXIDES OF NITROGEN
Xame Symbol Melting Point Freezing Point Colour
Nitri
Nitrr
Diizer
1,'itro
c Oxide ICO
gen Dioxide N00
of :co2 N2ou
gen Trioxide Np^3
-151
21.
21.
3.
.1
0
15
o
15
o
5
C
c
c
c
-163
-11
-11
-102
O
.6
o
.3
o
.3
o
.6
c
c
c
c
pale blue
brown
brown
brown,
preen,
blue
Nitrous Oxide N00 -89.5 C -102.h C colourless
Because all of these compounds with the exception of "0 will freeze out
o
at temperatures below -102.6 C, it is possible to separate the nitric oxide
q
frc-s the rer.airJer of the oxides by standard vacuum distillation techniques.'
35
-------
JU
"o
w
r--
CO
£
O>
36
-------
o
To this end a solution of cyclohexane having a free?.ing point of -1?6 C was
prepared nnd was used to force the separation.
A schematic diagram of the vacuum distillation system ir, shown in figxire
3.8. The apparatus is initially evacuated up to the high pressure valve on the
gas bottle and then a sample of NO to be purified is passed in through the
millipore filter and the P^CL water vapour trap. The method used to isolate
a sample of NO is the standard one of transferring the sample back and forth
through a bath sufficiently cold to trap out the impurities but not the sample.
The NO is forced through the bath by the application of liquid nitrogen to the
traps on either side. Care was taken to remove non-condensables that would
hinder the movement of the sample back and forth under the action of the
liquid nitrogen and which also might be trapped in a matrix of the sample.
Two passes through the trap were sufficient to remove enough of the
unwanted oxides that their presence was not detectable. (NO's large absorp-
tion cross section at visible wavelengths would halt intra-cavity action or
become visible as an orange flourescence if it were present in the sample).
The purified sample was then passed into the gas cell through a Swage-lok
coupling between the system and the cell. The cell and vacuum apparatus had
previously been seasoned overnight with NO to prevent oxygen adsorbed on the
wall from reacting with NO in the cell after a sample had been purified and
isolated. The cell was sufficiently leak proof that the samples of NO could
be contained for three weeks with no apparent degradation and may have held
longer but for lack of patience with the experimenter.
3-7 Plate Spacing Measurements
Accurate plate spacing determinations (and hence free spectral ranges)
were made usinr, the method of fractional orders. In this procedure, a scan
37
-------
o>
ti
c
o
T3
E
O
03
00
CO
03
3
o>
38
-------
of a free spectral range was rnndn vising several different laser wavelengths
(section 3.3 gives tho precise wavelennths used) and the relative phase
shifts between them were then measured. See figure 3.9- From equation 2.2
we have
that 2k. t = n + e.^
where
k = the i wavelength
n = an integer, the order of the interferometer
and 0 <£. < 1 is the fractional amount that the spacing t is off from being
an exact order.
Inverting this, if one knows k. and measures C"., a series of spacings
it ) = (n+ e.) can be generated, each of which will have the required
n tz K . i
phase shift. These sets are then compared to find those values of t held
in common and this will be the required spacing. For this method to give a
unique answer, the plate spacing must be known to lie within a reasonably
small region of values. When four wavelengths from the Argon ion laser were
used, this range amounted to 280 orders or approximately 3 thousandths of an
inch. Consequently the etalons were set to within a few thousandths of the
expected value using feeler guages. This was not a difficult procedure.
The above calculations were computerized with account being taken of
the limited accuracy to which a phase shift could be measured. That is,
correspondences between plate spacing estimates given by different wavelengths
v;ere considered equal if they fell to within the accuracy set by the measure-
ment of a phase shift, typically - 5> of an order. In addition, the light
used to perform the measurements came from the same scattering volume as the
light used jn the actual experimental runs. Thus, any angular effects due to
39
-------
o<
in
2
to
O
v>
O
A
in
CD
05
CO
CD
L.
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CD
CD
Si"
M;
O
GO
CO
^r
«*;
in
Idd
UOJSSIIUSUDJJL
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tli-' coc. Q term in the phase were removed.
Phase shifts incurred at the* dielectric coatings on the mirrors do not
cause difficulties us these shifts are approximately the same for all
wavelengths and can be incorporated into the equations in such a fashion that
the true plate spacing is augmented by on amount A't (a constant depending upon
the phase shifts). But, this new spacing t + At is used in all calculations
and is measured in all experiments so that its effects are never noticed (at
least in the quantities measured here).
The accuracy to which the spacing can be measured is equal to the full
o
vidth of a fringe at half maximum and this amounted to approximately 5° A for
the wavelengths and finesses commonly used in these experiments.
41
-------
References
1. J. Born, Dept. of Astrophysical Sciences, Princeton Univ.
2. D. L. Mickey, P. Zucchino, and W. H. Smith, Rev. Sci. Inst.,
41, 276 (1970).
3. R.C.A. Photomultiplier Tube Manual, Technical Series PT-61
I1970;.
4. H. Kogelnik, The Bell System Tech. Journal, March (1965), p. 445,
5. H. Kogelnik and T. Li, Applied Optics 5., 1550 (1966).
6. Atomic Transition Probabilities Volume II, National Bureau
of Standards NSRDS-UBS 22 (1959j, W. L. Wiese, M. W. Smith,
and B. M. Miles.
7. Tables of Spectral Lines of Neutral and Ionized Atoms, Atomic
Spec. Lab. I. V. Kurchatov Institute of Atomic Energy (1968),
IFI/Plenum New York, A. R. Striganov and N. S. Sventitskii.
8. Matheson Gas Data Book, Fourth Edition.
9. Denny, Techniques and Methods in Organic and Organometallic
Chemistry (M. Deker, New York, 1969), P- 33.
10. M. Born and E. Wolf, Principles of Optics, (Pergamon Press,
New York, 1959), pp. 338-340.
42
-------
SECTION 14
MULTIPLEXING ROTATIONAL RAMAN
A brief discussion of the pure rotational Reman effect will be given,
leading to the multiplexing of molecular rotational Raman spectra through a
Fabry-Perot interferometer and to an estimate of the width of the transmitted
interfercgrams. The apparatus is first tested at the i(B and &B resonances of
carbon dioxide, the accuracy of the procedure determined, and then nitric
oxide, a more complex system and atmospheric pollutant, is studied to give an
indication of the resolving power of the technique. Finally, a search is
made for the pure rotational Raman spectrum of methane.
U.I The Rotational Raman Effect
Raman scattering is the inelastic scattering of light from a quantum
mechanical system with the energy change in the light reflecting the energy
transitions in the scatterer. Because the cross-section for the rotational
Raman process depends upon the system having a time dependent polarizability,
Raman studies give information about systems unable to radiate by normal dipole
transitions.
In the case of rotational Raman, the energy levels of the system corres-
pond to the rotational energy levels of a molecule and for a simple diatomic
molecule are given by :
ET = BJ(J+1) - DJ2 (J+l)2 (H.I)
«J
J = 0,1,293i
43
-------
where
J = the rotational quantum number
B = h/8 TrClQ, the rotational constant for the ground state level
I = the moment of inertia
D = the centrifugual distortion constant.
At room temperature with vibrational energies on the order of 2500 cm , only
the ground state will have a significant population.
3
The selection rules for rotational Raman in the case of a singlet ground
state are AJ = 0, ±2 yielding a rotational Raman spectrum that consists of
elastic scattering (AJ = 0) forming one component of Rayleigh scattering, and
two side bands Stokes (AJ = 2) and antf-Stokes (AJ = -2). The displacements of
the Raman lines from the exciting line will be:
|aE| = (4B-6D) CJ+3/2) - 8D(J+3/2}3 (4.2)
J = 0,1,2,...
Values of the molecular constants B and D for gases used in the experiments
are given in table 4.1 below, along with cross-sections and depolarization
ratios when available or appropriate. For comparison, the ^ Raman Q branch
-1 -31 2
at 2331 cm , a vibrational mode, has a cross-section of 5.4x10 cm '
The intensity of the Rayleigh light viewed along a given direction and having
a polarization vector making an angle e to the incident polarization
12
vector will be
44
-------
U
01
re
>5
d
cn
Q.
!H
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-P
CQ
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H oj OJ in vo * *-
co co I-H in in OJ OJ
^ H OJ rH ^f OJ OJ
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CO OJ VO
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t^- .=* H
H
cc
H
S
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CM
0)
in
co
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O H
m
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0
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t-*
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|
CQ
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d
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45
-------
IRay(0) = IRay(o) [p + 0-p)cos2e].
(4.3)
A similar expression can be written for rotational Raman scattering with
p = 3/4. That is, completely depolarized.
W0) = W0) [3/4+l/4cos2e]. (4.4)
The total intensity I* ($) scattered at an angle $ to the incident polarization
vector is
I* (*) = I Co) [2p + (l-p)sin2*]. (4.5)
with the appropriate p and I (o) being substituted for Rayleigh or Raman
scattering. The ratio 8 of Raman to Rayleigh scattering is maximized for the
situation illustrated below where the scattering is observed in a direction
parallel to the incident polarization.
incoming flux
direction of incident polarization
scattering into solid
angle omega about the
z axis
46
-------
For a small viewing angle ft, this may be approximated by
aRarr/° [1/4 0+3*] (4.6)
~
w57
Since n must be kept large enough to obtain reasonable photon counting rates,
O
g cannot be optimized to qRam . In practice, with an f/3 collecting
4°Rayp Ray
lens,e was about unity, and Raman count rates were up to 100 kHz.
The intensity distribution of both the Stokes and anti-Stokes scattering as
a function of energy for rotational Raman scattering is primarily Boltzman
with additional factors from the matrix elements as well as nuclear spin
statistics influencing these intensities. Placzek and Teller have calcul-
ated in detail the line strengths and these are given in appendix A along with
the line strengths for the case of a degenerate ground state. As with Rayleigh
14
scattering there is an v dependence on the scattered frequency.
The selection rules for NO are modified because it has a doublet ground
state. Equation 4.2 becomes
AJ = 0, ±2
with |AE| = (4B-6D) (J+Omin+ 3/2) - 8D(J+Jmin+ 3/2)3 (4.7)
for |AJ| =2
and |AE| = 2B(J+J . + 1) - 4D(J+J . + I)3 (4.8)
mm mm
47
-------
for
|AJ| = 1
where
J . = 1/2 for the IT 1/2 state of NO
mm
J . =3/2 for the -n 3/2 state of NO.
mm
Figure 4.1 gives the pure rotational Raman stick spectra of two imaginary
molecules with the same B value so that comparisons of the different expected
Raman spectra may be made. Part a_ shows line separations for a non-degen-
erate ground state (say C02 negelecting nuclear statistics), the first line
falling a distance 6B from the Rayleigh line with successive lines separated
by 4B.
Parts b^ and c_, show the structure for the AJ = 1 and AJ = 2 transitions
of a molecule with a doublet ground state (NO). Only the spectra for the
state with J . = 3/2 are shown, but there will also be another with Jmin = 1/2
and a slightly different B value. Again the important point to note is the
separation of the first line in the series from the Rayleigh line as compared
with the separations between successive lines of the Raman spectra itself.
This fact will make it possible to pass the Raman spectra for certain Raman
states through the Fabry-Perot while rejecting the Rayleigh line.
7.2 The Multiplexed Fabry-Perot Interferometer (Spin Zero Ground State)
For a rigid rotor (D = 0), the interval between rotational Raman
lines, 4B, is a constant in wavenumber. Since the Fabry-Perot can be set to
arbitrary values by altering the plate spacing, it is possible to match the
rotational spectrum to the Fabry-Perot bandpass in such a fashion that all the
Raman light is transmitted through the Fabry-Perot, but the Rayleigh line is
not.
48
-------
8
8
1*
">»
5 8
CD
^r
o
Jtf
0 '
W
ro
CM §
0 S
o g
CM g
ro
it
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O CM
, c
ol .E ii
E -D
^ <
CM
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-01 14
^ <
o, "it,1
49
-------
This is shown in Figure 4.2^, with sufficient conditions to be satisfied
being:
free spectral range = 1 = 4B (4.9)
2t
8B
and the Raman spectra be offset from the Rayleigh line by an amount not an
13
integer multiple of 4B. This was first observed by Barrett and Meyers.
It is clear that other free spectral ranges will pass many of the Raman
lines and not the Rayleigh. However, the above is the only one to pass all
of the Raman and exclude the Rayleigh. Other resonances are given by:
t = _S_ (4.10)
8B
where ^ is a rational number. Two such resonances are shown in figure 4.2t^,c_.
As the Fabry-Perot is scanned, it is possible to imagine that the markings
representing the Fabry-Perot fringes in figure 4.2 have been drawn on a strip
of rubber that is being stretched so, not only is the free spectral range
slowly increasing, but fringes are also moving past the lines of the spectrum.
If a plot is made of plate spacing against intensity of light transmitted by
the Fabry-Perot, the results will be figures 4.2a/,b/,£'. The intensity of
the Raman light between the Rayleigh fringes will decrease slowly in ampli-
tude as the free spectral range moves away from resonance because the period-
icities of the Raman and Fabry-Perot combs no longer match precisely.
50
-------
v>
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o
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O>
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0
.
H
T3
E
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c
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C
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ex
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5B
0
nj
O
8
to
0>
J£
O
*-
to
u
.*:
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E
o
o
H
Q.
U_
CO
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-------
In practice a number of additional factors must be taken into account.
Finite widths of both the Raman lines and Fabry-Perot fringes cause the
pattern to smear out and become smoother than that generated by the stick
spectra of figure 4.1. In addition, real molecules have D values differing
from zero and although on the order of 10" -10" B, they have the effect of
broadening the resonance and moving it's position towards smaller free spectral
1 3
ranges (fsr). This shift was estimated by Barrett and Meyers for N20 by
arguing that the portion of the spectrum contributing most strongly to the
transmitted pattern is near the peak of the Boltzman distribution. The dis-
tribution is:
,(2J+l)e-BJ(J+1)hc/kT
with the peak at
Bhc
The line positions are given by equation 4.2 and so the
fsr at J = Jmax is
Ejmax+1 -EJ=4B-8D(3J2+12J+13). (4.11)
The correction to the B value being
52
-------
Typical values at room temperature for a 4B fsr are given in table 4.2 below.
Table 4.2. RESONANCE DISPLACEMENTS DUE TO DISTORTION EFFECTS
Gas Blcm"1) Dx106(cm"1)
AB(cm
change in
plate spacing
C02
°2
N2
NO r3/2
NO Trl/2
1
1
1
1
.39027
.437682
. 98950
.720178
.671854
4.
5.
10.
.
135
85
48
24
34
16
8
7
7
7
.4
.3
.0
.6
.7
2
3.
2
5.
1.
.7x10
09x10
.7x10
68x10
92x10
-4
-3
-3
-3
-4
^8.9
^7.5
<3.4
^9.6
^3.4
orders
orders
orders
orders
orders
Because the position of the Boltzman peak is temperature dependent, it should
be possible in principle to measure the fsr at which a resonance occurs for
two different temperatures of the sample and from this calculate D. In
practice, line broadening, statistics, and impurity scattering make the
absolute shift of the peak difficult to measure for temperature changes less
than several hundred degrees.
A measure of how the rotational constant B of the molecule affects the
width of the resonance (the number of orders across the transmitted interfer-
orgram at half maximum) is important in that distinguishing resonances from
simultaneous scattering from two different B value states will be more diffi-
cult if their respective resonances are so broad as to overlap. An estimate
can be made as follows.
The J value which the Boltzman distribution falls to some chosen fraction
-1 /2
of its peak will go roughly as B ' and correspondingly, the number J value
across the Stokes-anti-Stokes distribution will be approximately proportional
53
-------
to B'1/2. For the intensity of the transmitted interferogram to fall to half
of its peak value, the FPI (Fabry-Peort interferometer) lines that correspond
to the J values at the 'edges' of the Stokes-anti-Stokes distribution at
resonance, must move off their positions by some amount e, and we may write
e <*Aa x {# of J values across the distribution) (4.13)
where Ao is the change in fsr that moves one to the half peak intensity position
of the transmitted interferogram. But, e must go as the line width (proportion-
al to B since the finesse is constant and fsr = 4B)
B - AO B"1/2
and using
At _ A£ _ _AB_ (4.14)
t " " a B
find
At - B~1/2 (4.15)
That is, the width of the transmitted interferogram will go approximately
as 1/JE~ (assuming FPI width » laser line width).
If the lines are broadened beyond the Airy width, the transmitted
interferogram will be even wider and will change more rapidly than B /
for small Airy widths compared to the line widths. Half widths or resonances
obtained by computer calculations neglecting the effects of line width, may be
in error, but the general structure can be found without time consuming
integrations over these line widths.
54
-------
Very recent computer simulations in the literature suggest that two close]y
Ik
lying resonances may be resolved, but data presented in this thesis on NO
with four effective scattering states demonstrates that this spectrum is
difficult to interpret without prior knowledge of the approximate form of the
transmitted interferogram. The hot bands of certain molecules may be observ-
able if the temperature is sufficiently high as to populate them well with
respect to the ground state and if their resonances are narrow enough so as
not to overlap in a destructive fashion.
The procedure to follow when measuring an unknown B value is to set up the
apparatus as in figure 3.1, and scan the Fabry-Perot until the peak of the
resonance is found. The plate spacing can then be measured as described in
section 3.7 and the effective B value calculated from equation U.9. In general,
the effects of distortion are not precisely known, and the error in the measure-
ment of the peak position can be on the order of the values given in table U.2
above. Since these errors are so large, it is not necessary to account for the
change with pressure of the index of refraction of air between the FFI etalons.
This creates an error of approximately .1 orders for a change of 50 Torr.
k,3 Analysis of C00 SB Resonance
v CL'-
The etalons used for this portion of the experiment were of reflect-
ivity 0.86. This, coupled with the broad laser line width and small B value
of carbon dioxide make the SB resonance more suitable than the UB resonance
for a measurement of the rotational constants because its features are less
wahsed out by the effects of broad line width. A single large Raman peak is
not formed between the Rayleigh fringes at this fsr (see figure U.2b) nnd
the method of maximizing the Raman signal to define the resonance position is
not applicable.
55
-------
/
L
/
7
/
7 "
/
/
7
y
/
/
7^
/_
Z ^
/ CM
/ CM
/ ^
/
- 7
. *
/
7
/
y
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1 1 1
CM O
CM w CM
i i
cr> co
a
ro
CO
CM
(D
CM
CM
CM
CM
0
CM
CO
£
CM
CO
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5f
CM
INGE NUMBER
RELATIVE FR
interferometer.
0>
.c
4-1
H
O
l_
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o
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to
'lot of normalized stokes-ant
n
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56
-------
Consideration of figure 4.2b for the case of C02 with odd rotational
lines absent indicates that at an 8B resonance, the distance between Stokes
and anti-Stokes peaks is half the distance between the Rayleigh peaks to
either side, while at fsr's smaller than the resonance, the peaks move
closer to the Rayleigh lines and vice-versa for larger fsr's. Figure 4.3
shows a plot of Y versus relative order number with
distance between Rayleigh fringes
distance between Raman peaks
and the FPI scanned over several orders in the neighborhood of the resonance.
Gamma was found equal to 2.0 at relative order number 19.75 ± 1.38
where the data was fitted to a straight line using the least squares method
and the errors determined by requiring a confidence of 95%. The
relevant figures are given below.
Y = -.01123n + 2.222
N = 29 = number of data points
s = 0.0399 =/z (residuals squared)
N-2
(N-2)
tg Qfj = 2.05 = Student's distribution
A plate spacing determination was done at relative order number 10, with the
wavelengths and fractional orders for this measurement given in table 4.3
below.
57
-------
Table 4.3.
FRACTIONAL ORDERS FOR CO2 8B PLATE SPACING MEASUREMENT
o o
Wavelength (A) Fractional shift (A)
measured calculated
5145.319 0. 0.
4879.860 1379. 1432.
4965.070 391. 389.
4764.862 659. 658.
o
A plate spacing t = .16004514 cm ± 50 A gives the phase shifts of column 3 in
table 4.3. Therefore the resonance occured at
t = 0.1602960 cm ± 1.38 orders
giving an effective B value of
Beff = 0-389903 ± 0.000086 cm "].
The literature value is 0.39027 cm"1. Beff is too small by 0.000366 cm,
which corresponds to a plate spacing error of At ^ 6 ± 1.4 orders at an 8B fsr
or ^ 12 ± 2.8 orders at a fsr of 4B.
The expected shift due to distortion effects at the 4B resonance is given in
table 4.2 as approximately 9 orders. The agreement is reasonable and it is
clear that is the rotational constants B and D of a pollutant molecule are
known, it will be possible to set the Fabry-Perot to pass the spectra of that
molecule.
58
-------
SUCCESSIVE GROUPS ARE 10 ORDERS APART WITH THE
RAYLEIGH FRINGE FIRST IN EACH CASE
Figure 4.4. Carbon dioxide 4B resonance.
59
-------
h.h Analysis of CO '»B Resonance
The etalons available for this experiment were of reflectivity
R = 0.9^. The improved finesse over that of the reflectivity R = 0.86 etalons
made possible an attempt at a fsr of UB rather than 8B as was tested in section
U.3. The UB resonance is a more favorable one to use when searching for weak
signals such as might be expected from atmospheric pollutants because it sums
all the Raman light into a single peak.
The gas cell was filled with slightly over one atmosphere of carbon
dioxide and a scan done over the region of the expected resonance. The
resultant data is given in figure U.U. The Raman light can be seen to emerge
from the wings of the Rayleigh lines (the larger peak is due to Stokes scatter-
ing and the smaller anti-Stokes) and coalesce in the center forming a single
peak. Its intensity exceeds that of the Rayleigh lines at resonance and the
process then reverses itself as the scan continues past the peak of the
interferogram.
The Raman intensity was normalized by Rayleigh intensity and a plot made
versus the relative order number. As the interferogram approaches the resonance
position, the Raman peaks increase in height and the Rayleigh lines decrease
because of the Raman light which was previously scattered throughout the order
merging in the center. The normalization procedure enhances this peaking
effect while additionally providing scaling against laser intensity fluxuations.
A least squares fit to a parabola was attempted with the coefficients
found to be
r
a . O.U69U - 0.0389
o
a » 0.1923 - 0.0119
60
-------
0.01338 - 0.000773
where
Raman - a + a p + a p"
Rayleit'.h o 1 2
and the relative order number n is given by
n - 111.0 + 10.0 p.
The peak occurs at
- 31 , 7.186 + 0.609
2*2
which corresponds to order number
n = 182.8 + 6.1.
The errors reflect the one a limit and have been calculated using
o _ Z(residuals squared] _ ,
s - -
and
a = s ./GJ/ = standard deviation of the a. coefficient
clj v J.-L 1
where the c are the matrix elements of the inverse nornsl equations' matrix
(see Experimental Statistics, NBS handbook $1, M. Natrella).
Plate spacing determinations were carried out at relative order numbers
1^1 and 26l. T^ie fractional orders and wave lengths for these measurements
are given in table k,h below.
61
-------
Table 4.4. FRACTIONAL ORDERS FOR CO2 4B PLATE SPACING MEASUREMENT
shifts shifts
Wavelength fringe #l4l fringe #261
4879-860
5145.319
4965.070
4764.862
measured
0
1533
240
160
calculated
0
160Q
183
179
measured
0
1213
158
2237
calculated
0
1251
78
2255
The plate spacing determined for fringe nunber 141 is
t = 0.3214119 cm ± 50 A
with fractional orders given in column 3 of table h.h. The plate spacing
determined for fringe number 26l is
t - 0.318508U cm - 50 A
with the fractional orders given in column 5 of table U.U.
The two measured distances are 119 rather than 120 orders apart because of
a fringe counting error as the Fabry-Perot was adjusted by hand to extend the
range of the PZT stacks.
Since the peak was found to occur at relative order number 182.8, the plate
spacing at which the resonance occurred was
t * 0.320140U2 cm - 6.6 orders
where the error now includes the effect of the miscounted fringe as well as the
degree of the curve fit. The effective B value calcxilated from this is
62
-------
B ff = _]_ = 0.39013 ±0.0002 cm"1
eTT 8t
and when the correction for the distortion shift of ± 8.5 orders is accounted
for, this becomes
B = 0.39030 ± 0.0002 cm"1.
The literature value is B = 0.39027 cm, giving a disagreement of 0.00003
cm" or -v 1 order. The agreement is better than that for the 8B resonance
but, is probably a chance coincidence, the large error bars reflecting the
effects of the broad line widths and small fsr washing out the peak position.
4.5 Analysis of Nitric Oxide Data
As noted in section 4.1, the selection rules for NO rotational Raman are
|AJ = 0,1,2. Since these arise as a result of a doublet ground state, it is
as if there were four separate molecular species contributing to the Raman
scattering, with the resultant transmission of the spectrum through the FPI
expected to be complex. The half integer spin of the NO ground states
(J = 1/2,3/2) gives the rotational Raman spectra a displacement from the
Rayleigh line of 8B and 12B respectively for these states. The conditions
for an interferogram that rejects the Rayleigh line and sums all of the Raman
lines are violated for AJ = ± 2 and the 4B pattern are of no value in searching
for NO Raman. The AJ = ± 1 rotational Raman spectra was therefore observed (a
2B pattern) although its intensity is weaker than that of the scattering with
AJ = ± 2.
The presence of NO as an atmospheric pollutant gives impetus to the study
of its rotational Raman spectrum. In the temperatures found in a smokestack
plume, the NO does not react with 0? to establish a significantly high equili-
63
-------
brium population of its other oxides and thus alone becomes the candidate for
observation. This is somewhat unfortunate, because of its complex spectrum.
Although the 2B resonance might be expected to provide the optimum summation
of Raman light and rejection of Rayleigh, this will be shown to be incorrect
and that other resonances of NO should be utilized for its detection.
The difficulties of preparing and containing a sample of NO have been
previously discussed in section 3.6 while the B and D values for the
IT, 12 and ir^/p states can be found in table 4.1. The gas cell contained
slightly over one atmosphere of NO and was positioned at the intra-cavity focus
of the laser. Because the TT, ,, and iro/o states are so close in B value, a
double passed arrangement of the FPI was used to give improved finesse and
contrast. Sandercock has s\
and contrast will be given by
contrast. Sandercock has shown that for such an arrangement, the finesse
f = /? f
double single passed
C = C2
double single passed
yielding expected values for this apparatus of
f = 29
C = 3x1O4
o
The measured values were f = 21 and 6x10 , with the discrepancy a result of
the laser linewidth.
The double passed arrangement is diagrammed in figure 4.5. The scattered
o
light from the gas cell is collimated, and then reflected by the 45 mirror
through the Fabry-Perot. A corner cube reflector returns the light along the
64
-------
Q_
O
c
'a.
h
«-o
II
CZ3
c j;
o :=
^= a.
o w a,
CD
M
05
O
I
OJ
+-I
c
0>
Q.
JD
03
U.
(D
a.
o
Q
05
65
-------
angle of incidence, but shifted spatially to pass through the Fabry-Perot a
second time after which it is focused onto a pinhole and the photomultiplier
tube. This arrangement is equivalent to the tandem passage of two Fabry-Perot
but without the alignment and fsr matching problems encountered in the latter
case. Care was taken to avoid front surface reflections and other sources of
stray light which could have decreased the contrast.
The general features of the transmitted intensity can be estimated from
figure 4.1 showing the NO spectrum set against a Fabry-Perot combe near the
2B resonance. At the TT , ,* resonance, theAO = ±2^-1/2 scattering will
form a peak in between the Rayleigh fringes just as the J = 2 did for
C02 at its 4B resonance (figure 4.4), while theA J =± ITT -|/2 scattering will
accumulate behind the Rayleigh fringes because of its offset of 8B from the
Rayleigh line. The transitions originating from the 113/2 state wil1 be slightly
out of resonance and w'll tend to wash out the visibility of the 1^/2 fringes.
At the 0/2 resonance, the same description will hold with the 713/2 anc*
iT-i/2 states exchanging roles. Although the vr*/? state loses intensity
over the TT-, ,~ state because of the Boltzman factor, this is more than
offset by the factors arising from the matrix elements, and as a result the
resonance will be more intense than that of the 711/-
Using euqations 4.7, 4.8, A7, A8, A9, and A10, the spectrum of NO was
calculated and a computer simulation done of its transmission through a
Fabry-Peort. These results are presented in figure 4.6 along with experimental
data sampled at various plate spacings through the resonance. The upper diagrams
in each set are the calculations without the Rayleigh lines superimposed, the
vertical bars above these diagrams the positions the Rayleigh lines would
o
occupy, and the numbers the order numbers of the Fabry-Perot \= 5145.319 A.
66
-------
The lower diagrams are the experimental data with the numbers above the Rayleigh
lines tliis tine representing the experimentally measured values usnrr, the
method of fractional orders. The experimental data given below each calcula-
tion represents that data whose order number was closest to where the cal-
culation vas done. As the pattern does not change appreciably over U-5 orders,
this represents no serious problem where a qualitative comparison such as the
above is made.
Quantitative data on B values and resonance positions was not easily
obtained, because the blurring of the features of the resonances by the
scattered light not in resonance caused them to have no clear cut maximum
although so~e build up of intensity was obvious. The -ft- / resonance was for
example, ill defined over 25 orders, and without the aid of a model calculation,
its identification would have been tenuous ut best.
-1/2
The B rule for interferogram widths is easily generalized to include
AJ = -1 as veil as AJ = ±2 transitions, the effects of laser line width,
and resonances other than the UB resonance. The result is
width = [i/2]G
c B"/
where a and f are the fsr and finesse of the FPI, g is a constant, y is
the incident line width, and the factor 1/2 is to be included for AJ = ±2
transitions only. Taking CCL UB resonance (figure U.U) width as ^ l60 orders
with an incident line width of .25 cm gives g ~ 1295 orders. Thus, an
estimate of the NO 2B resonance widths for the TT_ /o and 77- states is ~ 80
l/^ 3/2
orders. Since the separation between these two resonances is on the order
of 150 orders, and there exists background scattering from theAJ a» £2 tran-
sitions, it is clear why the measurement of the peak positions for these
resonances is difficult.
-------
or
<
CO
o
co
CD
to
O
s
to
o
CD
CO
to
LJ
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z
o
CO
o
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n:
C£
LJ
cc
X
\-
o
LJ
o
o
LJ
<
Q
LJ
CC
ID
LJ
LJ
CC
<
CO
LJ
O
O
CO
LJ
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o
CO
CO
to
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Q Q
LJ UJ
< ^
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to co
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68
-------
4.6 The 8B/3 NO Resonance
The detection of rotational Raman from an inpurity molecular species
with the multiplexed Fabry-Perot interferometer requires not only that the
scattering have a sufficient cross-section, but also that its transmission
profile be sufficiently well defined as to distinguish it from other resonances
and from the background. The 2B resonance of NO with its intensity spread
over ^ 160 orders and reaching a peak value of only 1/28 that of the Rayleigh
line did not satisfy these conditions.
Figure 4.7 shows a scan of the NO sample done at a fsr of 8B/3. Because
of the offsets of the J = ± ITT , ,~ and u ~.,~ spectra from the Rayleigh line
(figure 4.1), the peak formed at this resonance cannot be generated by
scattering from these transitions and is in fact due to AJ = ± 2 Raman. For
the TT 1/2 resonance in figure 4.10, only the odd lines contribute to the
Raman peak with the even lines falling behind the Rayleigh fringe.
The opposite holds true for the .^ state wMch -s just beginning to form
into a resonance towards the end of the sequence shown. The single (as opposed
to double) Raman peak between Rayleigh fringes produced at this 8B/3 resonance
is a direct result of the non-zero spin of the ground rotational states which
causes the Raman spectra to be shifted away from the Rayleigh line by 8B
(for IT 1/2) and 12B (for v 3/2) instead of the normal 6B shift found for the spin
zero ground state. Computer simulations of these resonances confirm the results.
Using the generalized rule for interferogram widths derived in the pre-
vious section with g = 1295 as determined from the CO? 4B resonance gives
an expected width for the 8B/3 resonance as ^ 29 orders, while the measured
69
-------
width is approximately 25 orders. The agreement is good. If incident line
-112.
widths had not been considered and the width was assumed to go as B ' ,
the predicted width would have been 160x j^ "" 78 orders, the error being
substantial. Clearly the 8B/3 resonance is superior to the 2B resonance in
terms of having a well defined and more intense peak to be detected (4.5 times
the 2B resonance maximum) and should be chosen in preference to the other when
it is required to ascertain whether or not NO is present in some mixture of
gasses without regard to which process generated the Raman light being observed.
It is not clear, however, that this is an optimal resonance to maximize
intensity and Smith has indicated the usefulness of long scans using an
air bearing interferometer or some equivalent system to determine other
resonance that may exist within detectibiltiy limits set by the line width of
the laser.
4.7 A Search for Methane Pure Rotational Raman
The spherical degeneracy of methane's polarizability ellipsoid
is removed by the zero point vibrational motions of the molecule leading to
a slight probability for pure rotational Raman scattering. Estimates of this
-4 -7
intensity place it anywhere from 10 to 10 down from the ordinary rotational
Raman cross-sections. Since the Fabry-Perot has a large entendue enhanced by
multiplexing and a strong exciting source was available in the form of an
intra-cavity operated laser, a search was made for this scattering.
With the cross-section for methane pure rotational Raman scattering ex-
pected to be so small, care was exercised in minimizing extraneous light from
the Rayleigh line, scattering from impurities in the sample, and dark current.
The rejection method to be described in chapter 5 (figure 5.2) was used to
70
-------
inn/
nn
VA
A
A
Figure 4.7. Nitric oxide 8B/3 resonance.
A
r
wriYnY
71
-------
remove a large fraction of the Rayleigh light, and care was taken to assure
the baffling of the optical elements from stray and internally scattered
light. (The rejection method being more efficient in this respect than the
double passed Fabry-Perot interferometer because it removes light at the
entrance of the system thus eliminating the possibility of scattering from
surface imperfections or scattering centers further down the optical path).
Ultra high purity methane (0.9997 purity) was passed into the gas cell
through the vacuum distillation system after both had been outgassed for
_5
two days at 10 Torr. Slightly over one atmosphere pressure of methane was
used with the other precautions mentioned in the section on vacuum distillation
4
followed. As the abundance of CHoD in ChL is on the order of 5 parts in 10 ,
this sets a limit to the purity that may be obtained at resonable cost.
To eliminate the effects of contaminant scattering, scans were taken
at two plate spacings separated by 280 orders. If the impurity scattering
comes from many sources with varied B values, their expected contribution is
approximately constant over many orders while the methane Raman should pak at
resonance and be absent in the second scan done at the off resonance position.
A chance peak could be produced by a resonance with one of the impurities at the
4B position of methane, but as no peak was observed at the resonance, this
does not become consideration.
Figures 4.8 and 4.9 are the interferograms taken on-resonance (corrected
for distortion shift) and off-resonance respectively, with each being the
average of 10 scans and the gentle slope in the base line a result of interfer-
ometer temperature scanning coupling in slightly more Rayleigh intensity to
one side than to the other. The dark count rate was 6 Hz with an estimate of
the Rayleigh contribution in the Lorentzian wings being approximately 5 Hz.
72
-------
The data does not permit the identification of a Raman peak, but an upper
limit on the cross section for pure rotational Raman scattering can be
placed by assuming that the entire count rate between the Rayleigh peaks
after subtraction of the two differently spaced interferograms is due to
methane. The analysis is given below.
(a) Using the generalized rule for interferogram widths with the
constant g evaluated from both the NO and (X^ data gives an expected width
of 6-7 orders at half maximum for the CH^ resonance. The C02 4B and 8B
resonance measurements demonstrated that the peak position could be accurately
predicted to within a few orders and the FPI set at that position. The ex-
pected transmittance of the CH^ rotational Raman spectrum should therefore be
in excess of 1/2.
After the subtraction of figures 4.8 and 4.9, the count rate between the
Rayleigh peaks had an average value of 2 Hz. With the assumption that this
is entirely due to CH* pure rotational Raman scattering, the Raman count
rates before entering the analyzing Fabry-Perot interferometer must be where
6x2 Hz (4.17)
6 " is the single line transmission efficiency of the Fabry-Perot interfero-
meter, its optics, the output pinhole, and photomultiplier tube. The loss of
CH^ Raman from the rejection Fabry-Perot interferometer is / 1-R \(see chapter
5) and so the Raman intensity leaving the beam splitter cube is
6x2 Hz. (4.18)
2R
Equation 4.5 gives the intensity of scattered light as
73
-------
24
22
20
18
16
O
o:
c
8 14
12
10
8
fc
,lr
IJ
L.l>
i.
I
Mr
1T
ii
Plate Spacing
Figure 4.8. Methane at the 46 resonance.
-------
24 -J
Plate Spacing
Figure 4.9. Methane off the 4B resonance.
75
-------
KB) = i (c^:,: + (I-PO)
(4.19)
A
3.
.-Altering geometry is sr-cv(\ polarized in the z direction with a viewing lens centered
:/is. The polarization beam splitter after the lens selects the
on component along the y axis.
'J
x incoming flux
direction of incident polarization
scattering into solid
angle omega about the
z axis
direction of the analyzing polarizer
direction of scattered light
A A
jnqle between s and z
A A
rotation angle of s about z with * = 0 placing
, in the xz plane.
76
-------
From the geometry for the polarization selected
cos P = sin t sin $ (4.20)
and equation 4.19 becomes
I (v,$) = I (0,0) [p + (1-p )sin2$ sin2f]. (4.21)
Collecting the scattered radiation over a solid angle ft yields
for the total intensity of light leaving the beam splitter cube
I (0,0) /[p + (1-p )sin2$ sin2f] dn.
Jo o
For the experimental geometry used here with an f/4 lens, this
reduces to
IRam(o,o) [3.7X10-2]
using p = 3/4 for rotational Raman. Equating this with equation
4.18 yields
\ 7x10-2 T (o ol - Iti 5x2 Hz. (4.22)
3'7xl° IRam(o'o) ' 2R
(b) A similar expression for the intensity of the
Rayleigh scattered light leaving the polarization beam splitter
-4
can be written using pD = 1.27x10
Kay
77
-------
IRay (0,0) |1.98xlO'4]. (4.23)
The intensity of the Rayleigh peak without rejection, but with the rejection
interferometer in position was 30 kHz. A factor C~ (see chapter 5) is lost
at the rejection interferometer when the Rayleigh line lies between rejection
peaks, and so the intensity of the Rayleigh line leaving the beam splitter cube
C 6 30 kHz. (4.24)
C-1
Equating this with equation 4.23 yields
C 6 30 kHz = IR (0,0) |J.98xlO~4].
C-1
Taking the ratio of this with equation 4.22 gives
f » / x 1+R
aRamlo) = °Rayl°j ~2R
1+R C-1 2 Hz 1.98xlO"4 (4.25)
where OR (o) and OR (o) are differential cross-sections for Raman and
Rayleigh scattering respectively, when the scattered and incident polarization
vectors are parallel. Using R = 0.4 for this experiment gives
[5.2xlO-7I.
The uncertainty in the measured B value (table 4.1) gives rise to plate
spacing error of ^ 0.2 orders while the uncertainty due to shifts, because of
distortion effects will be on the order of 2-3 orders as was measured for the
4B and 8B resonances of C02-
78
-------
(An estimated correction of 5-6 orders has been applied for distortion
effects using the D value given in table 4.1). Because of this, uncertainty
in the peak position coupled with the narrow width of the transmitted
interferogram, a factor 0.25 will be allowed for intensity loss due to
possible plate spacing errors.
The results of Chapter 5, and calibration measurements, give confidence
that the calculations involving light loss at the rejection FPI and fluxes
scattered into the collecting solid angle are good to a factor 2. The final
estimate therefore, for an upper limit to pure rotational Raman scattering
in CH4 is
o) < 4.2X10-6 aRay(o)
where the cross-sections are as previously defined.
79
-------
References
1. G. Placzek, The Rayleigh and Raman Scattering (translated from Handbunch
der Radiologie, Leipzeig, UCRL Trans. No. 526 (U. 1959).
2. G. Hertzberg, Infrared and Raman Spectra of Polyatomic Molecules, (Van
Nostrand Reinhold, New York, 1945) p.W.
3. Ibid., p. 20.
4. (a) Ibid., p. 396.
(b) Alfons Weber, Sergio P.S. Posto, Leonard E. Chessman, and Joseph J.
Barrett, J.O.S.A. 57, 19 (1967).
(c) C.M. Penney, R.L. St. Peters, and M. Lapp, J.O.S.A. 64^ 712 (1974).
(d) C.M. Penney, J.O.S.A. 59., 34 (1969).
(e) J.J. Barrett and Alfons Weber, J.O.S.A. 60, 70 (1970).
5. (a) G. Hertzberg, Spectra of Diatomic Molecules, (Van Nostrand Reinhold,
New York, 1950J;
(b) R.J. Butches, D.V. Willetts, and W.J. Jones, Proc. Roy. Soc. London,
A 324, 231 (1971).
(c) reference 4b, 4c.
6. References 4b, 4c, 5a, 5b, 7.
7. Ralph R. Rudder and David R. Bach, J.O.S.A. 58, 1260 (1968).
8. A. Rosenberg, I. Ozier, and A.K. Kudian, J. Chem. Phys. (Lett. Ed.)
27, 568 (1973)
9. Richard T. Hall and Jerome M. Dowling.J. Chem. Phys. 45, 1899 (1966).
10. G. Placzek and E. Teller, Z. Physik 81_, 209 (1933).
11. Reference 5, p. 121.
12. C.M. Penney, R.L. St. Peters, and M. Lapp, J.O.S.A. 64-, 712 (1974).
13. Reference 2, chapter 1.
14. P.J. Hargis, Jr. and R.A. Hill, J.O.S.A 65_, 219 (1975).
15. J.R. Sandercock, New Experimental Methods, p. 9, R.C.A. Laboratories,
Zurich, SwiterlancT
16. W.H. Smith, private communication.
80
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SECTION 5
FABRY-PEROT INTERFEROMETERS IN REFLECTION
5.1 The Feasibility of a Single Passed Fabry-Perot Interferometer as a
Remote Pollution Monitor
In a remote detection scheme using the rotational Raman effect, the
backscattered Raman light from a laser directed onto the plume of a smoke-
stack is collected by a telescope and analyzed for impurities in the effluent.
(See the review article by Kildal for a description of the various remote
detection proposals). The Fabry-Perot constitutes the analyzing part of the
scheme and is set at a resonance pattern for the pollutant molecule under
study. A large number of pollutant gases have Raman spectra that are periodic
or near periodic and are thus capable of being multiplexed by the Fabry-Perot.
2
Smith has pointed out that for certain J values even asymmetric rotors will
3
approach a prolate or oblate form having a near periodic spectrum. Smith
has also argued that the use of multiplexed rotational Raman instead of
vibrational Raman, gives an increase in sensitivity of several thousands as a
result of the increased cross-section, the greater entendue of the Fabry-Perot
over a slit spectrograph, and the effect of multiplexing the rotational Raman
spectrum.
Consider first the simplified case of a two component mixture, with COp
an impurity against an N~ background. If impurities to concentrations of
100 ppm are to be detectable using a multiplexed interferometer, the Fabry-
Perot must have a contrast of 10,000 in its ability to reject a background
81
-------
rototional Honum line for a signal to noise ratio of unity to be achieved.
Coi';cj -JOMCOG between some of the N^ lines and the FPI fringes t:et to pr.r.s C00
t-' C-
(illur.tratod in table 5.1- below) make this difficult to obtain in a straight-
forward manner.
Table 5.1. COINCIDENCES BETWEEN N2 RAMAN LINES AND CC>2
_ ,t , Coincidence with FPI Fringe
K_ J Value . . -i
? to within _____ci?. *
18,19 0.025 2m"
8,20 0.150 era"1
7,9AO 0.275 cm"1
Even with a single moded laser, atmospheric pressure broadening will give line
widths of 0.05-0.1 cm" . This combined with the fact that the FPI fringes are
Lcrentziar w.-i.th broad wines, implies that the transmission of l\ Raman will be
high. If the reflectivity of the etalons is increased to give finesse and a
narrower Fabry-Perot linewidth in the hope of avoiding a coincidence, the
transmission of the CO rotational Raman scattering will fall drastically.
Calculations involving the multiplexing of C02 and N spectra through a
FPI indicate that concentrations of CO on the order of 1-2$ are tne lowest
that one can hope to observe under the conditions of a remote field measure-
ment. These calculations are confirmed by laboratory experimental data
taken on gas mixtures having high concentrations of C00 and then extrapolating
to much lower percentages. The results are presented in figure 5.1 with the
numbers against the curves giving the ratio of nitrogen to carbon dioxide by
volume. The double peaks between the Rayleigh lines are due to the Raman
scattering from C00 anc* N . At the higher CO concentrations, the peaks
82
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83
-------
can be seen to decrease in proportion to the decreased percentage of C0p,
indicating that the scattering is du" mainly to C00 Kaman. At the lower
concentrations, however, the scattering is due mainly to K0 and without sub-
traction of the Np Raman, the CO peaks are difficult to observe. Chopping
against the K background should permit the detection of CO down to a
fraction cf a percent, but this will be difficult in a remote measurement
where one cannot be certain that the concentration of N_ in smokestack plume
will be the same as that in the nearby region used as a background reference.
Double passing was attempted with no significant improvement. A factor 10 or
so better could probably be obtained with extended integration times end a
single moded laser not having the broad line width of the laser available
for these experiments, but a field measurement would still be extremely
difficult. To overcome these difficulties, a prefilter must be inserted to
remove the background Hainan and Rayleigh scattered light. One method of doing
so Js presented in the following section, and a second proposed in Chapter 6.
5.2 The Fabry-Perot as a Rejection Filter
For the remote detection of atmospheric pollutants with multiplexed
Febry-Perot interferometers it will be necessary to prefilter and remove
contaminating light from three major sources:
(1) Rayleigh and Mie scattering
o (2) N2 rotational Raman
(3) 00 rotational Raman.
Other molecular contaminating species will hi.ve concentrations on the order
of the pollutant to be detected and their contribution will be reduced by
the comb of the analysing FPI, or will have their lines in know positions
84
-------
(such as CO ) and con be calibrated out in part, or if necessary, prefiltered
ns are N and 00 with another rejection filter.
The following discussion will show that a method of using FPT' s in
reflection can provide the necessary prcfiltcring action with the pure rotat-
ional Raman spectrum of N^ used as the spectrum to be rejected for two reasons.
Firstly, IJ0 comprises 80% of the atmosphere and its rotational Raiuan scattering
must be removed in any scheme of remote detection using the multiplexed rotat-
ional Raman effect. Secondly - as will be shown in a later section - the
ability to reject light by this method is a strong function of the line width
of the line to be rejected divided by the fsr of the rejection FPI. This
ratio is more favorable for N than for 0 because of its larger B value.
This will not prove a fundamental limitation in a situation where a single
moded laser can be used to narrow the lines until the limit of pressure
broadening is reached, and sample scans done with 0 even under the poor
conditions of broad line width and small free spectral range indicate that
the method is applicable.
The reflected spectrum of the Fabry-Perot interferometer is the compliment
of the transmitted spectrum (neglecting absorption losses; a^0.05^)-
Calculations indicate that if the Raman light from two distinct molecular species
is incident upon the FFI, it is possible to transmit the light from one while
reflecting nearly all the light from the second. To this end, etalons of
low reflectivity and high surface quality are required. With the interfero-
meter set to the periodicity corresponding to one of the molecules, the trans-
mission of light from the other is slowly increasing with reflectivity while1
the transmission of the component in resonance with the FPI periodicity
increases much more rapidly. Experiments show that the rejection of the
-------
unwanted component can be as large as 135 with the non-resonant light suffering
a loss of approximately 40%. Rayleigh and Mie scattering can be rejected in
the same fashion as the Raman except there are no considerations as to the
periodicity of the spectrum.
The experimental configuration is diagrammed in figure 5.2 with the
Raman scattering derived from the same intracavity gas cell used for the
single and double passed interferometers, collimated by the collecting lens,
and directed to a polarization beam splitter. One polarization component
was lost while the other was converted to circular polarization by the A/4
plate before entering the rejection Fabry-Perot. This Fabry-Perot was set
to pass either a Rayleigh fringe or the Raman light from a specific molecule
such as No- The remainder of the incident spectrum was reflected back
through the A/4 plate which restored the light to linear polarization, but
with the plane of polarization rotated by 90° so that it now passed through
the polarization beam splitter to enter the analyzing Fabry-Perot interfero-
meter where the impurity COp was detected. The remainder of the system is
the same as for the other FPI configurations.
5.3 Optimizing the Rejection Mechanism
Several factors must be considered in order to achieve a good
rejection of unwanted light.
(1) Optical components should be of laser quality material with
good scratch and dig ratings, few bulk scattering centers,
good anti-reflection coatings, and in case of the etalons,
wedged to eliminate first surface scattering.
(2) Effects due to misalignment and surface figure of the Fabry-
Perot etalons in the rejection interferometer are critical
and have been estimated using the formulae4:
86
-------
H
2
Q.
u
to
cn°
.£: o
£ go
8.2
-------
1000
1^
o
0>
"o
J 500
"o
o
10
20
X/200
X/150
X/100
X/250
30 40
% Reflectivity
50
60
70
Figure 5.3. Fraction of reflected light vs. degree of alignment.
88
-------
(1+F)1/2 |arctan l~(l+F)1/2tanl (**A*)]
- arctan (l+F)1/2tan 1 (*-A$) > (5.1)
where
I/I is the ratio of transmitted to incident light
$,A$ the phase and change in phase across the etalon due to
misalignment
F is 4R/0-R)2.
Figure 5.3 shows the fraction of radiation reflected for a given
reflectivity and degree of misalignment with the phase converted
to a distance expressed as x/n using the relation A$ = 4irkAt
= 4irk(x/n). The fraction of reflected light increases rapidly
with misalignment at the higher reflectivities.
The effects due to finite line width and surface imperfections (both
assumed to be Gaussian for the sake of an estimate)
!}
1 + 2V"RPcos k 9 exp (-P2/4Y2)> (5.2)
L*i )
where I/I , R, and 0 are as above, and
Y = /2~ n for a Gaussian distribution of surface
4TT error with standard deviation a = X/n
/fsr\ 1 for a Gaussian line incident
Y \ a / o/o" with standard deviation o
\ / / Vf IT
89
-------
Figure 5.4 shows a plot of the fraction of radiation reflected
for a given reflectivity R and ratio y where
incident line half width A/n for surface
Y
9
12
18
25
at tsr = 8 cm A
0.1 cm"1
0.075
0.05
0.036
detects
n = 80
107
160
225
Again the reflected intensity increases rapidly for increasing values of
Y and R (increasing linewidth, surface defects, and reflectivity, for a
fixed free spectral range).
The way to increase transmission of the unwanted light is to decrease
the reflectivity of the etalons. Since the amount of C02 Raman lost will
also increase, the reflectivity cannot be made arbitrarily small. If the
assumption is made that the (XL lines fall at random on the N~ rejection
comb, the fractional loss of COp Raman will be proportional to the area under
one order of the Airy function.
C02 loss * . (5.3)
Some rough calculations using these ideas are outlined in table 5.2
below. The figures are only estimates because it is difficult to know what
precisely is meant by the surface figure of an etalon, what the incident line
shape will be, and how to account for imperfections in the multilayer dielec-
tric coatings. The trends however are apparent.
90
-------
600
500
o
OJ
400
- 300
<*-
o
c
o
o
o
200
100
10
20
30 40
% Reflectivity
50
60
70
Figure 5.4. Fraction of reflected light versus etalon surface figure versus incident line width.
91
-------
equation 4.2 and as a consequence will not perfectly match
the comb of the rejection FPI IKFPI). This effect can be
lessened for small R because the Fabry-Perot line widths
become so broad as to accept the small shift in the N~
lines.
The non-periodicity sets a limit to how closely the RFPI must be to
resonance to behave as good rejection filter. Equation 4.9 yields.
At - AB
At = - 5-
8B 15.4)
A change in free spectral range of 4 AB will cause the J = 13 line to shift by
13 (4AB)cm~ . At the 4B resonance for iNk, the ratio of laser line width to
fsr is ^140 (ratio of incident to reflected intensity for the rejection
Fabry-Perot) can be expected at this fsr and line width. A tolerance on the
width of the rejection resonance can be estimated by requiring that the J = 13
line be shifted away from its optimum position by not more than half the
incident line width or ^ 0.1 cm~ .
13(4AB) * 0.1
For nitrogen with B ^ 2 crrf this gives the severe limit of
|At| % 2-3 orders.
The choice of J = 13 in the above can be justified by requiring that the
shift in line position due to distortion effects also be no more than 0.1 cm"
for some line J
80
Using the D value for N9 gives Jm3v ^13.
c. max
92
-------
In prnctic" the epti 'irar.i rejection resonance ir. shifted to slightly i-.raller
f.or'i; by distortion effects in exactly the name farhi on as the ('0 resonances
v.'cre r.hifl.c i 1:, chapter -I, and a range of J vt IIK ;; from J - 0 to appnT'inntcly
J -- c\i wni ! coY.-roa by the rejection coi.ib when at this ontimum nositicn.
i' i.U X
Thf 1ot-j.l in*-jin.ity iu the .line?; beyond J - 2 6 will be down by at lea,;t a
factor 10" from the ir't?:,sLty in tho region of the rejection cc;nb and should
not contribute >c':' £;nif:i c;mtly to the sif.nal. Distortion effects, while deleter-
ious and ir-por.in^ limitations to the rejection ability, should not pose serious
problems.
In summry therefore, the non-periodicity of the spectrum to be rejected
will .limit rejection ratios to the single line rejection ratio of'-l'iO for a
T
line \.-idth of 0.25 en x and the N resonance for, the tolerance on the plate
spacing to achieve the above ratio is + 2 orders for N (a worst case because
of the lar=:,e B vc.lue), and low reflectivity etalons of high surface quality are
required with extreme care in alignment to be expected.
5.^.0 Experi:-r,-ntpl Data
A calibration scan of the apparatus diagrammed in figure 5.2 is
given in figure 5.5 where the plate spacing of the RFPI is plotted against
the reflected light for a single laser line incident and the analyzing
Fabry- Perot interferometer (AFPI.) removed. The rejection ratio (the ratio
of the maximum to minimum light received by the detector) is
238 ± 2
with the error primarily due to the ^/TT noise on the I . measurement (for the
curve shown in figure 5.5).
Since the Kayleigh and Raman scattered light will have line widths in
excess of the laser line widths due to pressure broadening, the above ratios
are a:; upper limit for the rejection in this system at this fsr (but not
nece.-rarily one, as mentioned previously, that has a single mo-ded laser).
Although reuv.ir;' ;:g delicate alignment of the RFPI, the measurements were
reproducible ftv:; day to dr.y to vithir: 10}'. Because, the etalons had such
a low reflectivity ana i'in-.T-se, the method of fractional orders could not be
used to give r.n accurate .measure of the plate spneinrs, but feeler guage
measurements Dialed it on the order of « few thousandths of an inch.
93
-------
max ^430,000
Q
LU
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y
u_
u
o:
CO
z
o
o
LJL
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ID
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Zero
PLATE SPACING
Figure 5.5. Calibration scan of FPI in reflection.
-------
If the ratio of incident intensity upon the interferometer to the minimum
intensity received by the detector is required, then the above rejection ratio
must be multiplied by the correction factor.
C-l
C = contrast of this interferometer.
This takes account of the fact that due to the finite contrast of the rejection
interferometer, the maximum of the curves given in figure 5.5 is slightly less
than the intensity incident upon the interferometer.
At the large fsr (>50cm~ ) used for this measurement, the rejection ratio
is limited by surface figure and alignment and not by line width considerations.
From figures 5.3 and 5.4, the limiting ratio expected is on the order of 300-400
assuming A/200 across the aperture. The measured value corrected for the con-
trast of the FPI was 290. The disagreement is not unreasonable considering the
number of unknowns involved, and reflects the expeceted variation in parameters
from eta!on to etalon or with type and degree of complexity of surface coatings
and figure.
5.4.1 Rejection of Rayleigh Scattered Light
A test was made of the ability of the apparatus to remove Rayleigh
light in the presence of C02 Raman. To this end the AFPI was set to the carbon
dioxide 8B resonance while the RFPI was given a small plate spacing to maximize
its free spectral range. The respective free spectral ranges did not divide
evenly.
95
-------
Figure 5.6a shows a scan of the AFP1 with the KFPI set so that Die Rayleigh
line fell betv-'en the rejection fringes. The peaks in the center ore the CO,.
Fain-.!;, Figures 'p.ui), c chow scattering from tho same gas coll sample (pure
C00 at silently ovar one atmosphere), but this time with the rejection FPT on
a rejection fringe. Figure 5-6b hoc an essentially constant base line when
viewed at the same scale as the previous scan without rejection, wl.ile figure
5.6c shows ti;:y Eayleigh peaks in the center as a result of a slight miGhlign-
ment of the RFPI etalons. Tne integrated intensity of the C00 Raman in arbi-
trary units with and without the rejection FPI set to a rejection peak is the
same, as should be expected (figure 5-6a ii8 ± 5$> figure 5-6b 50+ 5l>)
The Rayleigh rejection ration, or the ratio of the Rayleigh intensity to the
base line noise or residual peak intensity after rejection, when multiplied
by the correction factor C/C-1 is greater than 2^0. (Original grapns more
easily read than the reproductions in figure 5.6, with the ratio probably
underestimated by 30$>) This ratio gives an upper limit to the expected
Raman rejection ratio es the non-periodicity of the Raman spectrum due to
distortion effects precludes its complete removal. That this ratio is smaller
than the previous one using a laser line directly upon the Fabry-Perot is
reasonable because of the increased line width upon scattering from the r.as
s ample.
The same experiment was repeated with N^ in the gas cell and both the
rejection and analyzing Fabry-Perots near the K ^B resonance. Firuro 5-7&
shovs the Rayleigh peaks on a Ix scale with the Raman suppressed whil3 figure
5.7b the same sample with the Rayleigh light rejected. The scale is now lOx.
From the areas under the curves, the Rayleigh rejection ratio is found
96
-------
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C02 Rayleigh
Zero
PLATE SPACING
Figure 5.6a. Rejection of C02 Rayleigh light.
97
-------
O
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98
-------
to be 125 ± 5% (expected value from table 5.1 is ^ is 140). That
this is lower than the measurement for CCL is reasonable because of the
smaller free spectral range used in this measurement. It is difficult to
say quantitatively whether the ratio has decreased in the proper fraction
because of different line widths and shapes in each measurement as well as
the problem in measuring the absolute free spectral range of the RFPI due
to its low finesse.
b.4.2 Rejection of Raman Scattered Light
The rejection of Rayleigh light is not sufficient to enable
the observation of low level impurities - the background Raman must also
be eliminated. To test the effectiveness of the rejection scheme in
removing No Raman, both the rejection and analyzing Fabry-Perots were set
at the N2 4B resonance. The gas cell was filled with an atmosphere of
pure No and the follwoing scans performed.
figure 5.7a No Raman rejected, scale Ix
figure 5.7b No Rayleigh rejected, scale lOx
figure 5.8 No Raman rejected, scale 2.5x.
A measurement of the areas under the curves gives a Raman rejection ratio of 135
± 5%. The flat background was assumed to be Rayleigh scattering in the Lorentzian
wings which would give a contrast of 160 to the AFPI. This is consistent with
previous experiments.
Although the scans will not be shown here, other measurements of the
Raman rejection ratio were made at plate spacings near to the one described above.
The results are tabulated below.
99
-------
UJ
6
o:
z
§
o
a. No Rayleigh
rejection
b. Rayleigh rejected
b.
Zero
PLATE SPACING
Figure 5.7. Illustration of Rayleigh rejection of N2-
100
-------
OJ
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g
CO
UJ
<
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a.
03
CC.
CSI
O
C
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DC
10
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Ll.
101
-------
above measurement
spacing decreased by five orders
spacing further decreased by five orders
ratio 135
ratio 81
ratio 39
with similar results for increasing plate spacings. This rapid decrease in
the rejection ratio is in agreement with the argument made in section 5.3
concerning the widths of rejection resonances. Because of the low finesse
of the rejection FPI, a plate spacing determination was not possible and
feeler guage measurements placed it as within the 4B resonance for N2 by
± 1 thousandth of an inch. The optimum position was extremely difficult to
locate ini tally as it had to be done by a trial and error method with no con-
verging search algorithm.
5.4.3 Detection of Impurities in a N2 Background
When used in the multiplexed mode, it is convenient to assign both
a Rayleigh and Raman contrast to the Fabry-Perot. The Rayleigh contrast
reflects the effectiveness of the interferometer in rejecting the light from
(\2
1+Rf while the Raman contrast reflects the
1-R/
effectiveness of rotational Raman spectrum rejection. Since the Raman spectrum
periodicities, it is approximated by C
1+R (see Section 5.3). An express-
Ram -
ion for the expected level of pollutant detection possible using the RFPI and
AFPI system can be written as follows:
Background Intensity
Signal Intensity
I (No)
Ray
_RRayCRay
(5.5)
SRSATRam (pollutant)
102
-------
where
IRam(pollutant)
are the intensities for No and pollutant
scattering at the 90° geometry calculated
using equation 4.5
Ram AFPI Raman contrast
CD AFPI Rayleigh contrast
Kay
RD RFPI Raman rejection ratio
Karri
D
Ray RFPI Rayleigh rejection ratio
S» Signal transmission through the AFPI
1-SR Signal loss at the RFPI
An estimate of the parameter Sousing equation 2.7 for any particular
fsr and incident line width will be too large because it is a singal line
transmission efficiency and consequently neglects distortion effects tending
to pull the lines off the transmission fringes of the AFPI comb. This added
effect due to distortion can be found from the data in figures 5.6a,b,c
by comparing the Raman intensity in the central peak to the total Raman
intensity. The data is given below in arbitrary units.
Total Rayleigh intensity 860
Total Ram intensity 720
^Peak Raman intensity ^600
103
-------
If the distortion constant were zero, all the Raman light would be concen-
trated into the central peak. Since it is not, the transmission of the signal
through the AFPI as calculated using equation 2.7 must be decreased by
^ (120/720) or ^ 16% to account for Raman signal losses into the baseline.
(SA = 0.84 times Sn calculated from equation 2.7).
Using equation 4.5 to calculate the scattering intensity gives a Raman
to Rayleigh intensity ratio of ^ 0.96 when corrected for losses at the RFPI.
/1 _p\
The measured value from the above data is 0.84. Since the yrn I rule for
\1+R7
light loss at the RFPI is only approximate, it is most likely that the dis-
crepancy is caused by a small resonance between the RFPI comb and the COo
spectrum.
The Rayleigh contrast was measured using a laser line directly incident
upon the RFPI (fsr set to COn 4B resonance) and found to be ^ 300. This is
consistent with the broad laser line width and small fsr.
Application of equation 5.5 using the measured values of RR and RR
at a fsr corresponding to the N9 4B resonance, an incident line width of
_i ^
0.25 cm , the above measurement of CRa , SR from table 5.2 with R = 0.4
(and confirmed by experiment), the intensities calculated using equation 4.5,
and the AFPI having etalons with R = 0.94, yields the following estimates for
the fractional level of impurity detectable when the background intensity
equals the signal intensity.
104
-------
N N RayleiGh Rejection Both Rayleigh and
Gas Mixture I!? Raman Rejection Raman Rejection
C02 in N2 ~l-3# 390 ppm
n In N ~1.5# ^50 ppm
U2 2
02 in Xe ' 20° P?m
If the b-.'ck'-rcu-:d intensity across the pollutant Raman peak to be
detected has fluxuaticns due to \> N noise alone, rather than due both to
v/F noise and fluxuations generated by the relative motion of tne AFPI comb
across the pollutant spectrum, then lower limits of detectability than those
calculated above can be expected. This vill be verified in the data presented.
It is also cletr that a laser line width narrower than the 0.25 cm" line
width narrower than the 0.25 cm line available here will Icwer the limits
of detectability through two mechanisms Firstly, the rejection FPI will
achieve better rejection ratios (until the limit set by etalon defects is
readied at a ratio of "^ 300-^+00) > and secondly, the transmission S of the
pollutant signal through the AFPI will be enhanced. Narrowing the line width
from O.2S cm- to 0.1 cm should give an improvement of»\/5-6 in detectability.
Because the parameters Cn , C , and S are all functions of the AFP!
Kay i\a,in A
reflectivity, t.'iis reflectivity can be chosen to optimize the detectability
limit, calculated vising equation 5-5 for the particular pollutant molecule
to be detected and laser line width available.
Measurements were made on mixtures of C0g in N0 and 0 in N_ with the
110 Raman scattering being rejected by the RFP1. Since only one rejection
interferometer war, available, it was not possible to simultaneously remove
both t.h
-------
measurement was made using 02 in Xe. With Xe having no Raman scattering
and its effective cross-section (cross-section calculated for the experi-
mental geometry used here taking depolarization ratios into account) approxi-
mately twice that of N2, any impurity seen against Xe scattering could be
seen against No if the N2 Raman were simultaneously removed.
In the following data, the quantity IRam (pollutant) in equation 5.5
was taken to be the area of the Raman peak resting on the baseline defined
by background scattering. The quantity J 53(^0^^ was taken to be the area
of a section of background below the Raman peak whose width was equal to the
width of the laser Rayleigh line. The Rayleigh rather than the Raman inter-
ferogram width was used because the latter has been broadened by distortion
effects.
Figures 5.9a and 5.9b show scans taken with 10. ± 0.5 Torr of C02 and
then with sufficient N2 added to give 1.5% C02 in N2. In each case, the
interferogram was recorded with the rejection FPI in position so that correct-
ions should not have had to have been made for signal losses at the rejection
interferometer. The intensities of the two Raman peaks, did, however, differ
by ^ 25% (assuming the base line is predominatly background scattering) and
this is a reflection upon the fact that the rejection interferometer fsr is
close to an integer times that of the C02 fsr and as a consequence resonance
effects can be expected. These effects were not as noticable for the C02
scans in figures 5.6a,b,c, where the two periodicities did not divide, and are
not seen when N2 is rejected and 02 sought (again the periods do not divide).
The predicted C02 Raman to base intensity should be unity for ^ 1.3% C02
in N2 with only the N2 Raman rejected. The measured value (corrected for the
25% loss due to resonance effects not considered in the calculation) is 0.71.
106
-------
10 torr C02
Rayleigh
Zero
Figure 5.9a. C02 calibration.
Rayleigh
1.5% C02 in N2
- N2 Raman rejected
3 units
Figure 5.9b. N2 Raman with and without rejection.
Base is 9 units
above Zero
Rayleigh
1.5% C02 in N2
N rejection
Figure 5.9c. 1.5% 02 in N2 with N2 Raman rejection.
Base is 18 units
above Zero
107
-------
Base line fluctuations are ^ 1/4 the Raman peak height and so signal to noise
ratios of unity can be expected at the 0.4% level of C02 in N2. With better
statistics so that the Rayleigh background could be removed, it should be
possible to see C02 in air at its normal concentrations.
in
Figures 5.10a and S.lOb show scans taken with 10. ± .5 Torr of 02 and then
with sufficient N2 added to give 1.5% 02 in N2, and as in the previous measure-
ment, both interferograms were recorded with the RFPI in position. The intensity
of the 02 Raman peaks in each scan agrees to within 10% as is expected (assuming
base line follows the curved slope of the Lorentzian wings). The predicted 02
Raman to base intensity is unity for ^ 1.5% 02 in N2 while the measured value is
% 1.3. Considering the number of variables involved, the agreement is probably
fortuitous. Figure S.lOc shows 760 mm of N2 with no Raman rejection at the
02 resonance (scale is 1/5 that of figure 5.10a,b). Clearly without Raman reject-
ion, the 02 peak would be not at all visible. The base line fluctuations in
figure 5.1 Ob are ^ 1/5 of the 02 intensity, and so concentrations of ^.3% 02
in N2 will give signal to noise ratios unity.
Because the 02 4B fsr is ^3.5 times as large as that for C02, the effects
of laser line width are diminished. This is seen both in the sharpness of
the 02 as compared with the C02 Raman peak, as well as the more rapid attenu-
ation of the Rayleigh fringe away from its peak position.
5.5.5 02 i Xe
Figures 5.11a and 5. lib show .7% in Xe without and with Raman
rejection. The intensity in the Raman peak divided by the background intensity
fRayleigh
108
-------
Raman
Rayleigh
Rejected
10 torr 02
Figure 5.10a. 02 Calibration.
Rayleigh
5 units
Figure 5.1 Ob. 1.4% 02 in N2-
Rayleigh
Zero
1.5% 02m N2
5 units above
Zero
760 torr N2
N2 Raman at 02 Resonance
\ \
(Scale is 1/5 of Figure b)
Zero
Figure 5.10c. 760 Torr N2-
109
-------
integrated over a wavelength range comparable to the laser line width is
^ 5/3 which is in contradiction to the prediction of a ratio near unity for
concentrations of ^.02*.
When the rejection ratio" for Xe was measured by integration over the
area of a Rayleigh fringe with and without rejection, the value was found to
be in excess of 100 and should have been quite sufficient to give the expected
level of detection. However, when the same ratio was measured using areas near
the center of an order the ratio was found to be only a.8. The background light
here could not have been normal incident Rayleigh (and the collimation was
sufficiently good as to exclude oblique Rayleigh also), was not dark counts
or light leaking into the PMT, and was not Op Raman spread into the
baseline. The likely explanation is impurity Raman scattering because of a
bad sample of Xe. If this value 8 is used for the rejection ratio, then the
predicted level rises to 0.3% with the measured value being 3/5x.7 ^ 0.42«.
In spite of the higher background, the Op peak is still clearly visible
with a S/N ratio of JO and concentrations of 700 ppm should give a S/N of
unity for these integration times.
Although the discrepancy between the predicted and measured Do in Xe levels
at which the Raman Oo intensity-to-base intensity will be unity is large when
impurity scattering is not accounted for, this is not quite as serious as
might be expected. The relevant number is the ratio of the Raman On intensity
to the base line fluctuations, not the base line intensity, and this will not
change appreciably with trace impurity scattering as this scattering will tend
to be averaged out to a smooth level by the multiplexing of several impurity
molecular spectra through the AFPI. With the exception of On in Xe, the agreement
110
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between expected and measured rejection ratios and levels of detection is good,
giving confidence to the projected levels when both the Raman and Rayleigh scatt-
ering can be rejected. Measured signal to noise ratios were on the order of
5-8 with an expected improvement of 5-6 when the laser width is narrowed from
-1 -1
0.25 cm to 0.1 cm , and assuming background sources to have concentrations
on the order of the pollutant to be detected (with the obvious exception of $2
and No), levels of detection of 350-400 ppm at signal to noise ratios of 8-16
for mixtures of C02 in N2 and 02 can be expected. The laboratory integration
times using an f/3 collecting lens were on the order, of 1-2 minutes across the
Raman feature fo this signal-to-noise.
The work on the 4B and 8B resonances of C02 demonstrates that the
correct setting for the FPI can be found to within 3-4 orders of the optimum
position if the rotational constants of the molecule under study are known,
-1/2
with the generalized B rule for interferograms giving the expected width of
the resonance. The use of the 8B/3 pattern for NO suggests that optimum res-
onances exist for maximizing the pollutant intensity and that these resonances
may not be the naively expected 4B or 2B ones.
Although not appreciated during the course of the work, both Raman and
Rayleigh scattering can be simultaneously removed with the use of a 2B pattern
( for A J = ± 2 scattering) but the rejection ratios will decrease somewhat from
those measured here, because of the decrease by a factor 2 of the fsr of the
rejection Fabry-Perot interferometer.
113
-------
References
1. H. Kildal and R.L. Byer, Proc. IEEE 59_, 1944 (1971),
2. Private communication, W.H. Smith.
3. W.H. Smith, Opto-electronics 4, 161 (1972).
4. J. DelPlano, J.O.S.A. 59, 724 (1970).
114
-------
SECTION 6
POLARIZATION REJECTION FILTER
The previous chapter noted the rejection of unwanted rotational Raman
light possible with a Fabry-Peort interferometer used in the rejection mode.
This method is limited by the requirements of high surface quality for the
etalons and by backscattering due to poor anti-reflection coatings and
alignment. These defects could be partially overcome in the filter operated
in transmission using a low index of refraction material. The polarization
rejection filter is discussed here as one possible solution.
6.1 Filter Theory
The relative orientations of the filter's optical components are
illustrated in figure 6.1. The light to be filtered is polarized and allowed
to fall on a crystal of birefringent material cut so as to fashion as a
retardation plate having a phase angle shift of
$ = 2-rrlan (6.1)
k = the wavenumber of the incident light
a = the thickness of the crystal
n = n.p . - n , = the degree of birefringence
If the electric field after the first polarizer is of strength /2"~, then
the field on the crystal axis will be
(Efast> =
115
-------
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116
-------
After passing through the crystal, the fast axis will have a phase advanced
by $ over that of the slow, and the fields will be
(ei$, 1). (6.3)
Now rotate the coordinate system to the A/4 plate axis
1/vT (ei$+ 1, e1$-l) (6.4)
and add a phase shift IT/ 2 to the fast axis
The difference in phase between the two components is now 0 or TT for all
$ and the light is linearly polarized with its magnitude on the two axes of
the polarizer being
1 ± cos $ .
Its angle to the x-axis of the polarizer is consequently
2
+a 2Q = 1-cos $ _sin
6 "
B = */2
The X/4 plate therefore changes a distribution of phase angle $ into an
angular distribution g with linear polarization.
Rotational Raman light has a spectrum of the form
Kj = KQ ± 4B(J+3/2) + 8D(J+3/2)3 (6.5)
k = wavenumber of the exciting laser line
B = B'- 3/2D
B',D = the rotational constants of the molecule
117
-------
and to first ordsr, the birefringence n of the material can be assumed to have
ft linear dependence with k..
nj
n = the birefringence at wavenumber k
o o
For quartz,
n0 ~ 0.009
a ^ 10"7 .
T'ne phase shifts $j for a Raman line passing through the filter will be
o ± ^B(J+3/2) + 8D(J+3/2)3][no ± a
no ± (J+3/2)(koa+4Bno) + 4Ba(j+3/2)2 + 8DnQ(J-f3/2)3
v'nere the estimates are for N^ Raman into a quartz filter.
Neglecting for the moment the terras greater than linear in J gives
(6.7)
The phase will be independent of J to within multiples of 2TT if
oa -h 4BnQ] =
I =
This is quite similar to formula U.9 for the multiplexing of a periodic spectrum
through a Fabry-Perot. The result then/is that all the Raman li,;ht will leave
the \/h plate with the same angle P of linear polarization, where
37T/2 .
(6.9)
118
-------
A polarizer placed after the X/U plate and having its axis properly oriented
will attenuate this Retr.an light by its extinction factor, typically 10 or 10 .
Other Raman light frorr: different molecular species with different periodici-
ties to their spectra will not experience such attenuation becau;v> , ne phase
angles thnt these generate will fall at random values from 0 to ? 7T, (assuming
the periodicity of the lignt and that of the filter do not fall in the ration
m/n where n and m are small integers).
The attenuation of this non-resonant species can be expected to be: on the
n
order 0.'; cr, the power factor for a polarizer goes as \sin / ~ 1/2 '^eudo-
randorr. $, ana we thus have a filter capable of selectively attenuating a
spectrum of given periodicity.
6.2 Fundamental li-rdtations
In practice the attenuation of the resonant spectrum is limited by
finite line widths and by tr.e neglected hic'ner order terms in (j+3/2)- The first
effect is on the order of
where A& is the 1/2 width of the phase shift caused by line width, but
2?r
we find that
For N with B-* 2 and using a full width 2Ak ~0.2 CnT
^ 2.5X10'3 .
119
-------
That is, 2.5x10° of the light that should have been attenuated will pass the
easy axis of the polarizer. This implies that the effective extinction is
only ^400 and since this assumed a uniform distribution of light over the phase
shift AO, the extinction of the light in practice may be somewhat better,
because of the concentration at small &<$> in the core of the line.
The second effect may also be approximately found by the following
argument.
Require that the phase error on the J line be no greater than its line
half width (say 0.1 cm" ). From the previous paragraph this should give an
extinction of UOO or greater.
For the quadratic term
find
J- 35
for the (J+3/2)3 tern
+2iM6Dn(J+3/2)3 ~ IE
o
fi"d j~ 25
for the (J+3/2) term
find
J ~ 200 .
So for Raman lines with J > 2.j, one should expect extinctions on the order
of UOO or better. For N , the Raman intensity for J = 25 is already down 100"0
from the peak of the Boltzman distribution and consequently higher J values will
not be troublesome.
120
-------
This second effect, was also estimated by direct calculation of the line
positions nnd phases us in-: known rotational constants. The results are r.iven
in tables 6.1 a-.u 6.? vnere the terminology filtered and unfiltered refers to
individual lino strengths before and after passare through the birefri::,;ent
filter. The mathematical filter was tuned to attenuate NO and pass 00 as a
consequence, rr , , _ . . . , .._ .,
Ng total attenuation 562.6
Og total attenuation 2.03
S/N gain 277.
As was the case with the rejection Fabry-Perot filter, the system was tuned
slightly off the expected resonance to compensate for the shift of the maximum
of the Ran.an light due to temperature and distortion effects. The B value of
N,~ is 1.9895 cni while the system was set to attenuate the B value 1.9876 cm
If the signal tc noise to be achieved were to remain above 250, the B value
could not deviate from optimum by more than-^0.0005 cm . This corresponds to
a change in the crystal length of"y60 microns, a tolerance that is easily achieved.
6.3 Corr.parision of FPI and Polarization Filters
In critical aspects, the birefringent filter and the Fabry-Perot inter-
ferometer scale as the ratio of the index of refraction of air to the birefringence
of the quartz with a sum-nary of the two methods presented in the table below.
Other birefringent materials such as magnesium flouride, calcite, and ADP are
possible, out will not be listed in the table as their properties will scale as
the ratio of their birefringence to the birefringence of quart?..
121
-------
Table 6.1 POLARIZATION REJECTION FILTER ATTENUATION OF N2 RAMAN
Stokes X 10
Intensity
-1
Value
h>
g>
OQ
05
0
C
H
J = 0 0.6
1.1
1.6
1.9
2.2
2.4
2.4
2.4
2.3
2.1
1.9
1.7
1.4
1.2
1.0
0.8
0.6
0.4
0.3
0.2
0.1
0.1
0.0
0.0
0.0
0.0
Stokes Filtered X 10'
Intensity
0.6
1.1
1.6
2.0
2.3
2.5
2.6
2.5
2.3
2.1
1.9
1.7
1.6
1.7
1.8
2.0
2.3
2.6
2.8
2.9
2.9
2.8
2.6
2.3
2.0
1.6
anti-Stokes is similar
122
-------
Table 6.2 POLARIZATION FILTER PASSING OXYGEN RAMAN
-1 -it
Stokes X 10 Stokes Filtered x 10
Intensity Intensity
J = 0
0)
H
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2.0
2.3
2.6
2.7
2.8
2.8
2.7
2.6
2.4
2.2
2.0
1.7
1.5
1.3
1.0
0.9
0.7
0.5
0.4
0.3
0.2
0.1
0.1
0.1
0.0
0.0
0.0
0.6
0.7
0.0
0.9
2.3
0.8
0.1
2.2
2.3
0.2
0.8
2.4
1.1
0.0
1.1
1.4
0.2
0.2
0.8
0.4
0.0
0.2
0.3
0.0
*
0.0
0.1
0.0
0.0
0.0
0.0
anti-Stokes is similar
123
-------
Table 6.3
COMPARISON OF FABRY-PEROT AND POLARIZATION REJECTION MECHANISMS
length or plate
separation*
birefringence or
index of refraction*
resonance width expressed
as tolerance on length*
tolerance on
colliraation
tolerance on flatness
of surfaces*
temperature stability
required
parellelness of
faces or etalons*
Quartz
12 cm
.009
error a
X/10 across
aperture
Fab ry- Perot
O.06 cm
1.000
error c d
.°c
X/250 across
aperturet
* these quantities scale approximately as the ratio of the index
of refraction and the birefringence.
f V250 is the technological limit.
124
-------
The temperature dependence of the Fabry-Perot arises mainly from the expansion
and contraction of the materials supporting the Fabry-Perot etalons us the
temperature varies. The temperature sensitivity of the crystal filter however,
comes about as a result, both the expansion and contraction of the crystal as
well as the dependence of the fast and slow indices of refraction on temperature.
This temperature sensitivity of both filters can be utilir.ed to tune the
optimum resonance.
6.U System Configurations
Two possible configurations for the device are shown below. The
first case shows the rejection of both 0^ and N using a linear arrangement of
components. The second (if back-scattering can be minimized) an arrangement
that uses a double pass of each crystal to reduce its required length by 1/2.
In the case of figure 6.2b, the \/U plate has been eliminated by tuning the
crystals using temperature. That is, the residual phase P -TT-Cn k -^^TT/2 rss
o o
been tuned to 27T using the temperature depende :ce of n and £ . 3ir.ce the
maximum change required P is ±7T or 1/2 an order while the resonance is ~5 '
orders wide, this adjustment is possible.
The conclusion then is that the birefringent filter should have filtering
properties equal to or greater than those of the Fabry-Perot used in reflection
*
because of the less severe restrictions on surface figure and parallelness and
because of its use in the transmission mode. There is no gain in terms of ease
of collimation or independence from temperature variations and as with the
rejection Fabry-Perot, the optical path length can be doubled to provide simul-
taneous rejection of both the Raman and Rayleigh scattered radiation. The major
difficulty will be to obtain a sample of quartz or magnesium flouride of suffi-
cient optical, quality that its characteristics do not change appreciably across
the aperture to be used. This may be possible with some of the synthetic
birefringent crystals that are now grown.
125
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APPENDIX A
Basic Equations
Al. The Fabry-Perot Interferometer
Concepts derived from the Airy equation that are useful in describing
the modes of operation of the Fabry-Perot interferometer are discussed briefly
below.
The Free Spectral Range (fsr)
i
fsr = 75
cos Q
- 1 for normal incidence and index of
refraction of air assumed to "be unity (A.I)
gives the separation in wavenumbers between successive orders of the interfer-
ometer, and sets an upper limit to the bandwidth of the incident radiation that
may be unambiguously resolved.
The Airy Finesse (f )
fsr
(A.2)
gives the number of full widths of a Fabry-Perot fringe within one fsr and is
thus a measure of the resolution of the instrument. It is useful in being a
function of the reflectivity alone.
127
-------
The concept of finesse may be generalized to include other effects that
limit the resolution, for just as f gives the maximum finesse for a given
reflectivity of the etalons with all other defects negligible, so f the
pinhole finesse sets a limit due to the finite size of the limiting aperture
of the system, and f, the defects finesse, a limit due to imperfect surface
figure on the etalons. The practical finesse is therefore given approximately
^ f - [f-2 -2 -21
with
fD ~ n/2 or n/3
where n is the n of \/n for the specification of the surface figure and
f = fsr
P 1/2 ka2
k = 1/X
a = the half angle subtended by the pinhole.
The resolution of the Fabry-Parot interferometer is the FWHM of a fringe
divided into the incident wavenumber.
Ic f A
resolution ='-^1^ = pf \A
where p * 2ktu is the order of the interferometer. A valid measure of resolu-
tion is more difficult to define when multiplexing a spectrum, because of
ambiguities introduced by the transmission of the spectrum through several orders
simultaneously.
128
-------
The throughput
Q = Jj(?0ds ^0 d>. (A. 5)
P °
J(>0 = incident energy /cm /sterrad/A
has been calculated by Jaquinot for a grating spectrometer and a Fabry-Perot
interferometer where K is the aperture stop of the system, T is the efficiency
of the optical train, and P the solid angle of light accepted by the system.
He found
Vating = p ET - 3.8
^Fabry-Perot = 2ir ET ~ 235
2
where Hirschberg and ',,'ilson have supplied typical values for modern instruments.
The Fabry-Perot interferometer is clearly superior to the grating spectrometer in th
in this aspect.
The Contrast (C) of the interferometer is the ratio of the maximum to minimum
intensity transmitted for a single v/avelength. Neglecting absorption losses
which only become important at high reflectivities, and the effects due to bulk
and surface scattering yields
/. ,-,
(A. 6)
where R = the reflectivity of the e talons.
129
-------
A2. Rotational Energy levels and Raman Intensities
(a) Nitric Oxide
The energy levels are E. where
J
EJ -
and Bj and Dj are the rotational constants for NO and
min min
J . = 1/2 for the Trl/2 ground state
min
J ; = 3/2 for the 7T3/2 ground state.
The TT3/2 state is 121.1 cm above the Trl/2 state.
The Raman selection rules are AJ = ±1, ±2, 0 leading to
displacements from the Rayleigh line of
for
|AJ| = 1
|AE| = (43-6D)(J+J+3/2) - 8D(J-rJn+3/2) (A.8
j
for
|AJ| = 2 .
The relative intensities -of these Raman lines are given by
li v o o -E./kT
^ 2(J^in) [^J+1) ; Jnin2^ie 1
= 1 -- J(J-KL)(J+2j^J+l) - : -
130
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where C = a constant.
h o ' o -E./kT
cA(J+l)2 - JgH(J+2)g - Jg]e
= 2
(J+l)(J-f2)(2J-H)(2J+3) (A. 10)
where g. and E. are the statistical weight and energy respectively,of the
initial state of the transition. An additional factor -121.1 cm /kT
e '
separates the TT 1/2 and77"3/2 states.
(b) Energy Levels and Raman Intensities for Op, C0p, N?
The selection rules are now AJ = 0, ±2 with tns enerey
levels, line displacements, and intensities given by the above formulae for
NO with J set equal to zero.
min
Additionally, CO ,and 0? have the odd rotational levels absent,
' nuclear spin S"
falling in the ratio 1/2.
because of nuclear spin statistics, while N has the odd and even levels
131
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APPENDIX B
Component Specifications
1) Multilayer Dielectric Coatings (Karl Feuer, Burleigh Instruments
a) R =0.94 from 5500 A to 4500 A
b) R =0.40 from 5500. A to 4?00 A
c) R =0.86 from 5500 A to 4500 A
2) Fabry-Perot Interferometer (Burleigh Instruments)
Model numbers RC50, RC40
High Voltage Power Supply number RC42
3) Filters (Millipore Corporation)
Lot #03225, type #AP 2501800 25 microns
4) Gas Samples (Ma the son Gas) , . ---
Gas Purity (minimum)
xe 99-995^
02 99-
N2 99.99^
NO 99-
C02
99-97$ analyzed
132
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5) Laser (Control Laser Corporation)
-2 watt Argon Ion
6) Photomultiplier Tube (Bailey Instruments: Centronic)
Model number 424QBA., blue sensitive with
quantum efficiency of approximately 10-12$
and dark current of 6 Hz uncooled.
7) Polarization Beam Splitter Cube (Per&in Elmer)
-2" aperture
IL
-extinction ratio of 10 at wavelengths of
488 0 A and 5145 A
-antireflection coated.
133
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TECHNICAL REPORT DATA
/Please read Instructions on the reverse before completing)
REPORT NO.
EPA-600/2-77-154
3. RECIPIENT'S ACCESSION-NO.
TITLE AND SUBTITLE
APPLICATION OF FABRY-PEROT INTERFEROMETRY
TO REMOTE SENSING OF GASEOUS POLLUTANTS
5. REPORT DATE
August 1977
6. PERFORMING ORGANIZATION CODE
. AUTHOR(S)
W. Hayden Smith and Robert A. King
8. PERFORMING ORGANIZATION REPORT NO.
PERFORMING ORGANIZATION NAME AND ADDRESS
Princeton University Observatory
Princeton University
Princeton, NJ 08540
10. PROGRAM ELEMENT NO.
1AD712
11. CONTRACT/GRANT NO.
Contract No. 68-02-0327
Grant No. 800805
2. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711 '
- RTP, NC
13. TYPE OF REPORT AND PERIOD COVERED
Final 8/71 - 3/75
14. SPONSORING AGENCY CODE
EPA/600/09
5. SUPPLEMENTARY NOTES
16. ABSTRACT
A method for the remote sensing of molecular species via the rotational Raman
effect was developed. The method uses the properties of a scanning Fabry-Perot
interferometer to multiplex the spectra in a manner specific for a given species.
Furthermore, the method allows the "in principle" sensitivity of remote pollutants
to be increased by as much as 104 over the vibrational Raman effect. To achieve
this goal, a scheme was developed for the rejection of the Raman spectra of the
abundant background gases, N£ and ©2. This was accomplished efficiently and with
little loss of the Raman scattered light from the pollutant species. Laboratory
measurements were conducted to demonstrate the method for a few specific cases;
results were encouraging. In addition to the light rejection scheme actually used,
a radically new technique utilizing the polarization properties of the Raman
scattered light was also developed.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
* Air Pollution
Flue gases
* Remote sensing
* Optical scanners
* Interferometers
Raman spectra
Fabry-Perot interferomete: -s
13B
21B
14B
171
20F
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCLASSIFIED
21. NO. OF PAGES
142
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
134
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