U.S. Environmental Protection Agency Industrial Environmental Research ',:',:•.. j; EPA-60U/7f'77-066
Office of Research and Development laboratory , :
Research Triangle Park, North Carolina.27711 : ; JUflG: 1.;977;. -: /
REVIEW OF LASER RAMAN AND
FLUORESCENCE TECHNIQUES
FOR PRACTICAL
COMBUSTION DIAGNOSTICS
Interagency
Energy-Environment
Research and Development
Program Report
-------
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S.
Environmental Protection Agency, have been grouped into seven series.
These seven broad categories were established to facilitate further
development and application of environmental technology. Elimination
of traditional grouping was consciously planned to foster technology
transfer and a maximum interface in related fields. The seven 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
This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from
the effort funded under the 17-agency Federal Energy/Environment
Research and Development Program. These studies relate to EPA's
mission to protect the public health and welfare from adverse effects
of pollutants associated with energy systems. The goal of the Program
is to assure the rapid development of domestic energy supplies in an
environmentally—compatible manner by providing the necessary
environmental data and control technology. Investigations include
analyses of the transport of energy-related pollutants and their health
and ecological effects; assessments of, and development of, control
technologies for energy systems; and integrated assessments of a wide
range of energy-related environmental issues.
REVIEW NOTICE
This report has been reviewed by the participating Federal
Agencies, and approved for publication. Approval does not
signify that the contents necessarily reflect the views and
policies of the Government, nor does mention of trade names
or commercial products constitute endorsement or recommen-
dation for use.
This document is available to the public through the National Technical
Information Service, Springfield, Virginia 22161.
-------
EPA-600/7-77-066
June 1977
REVIEW OF LASER RAMAN
AND FLUORESCENCE TECHNIQUES FOR
PRACTICAL COMBUSTION DIAGNOSTICS
by
A.C. Eckbreth, P.A. Bonczyk, and J.F. Verdieck
United Technologies Research Center
East Hartford, Connecticut 06108
Contract No. 68-02-2176
Program Element No. EHE624
EPA Project Officer: William B. Kuykendal
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, N.C. 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, D.C. 20460
-------
FOREWORD
Under Contract 68-02-2176 sponsored by the Environmental Protection
Agency, the United Technologies Research Center (UTRC) is conducting an
analytical and experimental investigation aimed at developing non-perturb-
ing, spatially precise, in-situ diagnostic techniques to measure species
concentration and temperature in practical combustion flames, i.e.,
luminous, particle-laden, turbulent. Under Task I, a comprehensive review
has been conducted and is reported herein of potential, nonintrusive laser
light scattering techniques for thermometry and chemical composition
measurements in hostile combustion environments such as furnaces and gas
turbine combustors.
ii
-------
TABLE OF CONTENTS
FOREWORD ................................... ii
LIST OF FIGURES ................ > . \ ............. V
LIST OF TABLES ................ ,; .............. Vi
LIST OF SYMBOLS ......... .......................
INTRODUCTION ................................. 1
REVIEW OF POTENTIAL IN-SITU, POINT, COMBUSTION DIAGNOSTIC TECHNIQUES ..... 3
Elastic Scattering Processes ...................... ^
Linear Inelastic Scattering Processes .................. k
Absorption ........ ....................... 7
Nonlinear Optical Processes .................. ..... 7
Selected Techniques ......... . ................. 10
SPECIES SPECTROSCOPY ............................. 11
Atomic Species of Interest in Combustion ................ 11
Diatomic Molecules ........................... 1^
Polyatomic Molecules .......................... 19
Raman Cross Sections .......................... 26
Interferences .............................. 26
Applicability of Techniques ....................... 29
PRACTICAL CONSIDERATIONS ........................... 31
Sources of Noise ............................ 31
Perturbations .............................. 1*3
Laser/Signal Transmission ........................ 1^7
Signal Averaging ............................ 1+9
Summary ................................. 50
RAMAN SCATTERING ............. '. . ................ 51
Introduction .............................. 51
Theory ................................. 52
Preferred Raman Approaches ....................... 56
Pulsed Laser Raman Signal to Noise Calculations ..... : ........ 60
iii
-------
TABLE OF CONTENTS (CONT'D)
Required S/N and Signal Averaging .................... 66
Practical Combustion Device Applicability ................ 68
Clean Flame Diagnostics ......................... °9
Near-Resonant Raman Scattering . .................... 71
LASER FLUORESCENCE
Introduction ............................ • • 7^
Fluorescence Theory ........................... 77
Signal to Noise Estimates ........................ 90
Summary .................. . ............ • • 100
COHERENT ANTI-STOKES RAMAN SCATTERING (CARS) ................. 102
Introduction .............................. 102
Review ................................. 102
CARS Signal Strength and S/N Calculations ................ 105
Medium Property Measurements ...................... 107
CARS Variants .............................. Ill
Practical Applicability ......................... 113
SYSTEMS CONSIDERATIONS ............................ 115
Raman Scattering ............................ 115
Laser Fluorescence ........................... 120
CARS .................................. 125
Systems Integration ........................... 128
CONCLUSIONS ................................. 130
REFERENCES .................................. 132
APPENDIX I - RADIOMETRIC MEASUREMENT CONVERSION ............... 1-1
APPENDIX II - AVERAGING CONSIDERATIONS FOR PULSED, LASER RAMAN SIGNALS
FROM TURBULENT COMBUSTION MEDIA ..................... II-l
-------
LIST OF FIGURES
Figure
Number
1 Scattering Processes 5
2 Nonlinear Optical Processes 8
3 Background Luminosity in EPA Rainbow Furnace 33
h Light Scattering Optical Collection Schematic 35
5 Laser Irradiated Particle Temperatures . 39
6 Particle Scattering and Absorption Cross Sections kl
7 Particle Characteristic Heat Transfer Times and
Absorption Coefficient kh
8 Raman Scattering Processes . 53
9 Temperature Variation of Stokes Bandwidth Factor 55
10 Bandwidth Factor Ratio Variation with Temperature 57
11 Pulsed Raman NO Detectability Limits 6l
12 Raman S/N Map over Soot Dispersion Characteristics for
Laser Modulated Particulate Incandescence 65
13 Single Pulse S/N Enhancement Via Noise Sampling and Subtraction. . 67
Ik CW Laser Raman NO Count Times 70
15 Molecular Absorption/Fluorescence 75
16 Laser-Induced Fluorescence for Three-Level System 78
17 Saturation for Homogeneous Broadening 8l
18 Doppler and Homogeneous Linewidths for NO 88
19 Fluorescence Power Versus Spectral Intensity 9^
20 Signal-To-Noise Estimate for CN 98
21 CN Fractional Population Variation with Temperature 101
22 Coherent Anti-Stokes Raman Scattering (CARS) 103
23 CARS Spectra 109
2k Spontaneous Raman Scattering Combustion Diagnostic System 116
25 Laser Fluorescence Diagnostic System , . 121
26 CARS System Schematic 126
27 Integrated Combustion Diagnostics System 129
1-1 Radiometer Schematic 1-2
II-l Bandwidth Factor Variation with Temperature II-3
II-2 Bandwidth Factor Ratio Variation with Temperature II-U
-------
LIST OF TABLES
Table
Number
Page
I Potential Combustion Diagnostic Techniques 3
II Atomic Species of Interest in Combustion 12
III Spectroscopic Data for Diatomic Molecules of Interest ...... 15
IV Spectroscopic Data for Polyatomic Molecules 20
V Raman Cross Section for Molecules of Interest 2?
VT Possible Interferences for Detecting Desired Species by
Raman/CARS Methods 28
VII Summary of Applicability of Techniques 30
VIII Potential Laser Vaporized Cn Interferences ^0
DC Particulate Extinction Effects ^8
X Summary of Practical Considerations 50
XI Continuous Wave Laser Raman/Background Luminosity Noise Ratio . . 59
XII N2 Raman Signal/Background Luminosity Noise Ratios 62
XIII N2 Raman Signal/Laser Modulated Soot Incandescence Noise Ratio . . 6k
XIV Effective Number of Rotational Levels 90
XV Saturation Term in Fluorescence Intensity 93
XVI number Density of Absorbing Molecules 93
XVII Saturation Laser Spectral Intensity ... 95
XVIII Fluorescence Emission Bandwidth 95
XIX Laser Modulated Particulate Incandescence Noise Power Levels ... 97
XX Detection limits for Species Measurement 97
XXI CARS Probe Volume 105
XXII Combustion Diagnostic Systems Assessment ..... 119
XXIII Laser Spectral Intensities (Watts/cm2 cm'1) 123
VI
-------
LIST OF SYMBOLS
A (l) excited molecular state designation
(2) aperture diameter
Aj_j Einstein coefficient for spontaneous emission
A , (l) area of laser beam
(2) area of lens
A0 principal axis rotational constant
a (l) molecular state designation
(2) particle radius
(3) lineshape parameter
a bond angle
aa absorption coefficient
B (l) excited molecular state designation
(2) molecular rotational constant
B. . Einstein coefficient for stimulated absorption/emission
J
Bg equilibrium rotational constant
BQ principal axis rotational constant
b molecular state designation
bji stimulated absorption/emission rate
C excited molecular state designation
CQ principal axis rotational constant
C ,C ,C point group symbols
oe 2v s
c speed of light
ca medium specific heat
cg particulate specific heat
F Raman linewidth
D (l) atomic state designation
(2) lens diameter
(3) particle diameter
D ,D ,D point group symbols
08
(l) molecular state designation
(2) fractional population difference
(c) change in associated parameter
vii
-------
LIST OF SYMBOLS (CONT'D)
A- population difference
rr differential scattering cross-section
ofi
6 absorption parameter
E (l) electric field intensity
(2) energy
e light collection efficiency
F (1) atomic state designation
(2) lens f-number
f (l) lens focal length
(2) fraction of energy absorbed by particle
fs Stokes bandwidth factor
f5 anti-Stokes bandwidth factor
fv=0 fraction of species in v = 0
fj_j fraction of species in J = JMAX
G (l) atomic state designation
(2) geometrical constant
g (l) stimulated Raman gain factor
(2) even inversion symmetry
gjL (l) level degeneracy
(2) susceptibility strength factor
Tj photocathode quantum efficiency
H atomic state designation
h Planck's constant
I± (l) CARS intensity
(2) laser intensity at frequency uij_
IA A-axis moment of inertia
IL laser intensity
IL laser spectral intensity
J (l) sum of spin and orbital momentum
(2) molecular rotational quantum number
viii
-------
LIST OF SYMBOLS (COKT'D)
K Knudsen number
k Boltzmann's constant
ka medium thermal conductivity
ks Stokes power calibration factor
ka anti-Stokes power calibration factor
L total electronic orbital momentum
1 (l) Raman or fluorescence sample length
(2) absorption path length
X, ,
|| coaxial light collection sampling extent
ti right-angle light collection sampling extent
A projection of orbital momentum on molecular symmetry axis
X wavelength of light
M number of populated rotational levels
MJJ transition moment between i and j
m refractive index
N (l) number density
(2) background luminosity
N total equilibrium species number density
N. instantaneous number density in state i
N.J_O total equilibrium species number density in state i
n number density
n particulate number density
nn number of noise photons
ns number of signal photons
VJL (l) frequency of light
(2) normal mode vibrational frequencies
vs frequency of Stokes light
VA frequency of anti-Stokes light
v^ frequency of laser
0^ point group symbol
ix
-------
LIST OF SYMBOLS (CONT'D)
P atomic state designation
r^
•-P- i~ T /pete atomic state designation
PJ_ (l) incident laser power
(2) CARS power
Prs Stokes power
a
Pr anti-Stokes power
P induced electric moment matrix element
Pj4 Mie power
II molecular state designation
rr pi
Q, Q-branch molecular transition
Q. . collisional relaxation rate between states i and j
-i- J
R saturation parameter
R' saturation parameter
R. radiation energy density
r bond length
p laser energy density
Pa medium mass density
Ps particulate mass density
S (l) atomic state designation
(2) total electronic spin momentum
(3) Raman signal power
S signal channel signal
S
S noise channel signal
Sp fluorescence power
Z molecular state designation
a light extinction cross-section
a , absorption cross-section
T temperature
-------
LIST OF SYMBOLS (COUT'D)
T^ point group symbol
T perturbation heat transfer time
TC heat conduction time
u odd inversion symmetry
V sample volume
Vi i coaxial light collection sample volume
Vi right-angle light collection sample volume
v molecular vibrational quantum number
0 CARS interaction region diameter
X molecular state designation
X molecular susceptibility
X' real part of susceptibility
x" imaginary part of susceptibility
X non-resonant part of susceptibility
0 light acceptance solid angle
z phase matching distance
ID circular frequency (radians)
uij_ circular frequency (radians)
xi
-------
INTRODUCTION
With the advent of laser light sources, light scattering spectroscopic
diagnostic techniques are assuming an ever-increasing role in a broad spectrum of
physical investigations. Of particular importance is the potential application of
laser spectroscopy to the hostile, yet sensitive, environments characteristic of
those in which combustion occurs. These diagnostic techniques should facilitate
greatly improved understanding of a variety of combustion processes which, in turn,
should lead to enhanced efficiencies and cleanliness in energy, propulsion and
waste disposal systems.
Recently, exciting experimental demonstrations of the potential of a variety
of Raman processes (spontaneous, near-resonant, coherent, stimulated) and laser
fluorescence techniques have appeared in studies dealing primarily with laboratory
flames. Unlike the situation prevailing in the field of remote detection of atmos-
pheric pollutants, where several comprehensive reviews have appeared comparing the
capabilities and systems aspects of various diagnostic approaches, little work of
a similar nature has appeared in connection with the remote, localized probing of
practical combustion devices, e.g. funaces, gas turbine combustors. Although the
pollutant detection review studies can be drawn upon, the measurement requirements
and potential problem areas in practical flame diagnosis are sufficiently different
to require a fresh perspective and review of measurement techniques more aptly
suited for the extraction of species and temperature information from combustion
devices. The objective of this report is to provide such a review. Realistically,
such a review of diagnostic techniques must focus keenly on the problems and sources
of noise which must be circumvented for successful application to practical devices.
Since it is unlikely that any one technique will provide the species and temperature
measurements over the range desired, systems considerations become important in
ascertaining how the various approaches can be integrated together with maximum
measurement rate and minimal redundancy. Such systems studies should also illuminate
the tradeoffs, between systems complexity and cost on the one hand, and probability
of successful measurements on the other.
In addition to the need for a comprehensive review of various practical flame
diagnostic techniques, there is the important requirement that the various approaches
undergo laboratory testing to realistically evaluate the assumptions of and explore
new research avenues raised by the review. Under Contract 68-02-21?6 sponsored by
the Environmental Protection Agency, the United Technologies Research Center (UTRC)
is conducting an analytical and experimental investigation aimed at developing
nonperturbing, spatially precise, in-situ diagnostic techniques for species and
temperature measurements in practical flames. Under Task I, the review described
above has been prepared and is presented herein. Under Task II, laboratory investi-
gations of the most promising diagnostic techniques will be conducted. Hence, another
objective of this report is to provide recommendations for the Task II experimental
development program.
-------
In the next section of this report, various laser diagnostic techniques
potentially suitable for "point" temperature and species concentration measurements
in flames are reviewed. From this list, four techniques are selected for detailed
evaluation including: (1) spontaneous Raman scattering, (2) near-resonant Raman
scattering, (3) laser fluorescence and (^-) coherent anti-Stokes Raman scattering
(CARS). The spectroscopy of species of combustion interest is discussed and the
applicability of the foregoing techniques to detection of the various species is
examined. Practical device considerations are reviewed with emphasis on sources of
noise (e.g., luminosity, particulates), medium perturbations, laser and signal trans-
mission, and signal averaging in temporally fluctuating media. Each diagnostic tech-
nique is then addressed in some detail in the order previously stated. Basic physics,
species sensitivity, thermometry applicability, signal to noise, problem areas, and
new variations of the techniques are included in these treatments. Measurement
systems approaches are described together with approximate cost estimates, probability
of success assessments and risk assignments. An integrated measurement system is
described. The report ends with a series of general conclusions suggestive of future
research efforts required for the evaluation and development of the more promising
diagnostic approaches.
-------
REVIEW OF POTENTIAL IN-SITU, POINT,
COMBUSTION DIAGNOSTIC TECHNIQUES
There are a large variety of diagnostic processes potentially applicable to
the remote, nonintrusive, point probing of combustion phenomena. Here these various
processes will be briefly reviewed and from them, a list of the most promising tech-
nqiues for flame probing will be selected for further detailed study. In this
review, attention will be directed ultimately only to those laser techniques which
permit the determination of local species concentrations and temperature. Velocity
measurements and emission spectroscopy techniques will not be considered.
The subject of combustion diagnostics has received a great deal of attention
in the past few years. In the summer of 197^-j the American Physical Society conducted
a one month summer study to evaluate the role of physics in combustion (Ref. 1).
Diagnostics for experimental combustion research received considerable attention.
In May 1975> Project SQUID conducted a several day workshop devoted exclusively to
combustion measurements in jet propulsion systems (Ref. 2). In January,1976, the
combustion sessions of the AIAA lUth Aerospace Sciences Meeting emphasized combus-
tion diagnostics (Ref. 3).
In Table I potential flame diagnostic techniques are listed; these have been
drawn from a listing of techniques applicable to air pollution measurements (Ref. k)
gasdynamics (Ref. 5)> and analytical chemistry (Ref. 6). Image formation and tracer
techniques (Ref. l) will not be considered.
TABLE I
POTENTIAL COMBUSTION DIAGNOSTIC TECHNIQUES
Elastic Scattering Processes
Rayleigh
Mie
Linear Inelastic Scattering Processes
Raman
Near-resonant Raman
Fluorescence
Absorption Processes
Resonant, Line of Sight
Differential Absorption
Nonlinear Optical Processes
Inverse Raman Scattering
Raman-Induced Kerr Effect (RIKES)
Stimulated Raman Scattering
Hyper-Raman Scattering
Coherent anti-Stokes Raman Scattering (CARS)
Higher-order Raman Spectral Excitation Spectroscopy (HORSES)
-------
Elastic Scattering Processes
Rayleigh Scattering
The elastic scattering of light quanta from molecules is termed Rayleigh
scattering (see Fig. 1) and is the phenomenon giving rise to the blue appearance of
the sky. Because the scattering process is elastic, the scattered light is unshifted
in frequency and, hence, not specific to the molecule causing the scattering. Thus
the technique can be used for total density measurements but not for individual
species concentrations. Temperature measurements can be made by resolving the
Doppler line-width of the scattering (Ref. 7). From a practical viewpoint,
Rayleigh diagnostics suffer from Mie interferences and spuriously scattered laser
light and have been employed in only very clean situations. The technique has seen
very limited utilization and is not suitable for practical combustor device probing.
Mie Scattering
Elastic scattering of light quanta from particulate matter is termed Mie scat-
tering. It is not dependent on molecular number density of temperature and, hence,
cannot be used to provide such information. It is the basic effect underlying laser
Doppler velocimetry and differential absorption backscattering (Ref. k) measurements.
It can be a very strong process depending on particle number density and particle
size, and is a potential source of interference as will be described later.
Linear Inelastic Scattering Processes
Raman and Near-resonant Raman Scattering
Raman scattering is the inelastic scattering of light from molecules as illu-
strated in Fig. 1, and is termed rotational, vibrational or electronic depending
on the nature of the energy change which occurs in the molecule. The process is
essentially instantaneous occurring within a time of 10"-^ sec or less. The mole-
cule may either become excited or deexcited depending on its original state prior to
the interaction. Raman scattering is ideally suited to combustion diagnostics and
has been widely applied in clean flames (Ref. 8). Visible wavelength lasers are typ-
ically employed since the strength of the scattering scales as the fourth power of
the Raman frequency, but no specific wavelength is required. Due to the quantiza-
tion of the molecular energy states, the Raman spectrum resides at fixed frequency
separations from the laser line characteristic of the molecule from, which the
scattering emanates. Thus the Raman scattering is species specific and linearly
proportional to species number density. Furthermore, spectral interferences between
vibrational Raman bands in gases are rare. Temperature measurements are readily
made from the distribution of the scattering. Unfortunately, Raman scattering is
very weak with cross sections typically around 10"3° cm2/sr, resulting in a col-
lected Raman to laser energy ratio of 10"-^ in flames. In practical combustion
-------
SCATTERING PROCESSES
VJl
\
RAYLEIGH
RAMAN
7
NEAR-RESONANT
RAMAN
RAYLEIGH
ANTI-STOKES
RAMAN
A
STOKES
RAMAN
LASER
LASER
ANTI-STOKES
RAMAN
STOKES
RAMAN
LASER
-------
situations, Raman scattering diagnostics are typically plagued by very low S/N
ratios. Despite this fact, because of its many advantages, it will be given
major consideration in this review.
If the incident laser wavelength is tuned near an electronic resonance of the
molecule being probed, (Fig. 1), the Raman cross section can be resonantly enhanced
perhaps by six orders of magnitude (Ref. 9). This process is termed near-resonant
Raman scattering and deserves attention because of the greatly increased Raman
signal strengths which may result. In the literature there is a great amount of
discussion in regard to the distinction, if any, between resonance fluorescence and
resonance Raman scattering. Most investigators now seem to agree that they are
variations of the same physical process distinguishable by the proximity to resonance.
It is generally believed that the nearly instantaneous process, insensitive to col-
lisional quenching, which is characteristic of a Raman process, occurs off but near
resonance. Consequently the terminology "near-resonant" Raman scattering is used
here to distinguish it from fluorescence or resonance fluorescence which occurs on
resonance, is longer-lived and subject to quenching. Unfortunately, many molecules
of combustion interest do not contain electronic resonances accessible to currently
available laser sources and hence are not amenable to near-resonant enhancement. In
some instances, the sacrifices in laser characteristics which result in tuning to a
certain resonance mitigate some or all of the enhancement achieved. Wear-resonant
Raman scattering will also be carefully considered.
Fluorescence and Resonance Fluorescence
Fluorescence is the emission of light from an atom or molecule following pro-
motion to an excited state by various means: electron bombardment, heating, chemical
reaction (chemiluminescence) or photon absorption (Fig. 1). Here only the last
means will be considered (Ref. 10). The precise definition of fluorescence requires
that emission occur between electronic energy states of the same multiplicity, i.e.,
same electronic spin states. Emission between states of different electronic spin
is termed phosphorescence. In general, fluorescent lifetimes vary between 10"^
and 10" 5 sec, much shorter than the phosphorescent lifetimes of 10 sec to seconds.
The light emission may be shifted in wavelength from the incident light, fluorescence,
or occur at the same wavelength, resonance fluorescence. In general it is desired
to examine shifted emission to avoid potential interferences from particle (Mie) or
spurious laser scattering. Fluorescence is of diagnostic interest since it is
species specific, and the cross sections for fluorescence are generally many orders
of magnitude stronger than Raman or near-resonant Raman scattering.
A molecule in an excited state may not necessarily emit radiation however;
several other pathways of energy loss are available which may compete with fluo-
rescence. Some of these are: dissociation, energy transfer to another molecule,
energy transfer to other internal energy states within the same molecule, and
chemical reaction. These processes competitive with fluorescence, termed quenching
-------
processes, reduce the amount of fluorescence which can be obtained and obscure
interpretation of the data. In principle, if all the quenching species densities
are known and if all of the appropriate quenching rate data is available, analytical
quenching corrections to the data would be possible. Because this is hardly ever
the case, fluorescence techniques involving partial or complete saturation will be
emphasized in this review since such approaches eliminate the problem of quenching
or permit in-situ experimentally determined quenching corrections.
Absorption
Absorption techniques employing tunable lasers can provde very sensitive
measurements of species concentrations using line-center techniques in flames (Ref.
11) or in the atmosphere (Ref. k). They provde measurements averaged over a path
and are not strictly point measurements. Mathematical inversion techniques can be
applied to obtain spatial variations of properties generally in spatially symmetric
situations but also in some nonsymmetric cases (Ref. 12). The results are, however,
sensitive to the assumptions in the inversion process and may not always be rigor-
ously accurate. Furthermore, the inaccuracy in the assumptions is often uncertain.
Absorption techniques are not considered in this review because of these uncertain-
ties and because they do not truly yield point,spatially precise measurements.
In differential absorption, one monitors radiation backscattered from distri-
buted Rayleigh and Mie scattering and tunes the incident wavelength on and off the
absorption line of interest. In this manner one measures the intial and final power
over some pathlength, the attenuation resulting from absorption which permits deter-
mination of the species number density. Although differential absorption permits
depth resolved measurements in pollutant detection (Ref. k), it is unlikely to be
successfully applicable to combustion diagnosis because of the short pathlengths
involved (i.e., spatial resolution) and the spatial non-uniformity of scatterers
(i.e., soot) from point to point in the combustor.
Nonlinear Optical Processes
Inverse Raman Scattering
Inverse Raman scattering is illustrated in Fig. 2 and is essentially an induced
absorption process first disclosed by Jones and Stoicheff (Ref. 13). Physically
the process originates through the imaginary component of the third order nonlinear
susceptibility. As shown, two collinear beams, one a high intensity monochromatic
source, the other a broadband continuum, traverse the medium under observation.
Under high enough intensity, absorption of the continuum occurs at frequencies
corresponding to the anti-Stokes Raman frequencies. Intensities just short of pro-
ducing stimulated effects are required and the absorptions produced by low density
-------
NONLINEAR OPTICAL PROCESSES
00
SPONTANEOUS RAMAN INVERSE RAMAN HYPER RAMAN
(LINEAR, SHOWN FOR REFERENCE)
ht>L
L
•h,s
1 hl>L
1
1 "S jf l>>
_! ^
2hl»L
,-A ,A
| ^S^
1 ^s^
I — I ^, •• —
— — "~ *• i £• t. *•
-s
"s
^*
^
t^
"I
STIMULATED RAMAN
h"L
"1
1 >^
1 h"s .Xx^
1 '^
1
I
COHERENT ANTI-STOKES RAMAN
p
K»
-------
gases are extremely weak. Clearly the absorption must "be significantly larger than
the anti-Stokes emissions produced by the intense source (Ref. lU). Inverse Raman
scattering possesses all the difficulties of any weak absorption process, namely
detecting a very small change in a strong signal. It does not appear to be a pro-
mising technique for combustion diagnosis.
Raman Induced Kerr Effect (HIKES)
This effect first disclosed in 1976 (Ref. 15) is remotely similar to the
inverse Raman effect in that an intense monochromatic pump source interacts with a
broadband probe source to produce a birefringence at the Raman frequencies. The
effect is resonantly enhanced when the frequency difference between the pump and
probe beams is tuned to the vibrational resonances of the molecule being probed.
To avoid interferences from the optical Kerr effect, the pump beam is circularly
polarized. The probe beam is linearly polarized and blocked by a crossed polarizer.
In the presence of the pump source, the probe beam experiences birefringence at
the Raman frequencies which are transmitted through the crossed polarizer to a
suitable detector. The effect has yet to be demonstrated in gases. Practically,
RIKES suffers from the rejection achievable with crossed polarizers which, at best;
is about 10" . Due to slight birefringence in intervening optical elements, e.g.,
lenses, windows, practically achievable rejection is less. Turbulent fluctuations
in combustion media may also produce undesired anisotropies. Clearly if the effect
is not stronger than the best rej-ection achievable, no signal is observed which
may well be the case in gases particularly at low concentrations. Until demonstrated
to the contrary, this phenomenon does not appear promising for gas-phase combustion
diagnostics.
Stimulated Raman Scattering
Stimulated Raman scattering (Ref. 16, 17) is illustrated in Fig. 2 and compared
to spontaneous Raman scattering. Under intense laser radiation, the spontaneously
generated Stokes photons experience exponential growth in the direction of laser
propagation and emerge as a coherent beam. The technique, despite high conversion
efficiencies in certain circumstances, is not promising for gas phase diagnostics
for several reasons. It can only be generated in certain selected gases, e.g.,
NO? Ho and then only at many atmospheres of pressure with very high intensity laser
pulses. Only selected lines of the Raman spectrum emerge which may make data inter-
pretation ambiguous. The effect to date remains in the realm of nonlinear optics
investigations and has not been applied for the above reasons to gas phase diagnosis.
Hyper Raman Scattering
Hyper Raman processes (Ref. 18) are illustrated in Fig. 2 and result in Raman
spectra relative to the second harmonic of the exciting laser frequency. The
scattering occurs into all solid angles and is very weak even at tens of atmospheres
-------
of gas pressure with very high intensity laser sources. The technique is of no
utility for combustion diagnosis.
Coherent Anti-Stokes Raman Scattering (CARS)
Coherent anti-Stokes Raman scattering (CARS) has received considerable atten-
tion over the past few years for combustion diagnosis based upon the pioneering
investigations of Taran in France (Ref. 19). It is schematically diagrammed in
Fig. 2. In brief two laser sources at ou, (pump) and u>2 (Stokes) generate an intense
coherent beam at u)o = 2w-. - u>2 (anti-Stokes or CARS) when the frequency difference
tu - uj is tuned to a molecular vibrational resonance. The effect has no threshold
per se and possesses two major advantages. The CARS signal produced is, first,
many orders of magnitude stronger than conventional Raman scattering and, second,
emerges as a coherent beam so that it can be completely collected. Since it is in
the anti-Stokes region it resides in a region free of fluorescent interferences for
the most part. The technique may well become to combustion thermometry what LDV
has in combustion velocimetry. A major section of this report is devoted to CARS.
Among its disadvantages are its double endedness (i.e., two opposed optical ports
are required), its more complicated spectra and limited species concentration sen-
sitivity. Several techniques have been proposed to circumvent this difficulty as
will be seen.
Higher-Order Raman Spectral Excitation Studies (HORSES)
HORSES have been observed in connection with CARS experiments in liquids
(Ref. 20). In addition to the CARS beam at 2 cu-, - cugs higher order signals at 3u>-i -
2 (JU2 and 3 u>2 - 2 UN were observed corresponding to sequential four-wave mixing.
These are very low intensity processes and it is unlikely that they offer any
potential advantage to CARS particularly for gas phase diagnostics.
Selected Techniques
From this list of techniques, only four processes appear to offer potential
promise for combustion diagnostics, namely: (l) spontaneous Raman scattering, (2)
near-resonant Raman scattering, (3) laser fluorescence, and (k) coherent anti-
Stokes Raman scattering (CARS). In subsequent sections of this report, the poten-
tial of these techniques will be examined in detail.
10
-------
SPECIES SPECTROSCOPY
Spectroscopic data, which are available from the literature for those atomic
and molecular species of interest in combustion processes are summarized in this
section. A literature survey, hopefully complete but by no means exhaustive, up
to December 1976 was performed. The data are presented in concise form in Tables
II, III and TV, for atoms, diatomic molecules, and polyatomic molecules, respectively.
An explanation of the often cryptic nomenclature used in molecular spectroscopy
precedes each table.
In addition to the Tables, each atomic or molecular species is discussed
individually with respect to spectroscopic (fluorescence, Raman, CARS, etc.)
observation in a combustion or similarly hostile environment (e.g., electric dis-
charge). Completeness has been attempted in the selection of combustion species
included in the Tables. Even though there may be little interest in the measure-
ment of some of the species considered, it is important to include them for
consideration of potential interferences in Raman or fluorescence measurements.
Atoms, diatomic molecules, and polyatomic molecules will be discussed respectively
in the sections which follow.
Atomic Species of Interest in Combustion
Table II lists those atoms which may be found in a combusting chemical system,
namely H, C, N, 0, and perhaps S. The Table lists the electronic configuration of
the valence shell, the electronic state, the J value for the electronic state and
the term energy in wave numbers. Both forbidden and allowed transitions are indi-
cated with their associated transition probabilities (in the form of the Einstein
coefficient,
The symbol for the electronic state gives the multiplicity of the state,
2S+1 (where S is the total electronic spin) as a left superscript, and the orbital
angular momentum, L, as a capital letter S, P, D, F, G, H, ... according to the
values 0, 1, 2, 3, k, 5, etc. for the orbital angular momentum. The possible
values for J, often listed as a right hand subscript, are listed separately. J is
the vector sum of the spin and orbital angular momentum. Atomic states are further
classified as odd or even states according to whether the sum, Z.S, , of the orbital
angular momentum of all electrons in the atom is odd or even. These three quantities
S, L, J, along with the energy of the state, completely define the state under the
classification known as Russell-Saunders coupling (or LS coupling). Russell-Saunders
coupling does not hold for high atomic weight atoms, which are of no concern here.
11
-------
TABLE II
• ATOMIC SPECIES OF INTEREST IN COMBUSTION63'
snflguration
Is1
2s1
2S22p2
2s22p3
2s22p23s
2s22p1'
2s22p33s
3.V
State J
2P 1/2
2P 1/2
2S 1/2
2P 3/2
3p o
1
2
^ 2
!S 0
3D 3
Us 3/2
2D 5/2
3/2
UP 5/2
3/2
1/2
3p 2
1
0
ID 2
^ 0
3S 1
3P 2
1
0
ID 2
*S 0
h 1
Term Energy
cm"
0.0
82281.285
82281-320
82281.650
0.0
16.1*
1*3.5
10193-7
2161*8.1*
61*088.0
0.0
19223.0
19231.0
88135.0
AVE
0.0
158.5
226.5
15867.7
33792.1*
76795.0
0.0
396.8
573.6
9239.0
22l8i.o
55331.0
12
Transition A^fsec'1!
2 2P1/2 - 1 2S1/2 U.TxlO8
2 2S1/2 - 1 2S1/2
tynan 1215&
3p -» I® < 1
Spin Forbidden
3p -. ^ < 1
Spin Forbidden
3p -• 3j) 1.5 x 108
156&8
Us-*2D5/2,3/2 **
Spin Forbidden < 1
I&porte Forbidden
'•S-^F 2.3 xlO8
1135*
3p - ID iQ-3
Spin Forbidden
3P ^ ig 10-k
Spin Forbidden
3P -3s 3.8 x 108
13038
3P -Q^ fc x 108
1807A
-------
The selection rules for transitions between states are:
AS = 0 no change in spin
AL = 0, ± 1
Aj = 0, ±1 but J=0 to J=0 is forbidden
A£ = ± 1 transition electron must change
angular momentum
The two selection rules concerning L and SL may be summarized by stating that only
odd and even states combine, i.e., odd -» even or even -+ odd are allowed transitions
but not odd -• odd or even -• even. This is termed the Laporte rule. Reference
to Table II shows that the allowed transitions have transition probabilities on
the order of 10 sec"-'-, whereas forbidden transition possess rates several orders
of magnitude lower. This discussion has been limited to a consideration of electric
dipole allowed transitions only; magnetic dipole and electric quadrupole transitions
have been omitted because of their low transition probabilities.
Detection of Atomic Species
For all of the atoms listed, detection by means of laser-induced fluorescence
in the visible region of the spectrum is impossible because all of the strong
atomic absorptions reside in the vacuum ultraviolet region of the spectrum.
Schlossberg has suggested that fluorine atoms may be detected and measured in
operating chemical lasers by means of CARS (Ref. 21). The method is based upon an
electronic Raman effect for the transition in the F-atom between the fine structure
r) r)
components of the ground state, ^3/2 an^ pl/2 • Thg separation of these two states
is kdk cm"-'-. Schlossberg has calculated the Raman scattering cross-section for this
F-atom transition for incident radiation of 5000A. A formula given by Vriens (Ref. 22)
was employed which relates the Raman scattering probability to the transition
frequency and the frequency of the first allowed transition. The value for the
calculated cross-section is 3 x 10~31 cm2/sr, which is comparable to that measured
for diatomic molecules. To our knowledge, the detection of F-atoms by means of
spontaneous Raman or CARS techniques has not been performed in a chemical laser or
even under laboratory conditions.
Both the carbon atom and the oxygen atom have fine structure in the ground
state, similar to the F-atom; unfortunately the nitrogen atom does not. The ground
states of the C-atom and 0-atom are both 3p. The position of the triplet levels in
C are 0, 16.U and U3.5 \crn~1 for 3po» pl and P2 respectively. In the 0-atom for
3P2> 3pi and 3pO the levels are at 0, 158.5 and 226.5 cm"1, respectively. The
inversion of J occurs because the 0-atom has the valence shell more than half-filled.
Certainly the transitions ^po -* 3pl» 3pO -* 2> 3pl> ~* 3p2 for either atom could
be resolved by a good Raman instrument, viz., a double monochromator with high
resolution and high rejection of scattered Rayleigh light. The Raman cross
sections for these transitions have not yet been calculated. A qualitative examina-
tion of the formula derived by Vriens and an inspection of the energy levels of C
and 0 leads to the conclusion that the 0- and C-atom Raman cross sections should
13
-------
be comparable to that of the F-atom. An important difference is that, for both the
0- and C-atom, there are real electronic states (see Table II) which are in the
spectral regions accessible to argon ion lasers and dye lasers. This opens up
the possibility of near-resonant enhancement of the electronic Raman scattering
from 0- and C-atoms. Near-resonance enhancement is not feasible for the F-atom
as the first excited state lies too high, ~ 100,000 cm"1 (1000A). Unfortunately,
this near-resonance enhancement for the 0- and C-atom may not be very large,
because the transitions mentioned are not very strongly allowed. Clearly, detailed
calculations are required to assess the situation in order to decide if 0- and C-
atom detection is feasible by means of electronic Raman scattering and, of course,
by CARS. In the latter case, sensitivity may be limited by nonresonant background
contributions as will be explained later. For the case of the C-atom, the small
electronic Raman shifts most likely would be obscured by rotational Raman
scattering from molecules present in the flame.
N is an extremely difficult species to measure because the lowest allowed
transitions are deep in the vacuum ultraviolet near 1200JL Radiation from a
microwave-driven hollow cathode lamp could, in principle, be used to excite
resonance fluorescence from N atoms. However, both the incident and emitted
radiation are likely to be strongly absorbed by other species. Raman scattering
cannot be employed since the photon energy from any available UV laser source is
considerably less than the excited state energy.
Diatomic Molecules'
The available data for selected diatomic species are summarized in Table III.
The species C2, CH (radical), CN (radical), CO, H2, CS, N2, NH (radical), NO, 02>
OH (radical), and SO are listed. Although not technically radicals, C2, CS and
SO are short-lived molecules; technically NO is a radical, but is long-lived.
The data is presented in a fashion similar to that of Herzberg (Ref. 23). The
term energy of the electronic state listed is given in wave numbers (cm-1). The
ground state is denoted by capital X (with the exception of C2) and states which
connect by spin-allowed transitions are denoted by capital letters A, B, C, etc.;
lower case letters are used for systems of different multiplicity. The multiplicity
of a state is given by 2S+1, as for atoms, by a left superscript on a Greek capital
letter which accounts for the total orbital angular momentum of a state. States
with 0, 1, 2 units of orbital angular momentum are termed S, IT, A states.
Additionally, homonuclear molecules require a g or u label (gerade-even or ungerade-
uneven) to designate whether the wave function is even or odd according to inversion
symmetry, and a + or-label (right superscript) to designate the symmetry of the
wave function with respect to reflection of the nuclei.
-------
TABLE III
SPBC1S06GQPIC DATA TOF DIAKHIC (OIZCUUS OF IKHEST 19 • 88 , *»2 , fill
Spec lei
Dl»*. Eoergy
C2
6.11 eV
CH
Radical
3.»5 eV
O
Radical
7.39 eV
CC
11.09 eV
"2
I..477 «V
CS
(7-35) «V
%
9.76 «v
NH
3.2 e»
(Kldlcal)
NO
6.5 eV
°2
5-115 eV
OK
Radical
4.40 eV
SO
3.* .»
Tern
Energy
" ,
0
714
64i* V
8145
199S8
34240
«*JO
0
17.9
23S17
25696
0
9117
25799
C
1.94-4
64746
0
91698
0
38797
0
49756
59310
6B951
0
a
.*e*s
29TT6
0
121
Iti-lMG
1*5486
ia.=i£
o
786S
13121
35006
1.931.9
0
126
32682
C
105 It
30Z92
AUK
Electronic
State
rn-l
X *£
X I.TU
A' ^£
B' *-*^
A 3r
c' ^
5 3"g
X ZT-^Z
a<13/B
A 2a
B 2I
X V
A *„
a 2c*
x 1r'
. 3n
A ^r
X %J
B *^i
^ V
> i«
x itj
A ifa
B 'ng
a V
X ^C"
. la
b H*
A ^n
X 2n
S/2
A 2E
_ ^
B rl/2
?"3/2
x ^r
" ^g
b 11?
* '*£
B 3i^
X /1/2
2"3/2
A £E*
x ^E"
b V
A 3^
B 3r
Vibr*t tonal
rrequrncy
CB"
1854.8
1641.3
Ifc70.4
1608.2
1788.2
18C9.1
U06.0
2858.7
2930.7
(2250)
2071.1
1912.5
21W..8
2169.8
1743.0
1515-6
1U05.3
1356.90
1285.1
10T2.3
2356.0
11(60.6
1735.0
169U.O
3203.0
3231.0
3355.0
31B3.0
1904.0
1903.7
2371.3
1036.9
1038.3
1560.2
1509.0
1432-7
(805)
700.4
3725.C
31S..3
11*9.0
Anharaonlclty
cm
13.4
11.7
11.2
12.1
15.8
39.3
63.0
96.6
13.8
12.6
12.2
13-3
14.0
17-3
125.3
19.0
8.5
10.0
14.2
13.9
15.2
13.9
78.5
6.3
7k .4
87.5
14.0
14.0
».5
7.5
7.5
12.0
12.9
13.9
(13)
8.0
82.8
97.8
5-63
Rotational
Constant Major Electronic fruultiona Llfetlae (gee)
ca"
1.82 8W> X -A' 4000 60008 185 • 1C"9 (1)
1.63
1.62
1.75
1.78 rcn-Herib«rg X -B 2300 - 3300}
1.19
14.19
14.58 U315A X -A 500C - li3«S _;.5 . i--* fh)
13.64 39»S X-B 4500 - 3600A -c.5xic"*!h;
1.899
1.715 Red X-A I4ooo - 5
-------
The fundamental vibration frequency is given in wave numbers as is the first
anharmonic constant and the rotational constant. Higher order corrections to the
vibrational-rotational energy terms are not given. The major allowed transitions
are listed along with the lifetime of the upper electronic state.
The selection rules for allowed transitions in diatomic molecules are:
AS = 0 spin does not change
&A = 0,±1 orbital angular momentum
thus, S - Z, S - II, II - Z, but Z /4 A
and g - u, u -» g even to odd, odd to even
g/£ g, u/i u (Laporte Rule)
and
It must be borne in mind that "forbiddenness" is a matter of degree and that
transitions which are forbidden do occur to some extent, and are observable.
Individual molecules are discussed in the order given in the Table, with
regard to detection by means of fluorescence, Raman or CARS techniques. As these
techniques are discussed in detail in later sections, only an abbreviated treat-
ment is given here.
The Swan bands, A^H -. x ^Hu, a strong emission found in flames, cover the
range from UOOO to 6?OoA with peak intensity at 5165J1 the 0-0 band. Although the
transition does not originate from the ground state, the lower state lies only "Jlk
cm~^- above the ground state and has ample population in flames. Laser-induced
fluorescence has been observed in flames by several workers (Refs. 2k, 25, and 26).
Both groups of workers claim that real time measurements of the C2 concentration
can be made in atmospheric pressure hydrocarbon flames. Jones and Mackie (Ref. 2k)
conclude that using a CW Argon ion laser yields marginal results. Baranavski and
McDonald (Ref. 25) employed a saturation technique utilizing a pulsed dye laser;
they claim concentration measurements of 10^° cm~^ and excited state lifetimes of
10"12 sec. The €2 fundamental vibrational frequency of 1855 cm~^ is, of course,
Raman allowed and, hence, could be detected by means of Raman scattering or CARS.
C2 measurements are precluded where soot is present because laser-generated Co
would interfere.
16
-------
CH
The methyne radical, CH, has two strong band systems in the visible and near
UV with strong features at 4300A and 3900A respectively. For both transitions the
lower state is the ground state, hence absorption of dye laser radiation is feasible
and has been carried out in a flame environment by Barnes and coworkers (Ref. 27).
A nitrogen laser pumped dye laser was employed to excite the (0,0) band at U315A in
an oxy-acetylene flame, presumably operating at one atmosphere.
CN
This radical has two main emission systems, the so-called "red" A 2n - X 2I+
and the "violet" B 2E+ - X 2i;+ transitions. Of the two, the violet system has the
more intense emission (absorption), and hence would be the more favored system
for laser excitation. Jackson (Ref. 28) has observed laser induced fluorescence
from CN produced by photolysis of cyanogen, C2N2- Therefore, laser-induced
fluorescence should be observable in flames.
CO, H2, N2, 02
All of these molecules have strong allowed transitions in the vacuum UV and
hence, cannot be excited with present technology dye lasers. The measurement of
these species must utilize conventional Raman or CARS techniques. There are no
strong interferences from other Raman lines from either diatomic or polyatomic
molecules; however, there may be fluorescent interferences from hydrocarbons or
radicals such as CH or NH. All of these have been monitored in numerous Raman and
CARS investigations. For example, laser excited vibrational Raman spectra of CO,
02, CHij. and N2 have been observed from a natural gas-air flame by Year and
colleagues (Ref. 29). Rotational Raman lines of H2 were also observed. No estimates
of sensitivity were given.
CS
Emission from CS has been observed in flames containing sulfur compounds
(Ref. 30) and from the photolysis of CS2 and OCS (Ref. 31). Laser-induced
fluorescence would require absorption in the region of 2575A (0,0), hence a
frequency-doubled dye laser is mandatory. The lifetime of the A -^I state is 176
nanoseconds (Ref. 32).
NH
Emission from the imino radical NH is seen in flames of nitrogen-bearing
compounds in the near UV with maximum intensity at 336oA (Q0,0) (Ref. 33). The
A 3ft state has a lifetime of 1*55 nanoseconds (Ref. 32); hence, absorption is
moderately strong. This wavelength region is accessible by means of frequency-
doubled dye lasers.
17
-------
NO
Until recently, nitric oxide has teen a difficult molecule to excite with
available laser sources and doublers because the strongly absorbing system, the
y-system (A-X) absorbs mainly below 2260JL With the relatively new doubling crystal,
potassium pentaborate (KBP) laser-induced fluorescence has now been observed by
Zacharias and coworkers under laboratory conditions at low pressure, 0.03 Torr
(Ref. 3*0. Doubling efficiencies into this region are relatively poor, however,
about 0.5 to 1 percent. Because of the extreme interest in this particular molecule
as regards pollution, it is important to find a reliable means of measuring its
concentration: An alternative is to attempt laser-induced fluorescence from the
B-band (&-X). The g-band (lifetime = 2-U microseconds) (Ref. 32) is weaker than
the y-band (lifetime = 200-300 nanoseconds), (Ref. 28) but occurs in a wavelength
region more amenable to efficient frequency doubling. This is true even though
the B state lies higher than the A state. This arises due to large shift toward
larger interatomic separations of the potential energy curve of the B state, causing
a large Franck-Condon shift. Thus, the maximum intensity bands (in emission) are
0-10, 0-9, 0-8, etc. This in turn means that laser absorption would have to be
from upper vibrational levels (hot bands) of the ground state. The low upper
vibrational level populations would most likely mitigate against the frequency doubling
efficiency gains.
Much of the work to date on NO has been performed using conventional light
sources. Quenching studies have been carried out by numerous workers (Refs. 35,
36).
OH
The resonance fluorescence of the OH radical has been intensively studied by
Wang and coworkers at the Ford Scientific Laboratory following the initial observa-
tion by Baardsen and Terhune (Ref. 37) of the same laboratory. Early efforts were
directed toward measurement of the concentration of OH in the atmosphere (Ref. 38).
That laboratory has also measured the ground state population distribution of OH in a
methane-air Bunsen burner flame (Ref. 39)- Quite recently (Ref. Uo), a detailed
study of the quenching effects of HgO and N2 on the OH radical was performed, along
with the saturation behavior of the absorption transition under high laser flux.
These experiments employed a pulsed, tunable dye laser which is frequency
doubled with ADP to the desired wavelengths at 2526A and 2822A, the P-|_(2) and P^l)
transitions respectively. Fluorescence is observed at 31^5A (l-O) and at 3090A (0-0).
Concentrations as low as 10"* cm^ have been measured in air. Becker's group at
the University of Bonn has also measured OH concentrations produced by a chemical
reaction in a flow tube, with a pulsed dye laser (Ref. Ul). A sensitivity range
comparable to that found by the Ford Scientific Laboratory was obtained. Additionally,
the quenching rates for ^0, H^, N2j He and Ar were measured. The water quenching
rate was highest with a rate constant of U.5 x 10"^ cm3 molecule' sec~l, nearly
gas-kinetic; however, the other quenchers were also quite efficient with the
following values given: H^, 66.5 x 10'11; Ng, 1 x 10'11; He, 1 x 10'12; Ar, 5 x 10"12.
18
-------
so
Emission from SO has been observed from sulfur containing fuels (Ref. U2).
The detection and measurement of this particular species would appear to be
important in unraveling the fate of sulfur in combustion. The main system,
B -» X, occurs in the near UV from 39UoA to 2UOOJL The strongest bands in emission
are: 0-10, 0-9, 0-8; which again indicates a strong Franck-Condon shift. These
bands may be more accessible than the NO 0-bands, because of the smaller vibra-
tional frequency (1150 cm"1 in SO compared to 190U cm"1 in NO); hence, SO is more
likely to have "hot band" transitions.
Polyatomic Molecules
Spectroscopic data for polyatomic molecules of importance in combustion studies
are given in Table IV. The Table also includes some hydrocarbon fuel molecules.
Because of the large number of vibrational modes they possess, these molecules could
exhibit interferences with desired Raman frequencies. Additionally, representative
aromatic ring hydrocarbons are given. These molecules are known to be formed in
combustion processes and again may be potential interferences. In these cases,
broadband fluorescence is produced from the aromatic hydrocarbons, which absorb
over a very broad spectral region, cf., Table IV.
A considerable amount of information is given in Table IV. Note that under the
species chenlical symbol, it is indicated whether or not the molecule is a radical.
If so, the lifetime of the ground state is of the order of 10~3 seconds. This fact
doesn't preclude laser spectroscopic measurements, but it certainly mitigates
against a conventional chemical method. The second column of the Table lists the
electronic term energy in wavenumbers. The third column shows the electronic state
as Xj A, B; the ground state, first excited, second excited, etc., and the symmetry
species of that particular state according to the symmetry point group (column U)
that the molecule belongs to. Also given with the electronic state symbol is the
spin multiplicity as a left superscript, 1 for singlet (total spin = 0), 2 for
doublet (total spin = j), 3 for triplet (total spin = l), etc., just as for atoms
and diatomic molecules.
The point group designation given in column k completely specifies the symmetry
properties of all of the electronic states (as long as the point group doesn't
change) and of all of the vibrational and rotational states of the molecule. The
reader unfamiliar with group theory can still picture the molecular geometry by
noting the following simplified rules: a C or D denotes an axis of rotational
symmetry given by the subscript 2, 3, U, etc. for a 2-fold, 3-fold, ^-fold symmetry
axis, etc. The infinity symbols, Doo, Coo are used for linear molecules (infinite-
rotation axis). The difference between Cp and Dp is that the D symmetry has addi-
tionally, p-C~2 axes perpendicular to the main symmetry axis. The subscripts h and
v denote horizontal and vertical (to the main rotation axis) planes of symmetry.
19
-------
T*nB Electronic
TABLE IV
66,6^,68
sreCTHOSCOPIC DATA FOF POUfA'TOHIC MDIaBO/LBS
RaBwi or
Infrared
Speciea
(RAD)
<*3
*
C21L
(acetylene)
(etHyl-M)
(-tcajl
(benzene)
^10%
( n&phibalene)
(Jtvffi™,
"2
Enerqj State Point Croup normal Vibrations! Frequencies Active
0 X JIL DOJJ v* R
\H I,B
70637 B V D^,
0 X 2Aa D,. v, R
(Planar ^ I.H
trljoml) vj (580) I,»
46205 B 2A, D.J,,
0 X !AJ T4 vj 2916.5 "
Tttrahedral ^ 1533.6 R
Pyra«id M, 3019.5 I,B
^ 1306.2 I,R
68730 A 1P2
0 X ^ 1^ \^ 3372.0 R
(Linear syn) ^ 197J-5 R
Vg 3294 .6 I
Mi 6-11.7 R
v^ 729.1 1
42197 A \ C2h
(Bent)
0 X 'A Da ^ (H) 3026.0 ^ (I) 9»9
Planar ay« \g (R) 1622.0 ^ (B) 950
v, (R) 1342.0 xt (I) 3105
^ oeith 10^7.0 v' (I) 810
\^ (R) 3132.0 ^ (I) 2988
%6 R 1236.0 v^ I 1443
< 23700 a \u (DJ.J)
40015 A H^ 1^^
j-fald biis, ^ R 1J86.4 \g I,F 1436
«ym stagg«rel v. R 94*. 9 vq I,R 320
or eclipsed ^ Mitb (278) v".0 R 2963
UHK . I 2S95.7 -", B )460
'4 I 1379.1 vjj B (1155)
6 x Vl, D6h ^3162 R
planar ^995 R
bexa«. vj 3O47 R
2951C. . \.^ ""^ """« R*™11
38086 A 'LJ,
"" " ''IE ^i-ii
planar syn
~ 303CO A ?
0 X *A.^ £1,^
planar ayB
26000 A ?
OX1! Ikn vj 1388 B
Llix ar aya w^ 667 ItX
v 2349 tjR
Rotational Conatants Major Electronic Trafl»l;loa»
£ ' 3-» B~n
C0 1415A
"o '•cr'9
o 180.0
A. (me
B0 (9.57)
co B-;
?0 1.079 216OS
a 120.0
B0 5.2412
r° 1.094 (1455 • 15001)
0
B^ 1.1766
C^ A-X
r0 CH, 1.058; CC, 1.206 2370 - 23OOA
a 120.0
=o 1-00>
r^ 1.066; rcc . 1.339
oHCH * 117.6°
a - X 2600 - 340CA
A - I 1600 - 2100X
A0 2.661
BO 66i-0
C0 A — X
r „ - 1.536; rnjl - 1.093 1350 - 16OO c&ntlnuoo* ABSN
oftfti . 103
»o
Bp 0.1396
r°c - 1-397: '.„ * 1.08k
tr 12C°
t — x 3400 - ynxt X
A — x zrrc - 2t7c ^
A-X WOO . 2400 8
A —X 3OOO - 38DOA1
A-X 3800 - 300oR
A-X 3800 - 4800 if
B0 0.3902 A-X HOC - 1700X
"o
1.161
«° 180.0
- 3800 f
20
-------
TABLE IV (COS'T)
SPBCTRCecOPIC DATA FOR POLYATOMIC HDLECUUS
Term Electronic
Specie* Energy State Point Group normal Vlbratlonal Prequenel.
CBjO OX \ Cjy uj 2766
v! 1500
V 2843
* 1251
25194 a 3A C, '
26186 A V Ca
BOO OX V c vj (2700)
«j 1083
»; 1820
9291. A JA"
iy> 0 X \ C2v .j 3657
(bent) xu 1594.7
^ 3755.7
53800 A Hj CJV
BC5 0 X H:" X 10000 - 32OOa
B - X 2580 - 235o5t
A — X 6650 - 5000A
«,I A 2.:~
R'! '» -^
~l 1-*3>'
» 115-5
a— X 3900 34CCA
A— X >00 - SoOOA
Coooeve, C. F. aol
Fajans, E. . Trana. for Soc.
£, 5X1 (1936).
21
-------
Two special point groups are T the former is used for the symmetry of the
regular tetrahedron (CH^), the latter, for the regular octahedron (SFg). A concise
but complete description of point groups is given "by Herzberg (Ref. ^3)- A very readable
account of group theory and its applications is given by Cotton (Ref. U4).
The set of normal mode vibrational frequencies is given in the next column.
The numbering of the particular vibrational modes for a given molecule follows that
of Herzberg (Ref. ^3) where one may find illustrations of the atomic motions. For
example, the v-[_-mode is the totally-symmetric stretch of a given molecule and is
always strongly Raman-active. This vj_ mode is not observed in the infrared if the
molecule has a center of symmetry because there is no induced dipole moment caused
by the nuclear motion. This is an example of a general rule, -the mutual exclusion
rule, that for molecules with center of symmetry (inversion symmetry, x, y, z -* -x,
-y, -z), those modes which are Raman active are infrared inactive and vice versa.
The Raman and/or infrared activity of the normal modes is indicated with an R or
I, respectively, or both, if the mode is observed by both techniques. There are
some vibrational modes which are inactive in both Raman and infrared, e.g., the
torsional mode of ethane, v^. These modes are marked "neither."
The rotational constants along with bond lengths and angles are given in the
next columns. The rotational constants are given by A = h/8rr^clA, where h is
Planck's constant and c, the speed of light. IA is the principal moment of inertia
about the A-axis. Similar definitions hold for B and C. The principal axes system
is the cartesian coordinate system for which the moment of inertia tensor is diagonal-
ized. For a linear molecule one is concerned with only the moment of inertia about
an axis perpendicular to the molecular axis. A symmetric top molecule has two prin-
cipal moments of inertia identical. A necessary and sufficient condition for this
to be true is that the molecule have a 3-fold symmetry axis (or higher). A spherical
top has all three principal moments equal, e.g., methane and CF^. Because of these
equalities, rotational constants which are equal are not repeated in the Table but
so indicated by a blank.
The major electronic transitions are shown in the last column. Absorption is
indicated by a right-to-left arrow, viz., B «- X, and fluorescence by the opposite.
With polyatomic molecules, fluorescence is often considerably red-shifted (sometimes
termed Stokes-shifted) from the position in the spectrum where absorption occurs.
This effect is more pronounced with polyatomic molecules than for diatomic molecules
because of the more rapid vibrational relaxation in the upper electronic state.
For some very large molecules, such as the aromatic hydrocarbons, absorption and
emission overlap very little, just at the 0-0 band. This phenomenon is indicated
in the Table. Fluorescence is not always observed following absorption. The
molecule may dissociate or predissociate, or fluorescent quenching may be so severe
that few molecules radiatively relax.
22
-------
The methylene radical absorbs deep in the vacuum UV, precluding its measurement
by means of laser-induced fluorescence. Since the vibrational frequencies are not
known, conventional Raman scattering or CARS cannot be applied either at this time.
CS3
The methyl radical has its strongest absorption bands in the vacuum UV; however,
there are some bands in the region of 2160 A. It would be difficult to reach these
bands with a frequency doubled dye laser, but in principle it could be done. The
frequency of the Raman active vj_ mode is unknown, so that Raman/CARS cannot be used
at this time.
CHu
Laser-induced fluorescence is eliminated because of the deep UV absorption.
Raman/CARS techniques could utilize the strong Raman active V]_ mode. It should be
noted that because methane is a spherical top it possesses no rotational Raman
spectrum. CARS has been observed in the v^_ band of CHj, using CW lasers (Ref.
Acetylene is a linear molecule in the ground state, but bent in the first 0
excited state. The absorption between these two states takes place between 2100 A
and 2370 A which would be accessible to frequency-doubled dye lasers. Fluorescence
has been observed from electric discharges in acetylene (Ref. U2). The v-j_ frequency
at 3372 cm"1 is strongly Raman-allowed and should be easy to observe by conventional
Raman or CARS spectre scopy.
Ethylene has a double bond rather than a triple bond as in acetylene and absorbs
further in the UV for the allowed singlet -singlet transition. Laser-induced
fluorescence is doubtful at best. The Vj_ C-H symmetric stretch is amenable to
Raman/CARS. It should be pointed out that for all carbon-hydrogen compounds the
CH stretch occurs in the neighborhood of 2900-3100 cm"1 and there may be interferences
with other hydrocarbons.
Ethane is0a saturated hydrocarbon and for this reason absorbs far in the vacuum
UVj 1350-1600 A. Moreover, the absorption is continuous, indicating dissociation,
hence, fluorescence techniques are not applicable. Raman/CARS techniques can be
used, however. In fact, the many Raman allowed frequencies could cause interferences
with the measurement of some desired species.
23
-------
C6H6' C10H8' clUHio
The aromatic hydrocarbons, benzene, naphthalene, and anthracene are listed to
indicate the potential for interference for both fluorescence and Raman/CARS
techniques. Note that the absorption and fluorescence of these species covers a
large portion of the near UV and visible spectrum. The large number of normal modes
are a source of interference for Raman/CARS methods. It should be pointed o'lt that
these hydrocarbons can be formed in combustion processes.
CO.
Carbon dioxide absorbs in the vacuum UV, eliminating laser induced fluorescence.
Raman or CARS methods are applicable to the detection of this molecule. Weber and
co-workers (Refs. U6, Uy) have performed high-resolution spectroscopy on C02 in the
gas phase, including a measurement in a low pressure electric discharge.
CH20
Formaldehyde absorbs in the near UV as indicated in the Table. Laser-induced
fluorescence has been detected in atmospheric air using a frequency-doubled dye
laser in the region 3200-3U50A (Ref. U8). The sensitivity was of the order of
5 pphm. The estimated quantum yield under the conditions of the experiment (i.e.,
with quenching by H20 and C02) was ~ 10"^. N02 and S02 did not interfere. It is
difficult to predict if a similar method would yield such good results in a flame
environment.
HCO
Little is known about this radical except that emission (termed Vaidya1s
hydrocarbon flame bands) has been observed from hydrocarbon flames (Ref. 30). The
broad emission range from this species is certainly a source of interference
for both laser-induced fluorescence and Raman/CARS.
HCN
Hydrocyanic acid absorbs in the far UV in the region 1600-1900A, as indicated.
This fact precludes laser induced fluorescence. The vj_ normal mode vibration,
essentially the CH group vibrating against the N atom, is very strongly observed in
the Raman spectrum, thus permitting conventional Raman or CARS methods to be attempted.
H20
Water does not absorb in the visible or near UV region of the spectrum. However,
there are vibrational overtones which appear in the near IR in both emission and
absorption. Laser-induced fluorescence is not applicable. The symmetric stretch
vibration, \>±, is strong in Raman scattering, and hence, is amenable to both Raman
2U
-------
and CARS techniques. Lapp and co-workers have performed extensive Raman scattering
studies on water vapor (Ref. ^9). The CARS method has been successfully applied to
H20 in the liquid phase (Ref. 50). The V2 and v^ vibrational modes are also Raman-
allowed but weakly so. However, these modes, along with the allowed vi mode, serve
as potential interferences to measurements on other molecules.
This radical absorbs in the visible region of the spectrum between U300 A
and 9000 -A. Laser-induced fluorescence has been observed by Welge and co-workers
(Ref. 51) using both a pulsed and CW dye laser. The Iffl^ radicals were produced
by the photolysis of ammonia. Quenching rates for several gases were measured to
be of the order of 10~9 cnP molecule"-'- sec" , which is gas kinetic. The lifetime
of the W-2 radical is estimated to be several microseconds. Because of the very
rapid quenching rates, laser-induced fluorescence measurements of NH2 ixi an
atmospheric pressure flame would be difficult to perform. However, the possibility
of fluorescence measurement should be assessed experimentally. The VQ_ symmetric
vib rational-mode, although not yet measured, should be strongly Raman allowed,
hence amenable to Raman/ CARS techniques.
Laser-induced fluorescence in ammonia would be difficult to observe because
there is only weak absorption in the quartz UV, wavelengths above 2000 A. The
symmetric VQ_ vibrational mode is strongly allowed in Raman scattering, hence should
be easily measured by Raman/ CARS methods. Ammonia, like water, may serve to provide
interferences to the measurement of other molecules.
A great deal of work has been directed to the detection of NOg in the atmosphere
by means of laser-induced fluorescence (Refs. 52, 53> 5^)« Although these attempts
have met with some success, it is problematical that this technique can be applied
to the hostile conditions existing in a hydrocarbon flame. W02 has been measured
in a hydrogen-air flame, up to the position of the flame front (Ref. 55). Beyond
this point, fluorescence was not detectable. The lifetime of the excited state
is ~ 50 microseconds, hence is easily quenched by the major flame constituents.
The strongly Raman- allowed v-^ mode at 1319 cm"1 would be suitable to Raman/ CARS
techniques.
Apparently very little is known about this molecule. Absorption has been
observed in the region 5^00 to 6600 A. Nothing is known about the lifetime or the
vibrational frequencies.
-------
so2
o
Sulfur dioxide absorbs in the near UV starting at 3500 A and extending to below
2000 A. Fluorescence has been observed in air at atmospheric pressure; this is
possible because the lifetime of the excited S02 is a few nanoseconds; hence,
quenching is not too severe (Ref. 56). Fowler and Berger at UTRC performed an
experimental study (Ref. 57) of laser-induced resonance fluorescence in S02 at
3000 A with a view toward remote detection. A commercial instrument based upon
the fluorescence caused by a pulsed, incoherent UV source is manufactured by
Thermoelectron Corp. (Ref. 58). The instrument is stated to be sensitive to a few
ppm of S02. Recently, Jahnke and co-workers 'at the Environmental Science Research
Laboratory of EPA have assessed quenching effects in this instrument (Ref. 59) and
found that the composition of the gas is quite Important due to quenching by oxygen.
This problem can be taken care of by means of suitable modifications. It is not
obvious from-the success of this technique if laser-induced fluorescence from S02
can be used to measure S02 concentration in the presence of more serious quenchers
such as water, radicals, etc. S02 has been detected in a stack plume by means
of laser Raman radar (Ref. 60). A Q-switched frequency-doubled Nd:YAG laser was
employed and the scattered light collected from the test volume was passed through
a narrow band filter. Photon counting with noise subtraction had to be employed.
Similar techniques have been employed with good success to atmospheric measurements
by Hirschfeld and associates (Ref. 6l) and by Kobayasi and Inaba (Ref. 62).
Raman Cross Sections
Absolute differential Raman cross sections for many species of combustion
interest are given in Table V. Values are given for excitation by three different
wavelengths 3371 A (nitrogen laser), ^880 A (argon ion laser) and 5320 A (frequency-
doubled neodymium). The 5320 A valuers were calculated from the 3371 A measurements
by scaling with the Xjp relation. A few values are given for pure rotational
scattering. In general, note that there is little difference between the magnitudes
of the cross sections for a wide variety of molecular species.
Interferences
Table VI presents some possible interferences to the measurement of various
species by means of\ Raman scattering or CARS. The Table presents the strongest
Raman-allowed transition for a given species in wave numbers, and the 'Stokes and
anti-Stokes Raman wavelengths relative to the frequency-doubled Nd laser line,
5320 A. Interferences are then listed as Raman interferences or fluorescence
interferences. For the former case, interference would originate from a similar
Raman process with an interfering molecule of nearly the same vibrational frequency;
hence, the interference would occur at both the Stokes and anti-Stokes wavelength.
26
-------
TABLE V
RAMAN CROSS SECTION FOR MOLECULES OF INTEREST
(Units of 10-30 Cm2/sr)
Species
^2
%
°2
NO
N02
NH3
CO
co2
H.O
•HgS
soa
C*4
C2H4
C2%
C6H6
SF6
CCL.
Vibrational
_Frequency
2330.7
4160.2
1556
1877
V-L 1320
u, 754
3334
2145
vj_ 1388
2^ 1285
3651.7
2611
1151.5
VL . 2915
v3 3017
V-L 3020 '
v2 1623
v3 993
v1 3070
v2 991
775
459
f^*69
3-5
2.8(Q)
4.6
3-3(Q)
1.5
51.0
24-. 0
11.0
3-6
4.2
3-1
7.8(Q)
19-0
17.0
21.0
14.0
16.0(Q)
5-MQ)
30.0
44.0
12.0
26.0
Vibrational
.46
•37(Q)
.65
.2
7-37
3-63
1.3
.48
.6
.^5
• 9
2.4
2.5
2.6
1.7
1.9
.76
3-7
5-6
1.8
4.04
Rotational
1 - kftflO?
AiT^vp — *fOOU**
f 4 880 A ) id
.68 5-4 (6 -» 8)^71^
1.32 i.o (1 ->o)
.88(Q)
.72 14.0 (7 -*9)
-15
2.75
0.27 (6 -»er72^
.77 53-0 (16 -»18)(71)
.49
1.473
3-5
2.9
3-3
.88
3.8
5.0
27
-------
TABLE VI
POSSIBLE IHTERFEREHCES FOR DETECTING DESIRED
SITCIES BY RAMAN/CARS METHODS
Species
C
0
C2 '
CH
Clt
CO
cs
H2
»a
HH
HO
o2
OK
Oifc
C-H
2 2
C2H1.
C2H6
C6H6
co2
CH20
HCH '
H2°
NH2
NH3
K°2
so2
Raman Shift
(en"1)
1-3
226
1832
2633
201-5
211-3
1272
1.169
2331
3018
1876
1556
3665
2916
3372
3026
2953
3162
1388
2766
3311
3657
(11-97)
3337
1319
1151
Stokes
Raman
5332
5385
5900
6186
5969
6001.
5706
6836
6073
63U9
'5901
5800
6609
6297
6383
631.1
6312
6396
577U
6238
61-57
6605
5780
61.68
5721
5667
Anti-Stokes
Raman
5308
5257
1.817
1.666
1-798
1-775
1-983
1*351*
1-733
1-578
1.837
1-913
1*1*52
1*605
1*510
U582
1.598
1.551.
1-951.
1.638
i-5?3
U5l
1-92?
U51P
1-971
5013
Ranan Fluorescence
Interferences Interferences
HH (AS)
HCO CH(AS)
CH , CH, CN(S), CN(AS)
HCN CH(AS), HCO(AS)
CH(AS),HCO(AS)
H02
CH(AS)
C2(AS) C2(S)
C HL CH 0(AS)
CH 0 CH(AS)
CHU
H?0 CN(S), CH20(AS)
CH CH(S), CM(AS)
m CH(AS)
3
C H CH(AP)
2 o
C^ CH(AS), CH 0(AS)
Cu F* v vf\ f c\ ^tin/AC^
•^ £ > * r^ 1 "v_\OJ. \.HnU\Ad^
26 2 ii 2 ' 2
CgHL,EC CK(AE)
HOg(F)
NH3 C2(S),NH2(AS)
OH CT:(S).CH 0(A£)
C,H C,(£),SK.(AS)
£ d e c
CS,C02 C5(S)
CH20 CS(A£)
Stokes Anti-Stokes
* and X
Raman Raman
are relative to \ • 53208
£XC
— Bo entry indicates no obvious interference from other noleculei from this
Table.
(S) Stokes. (AS) Antl-Stokci
( ) Indicates doubtful value
28
-------
For the case of fluorescence interference, the emission from molecules present in
the flame which are excited by whatever means, i.e., laser irradiation or chemi-
luminescence, is taken into consideration. For either case, overlap was considered
to occur if lines were within 20 to 30 cm'1 because of the broadening in the
rotational wings.
The Table is by no means exhaustive and the reader is cautioned that interferences
may exist where none is indicated. It should be noted that most of the fluorescent
interferences come from CH, CN, NH/^ and formaldehyde, and a few other species.
Obviously then, the extent to which these species interfere depends upon their
concentrations in the flame. Unfortunately, for a given flame there is no way to
control these concentrations. Hopefully, with suitably narrow slits and/or appro-
priate time gating, sufficient discrimination against these interferences can be
obtained.
Applicability of Techniques
In Table VII, the applicability of the four potential measurement techniques,
laser fluorescence, spontaneous Raman, near-resonant Raman and CARS, have been
summarized for a.n of the species considered in the preceding text. Potential
applicability is indicated by a scale ranging over excellent, good fair, poor and
not applicable. Also appearing is the label indicating insufficient information,
or an untried method. Detection of 0 and C atoms by means of the electronic Raman
effect (discussed before in the section on atomic species) is listed as possible
under Raman, near-resonant Raman, and CARS.
It must be pointed out that this assessment of applicability is not absolutely
certain nor is it meant to be. Rather, the Table should serve as a guide to which
method is most appropriate for the measurement of a given species. Various factors
were considered such as absorption region, lifetime, concentration, etc.; inter-
ferences were not accounted for in this assessment since they were considered in
Table VI and, depending on the circumstances, may not be troublesome.
29
-------
TABLE VII
SIMSAKY OF SPBCTROSCOPIC APPLICABILITY OF TBCHHIftUES
Species Fluorescence
C NA
H NA
0 NA
li NA
<:„ E
CH E
CM E
CO NA
CS F
E, to
N~ NA
Nil E
NO E
Oj NA
OH E
CHj NA
CB, RA
CHjj NA
Cyt, -.
CgH,, NA
CjHg NA
CfiHg E
ClA E
C»«H> E
C02 NA
n^O E
HCO !
ECN F
HjO NA
Ifflj F-G
HH, NA
H02 P
«o3 t
S02 G
S03 7
E excellent MA
C good ?
T f»ir
P poor
Hunan
possible
NA
possible
NA
E
P
P
E
P
E
E
F
G
E
G
:
?
E
E
E
E
G
G
G
E
G
?
G
E
G
E
G
?
E
1
not applicable
N«er-Ressr,ar.t
Ramar
posslblf
NA
possible
NA
E
P
P
NA
P
NA
NA
P
P
NA
G
NA
NA
NA
NA
NA
NA
P
p
G
NA
NA
1
NA
NA
C
NA
G
?
P
7
CA-3
pOSSlbl*
HA
possible
SA
f
f
P
E
P
£
E
3
-
I
G
?
:
G
C
G
G
F
r
F
E
a
:
G
E
F
G
G
7
G
f
not enough Inforratlon or untried
30
-------
PRACTICAL CONSIDERATIONS
Practical combustion devices possess flames which, generally, from an
instrumentation standpoint, differ markedly from flames often investigated in
fundamental or laboratory devices. Many diagnostic approaches developed for use on
relatively benign flames in ideal laboratory environments are often unsuited for
practical application. Consequently, in evaluating any diagnostic approach, the
ultimate environment of application must be factored into any decision concerning
the feasibility of a given technique. The application of interest here is a research
scale furnace. Liie most practical combustors it contains flames which are highly
luminous and particulate laden when burning a hydrocarbon fuel. The high luminosity
levels preclude the use of a continuous wave laser source for most diagnostic appli-
cations. However, use of a pulsed laser source engenders a variety of laser induced
particulate effects which can-mask detection of the sought-for signal. In addition,
practical flames are generally highly turbulent which leads to large temporal varia-
tions in medium properties. In measurement situations where signal averaging is
required to enhance signal/noise ratios, averaging over these temporal fluctuations
often introduces ambiguity into data reduction and interpretation. In addition
there are other factors, such as the presence of windows with limited aperture, and
large distances from the device periphery to measurement location, which constrain
diagnostic freedom. These factors often decrease signal to noise by introducing
additional noise, e.g., window fluorescence, and diminishing signal strength in
intensity dependent processes. In addition, there are other effects common to both
laboratory and practical devices, such as gas breakdown, which need to be considered
and which limit laser source intensity. In this section these various considerations
will be reviewed. In the sections which follow, these factors will be taken into
account as the feasibility of the various diagnostic techniques is assessed.
Sources of Noise
Background Luminosity
The laser light scattering diagnostic techniques to be considered here are
generally situated in the visible or near UV portion of the spectrum due either to
cross section scaling or the location of electronic resonances. Consequently, con-
cern is centered in flame source radiations in this spectral region, hence, the use
of the photometric term luminosity. Luminosity in this region is comprised pri-
marily of chemiluminescent emissions and the gray/blackbody continuum from soot and
other particulates (Ref. 30). The former emissions arise from electronic states
excited during chemical reactions. The emissions are generally narrowband although
continuum radiations are also present. The narrowband emissions consist either of
line (atoms) or band (molecules) structure, specific to the emitting species and in
31
-------
distinct spectral regions. For certain diagnostic processes, their possible inter-
ference can be avoided by appropriate laser wavelength selection. In premixed, near
stoichiometric flames these emissions are dominant. In hydrocarbon-fueled diffu-
sion flames, however, their contribution to the total luminous intensity is generally
small compared to the soot blackbody continuum. In certain instances (Ref. 30)
some fine structure may exceed the soot continuum in certain spectral regions.
An extensive series of luminosity measurements have been performed on the EPA
"Rainbow" furnace and reported in Ref. jk- as spectral radiance. A Gamma Scientific
Model 2020 radiometer (Ref. 75) was employed to measure the spectral radiance at
various locations In the furnace operating with various fuels and swirl vane com-
binations. ;For an optically thin flame, it is more appropriate to use spectral
radiation energy densities to account for the actual volume subtended in a particular
instrumentation approach in a manner to be illustrated shortly. The conversion to
radiation energy density was made by dividing the spectral radiance by the depth of
field of the radiometer as described in Appendix I. In Fig. 3, several converted
measurements are displayed which illustrate the range of radiation energy densities
one is likely to encounter. As may be seen, depending on the measurement location,
fuel employed, and spectral region of interest, the radiation energy densities
i O ^
range from a few tenths to a several thousand nanowatts/cm-3 A sr. Also shown in
Fig. 3 is the radiation energy density emitted by a dispersion of ^00 A diameter soot
particles at 2000°K, at adensity of 10" cm~3, corresponding to a rather modest mass density
of about 7«6(10~9) grams/cm3 or volume fraction of 3»^(lO~9). This calculation was
performed by merely summing the individual particle radiation contributions as cal-
culated from the Planck radiation formula. Since the dispersion assumed can be
shown to be optically thin, aggregate extinction effects, i.e., absorption and
scattering,can be neglected. As seen the spectral variation of the measured radia-
tion energy density is very nearly blackbody and is easily accountable in magnitude
by a soot dispersion of moderate density. For a given mass density or volume
fraction of soot, larger sized particles result in less luminosity due to a decreased
surface/volumeoratio. A more complete discussion of soot sizes is given in the next
section. hOO A was used in the Fig. 3 calculation for illustrative purposes, and
because it corresponded to the average particle diameter obtained in measurements
at UTRC on an air-sustained laminar propane diffusion flame using an absorption/Mie
scattering technique, Ref. 76. For comparison with Fig. 3 it should be noted that
a ten watt Argon ion laser will produce a Raman scattered power of about 10"^-
watts/sr over a centimeter pathlength from flame nitrogen at atmospheric pressure
and 2000°K. Roughly then, note that even for the lowest radiation energy density
displayed in Fig. 3 that the background will exceed a high power, continuous wave
laser Raman signal by at least an order of magnitude. This means that in luminous
environments, pulsed laser sources are generally required to produce signal powers
comparable to or preferably in excess of the background power.
The signal/noise ratio attained will actually depend on details of the optical
collection system and bandwidth. To illustrate this point, consider the signal/
noise for a Raman experiment in a luminous background for the optical collection
32
-------
BACKGROUND LUMINOSITY IN EPA RAINBOW FURNACE
FIG. 3
10,000
o<
tr
w
ro
5
CJ
o
I-
c/5
O
r>
_i
01
EC
D
1000
100
10
0.1
SIDE WALL,FUEL OIL, ALL VANE POSITIONS
-------
system of Fig. U. There a double lens system is used to collect scattered light
and focus it upon an aperture. The double lens system, as opposed to a single lens,
possesses the advantage of being able to probe different sample volumes simply by
translating the forward lens. The Raman signal power S is given by (Ref. 8)
S = P.n — n e a (1)
where Pj_ is the incident laser power; n, the number density of scatterers in the
appropriate initial quantum states;^, the Raman cross section; Q, the solid accep-
tance angle;;e, the collection efficiency; and &, the Raman sampling extent. For
right angle scattering and a unity magnification optical collection system, I is
simply set by the aperture diameter, A. For coaxial or backscattering, JL. , is
approximately equal to .the depth of field 2AF where F is the f number of the indi-
vidual lenses, i.e., f/D where f is the focal length, D the lens diameter. The
background luminosity N collected is
N = (RAX Q e V (2)
where (R is the radiation energy density; AX, the optical bandwidth; and V the
volume subtended by the optical system. V is approximately cylindrical with
diameter A, and a length equal to the depth of field.
V = ^ A2 2FA (3)
Substituting for A in terms of the Raman sampling extent, one finds
_ - 3 _ n 1 3
-L~2 a. 11 ~ 6 i?2 11 "
Note that
V.
i.e., for a given Raman sampling extent, the volume subtended in right angle
scattering exceeds that "seen" in backscattering. For example, with F = 5 optics,
this ratio is 103. This means a right angle scattering approach will collect three
orders of magnitude more background than the equivalent coaxial approach. Physically,
the reduction with backscattering occurs because the Raman scampling extent is
matched to the optical system depth of field. Another point worth noting is that
for any geometry, the signal/background noise scales as
-------
FIG. 4
LIGHT SCATTERING OPTICAL COLLECTION SCHEMATIC
35
-------
S/N
j
In any geometry it is thus desirable to maximize the spatial resolution. For example,
a reduction in Raman sampling extent from 1 cm to 1 mm will result in a two order
of magnitude increase in S/N. Of course, the sampling extent must be kept large
enough to collect a statistically significant number of photons on a pulsed basis or
expedite photon collection on a continuous wave basis. Similar conclusions would
also apply to the case where the aperture A is rectangular, e.g., the entrance slit
of a monochromator, although the results are analytically less tractable. Quantita-
tive signal/noise calculations will be presented in later sections for each diagnos-
tic technique. Background luminosity can also be suppressed, if, as is sometimes
found (Ref. 77), it is slowly modulated by combustion instabilities, aerodynamic
effects (e.g., swirl) or turbulent fluctuations. In these instances electronic
filtering techniques can be used to suppress the gross excursions from entering the
signal processing equipment. As a final note, for light scattering processes pro-
ducing polarized signals, the background can be halved by use of a polarization
filter.
Farticulate_s
In the previous section, it was seen that particulates are primarily responsible
for the large luminous backgrounds characteristic of hydrocarbon-fueled diffusion
flames which loom as a major source of noise in laser light scattering diagnostics.
Unfortunately, that is only part of the noise problem that particulates engender.
In interacting with the signal producing laser source, particulates can fluoresce
(Refs. 78, 79, 80, 8l, 82), Raman scatter (Refs. 8l, 83) and incandesce (Ref. 8U).
With pulsed laser sources, incandescence has been found to be especially severe.
Particulates may range in size from a few tens of Angstroms in diameter to
several tens of microns. Particles a few hundred Angstroms in diameter (Ref. 76)
to a few thousand Angstroms (Refs. 85, 86) appear typical in low molecular weight
hydrocarbon-fueled diffusion flames. With higher molecular weight liquid fuels,
size distributions skewed to larger particle sizes have been found. For example,
measurements (Ref. 87) made in a model gas turbine combustor burning JP-U, indicated
a particle size distribution which varied with particle radius as r ^ over the
diameter range from 0.01 to
Fluorescence
Laser induced particulate fluorescence could pose a serious noise problem for
laser light scattering diagnostics. Fluorescence generally occurs over a large
wavelength extent on the Stokes side of the exciting laser source and is not easily
avoided. In Raman probing of a gas turbine exhaust, Leonard (Ref. 78) encountered
severe hydrocarbon fluorescences which precluded NO detection using a pulsed No
laser at 3371 A. In fact, this phenomenon was utilized ultimately as a total hydro-
carbon content diagnostic.. However, Raman spectra from major species were generally
36
-------
observable with the N2 Raman signal-to-noise decreasing to unity as the hydrocarbon
fraction reached 1000 ppm. Fluorescence excitation studies reported in Ref. 78 on
jet oil indicated fluorescence could be significantly curtailed at laser wavelengths
above 3750 A. In Ref. 80, in combustor exhaust measurements at 51^5 A, strong
fluorescence was found to swamp the Raman spectrum at exhaust temperatures below
1100°K. The fluorescence was believed due to incompletely burned pyrolyzed products
of high molecular weight. Following the lead of Leonard, the authors also suggested
the use of the laser induced fluorescence as a hydrocarbon probe. In Ref. 79
fluorescences from hydrocarbon aerosols excited at 1+880 A interferred significantly
with laser Raman studies of the exhaust of an internal combustion engine. The
fluorescent interferences were on the same order as the major Raman signals in
regard to signal intensity for hydrocarbon concentrations on the order of 5000 ppm
(as Glfy), corresponding to a hydrocarbon mass density on the order of 10"° gm/cm3.
Detailed excitation and fluorescence studies of a wide range of particulates are
reported in Ref. 8l where a variety of fluorides, oxides, chlorides, sulfates, and
phosphates were examined. In general, little fluorescence occurred for excitation
wavelengths above U500 A. Fluorescence of unidentified atmospheric aerosols has also
been studied in Ref. 82 using a continuous wave argon ion laser at U880 A. Based
upon the above results, it appears that hydrocarbon fluorescences are probable for
o
excitation wavelengths below 5000 A; for mass densities corresponding to concen-
trations of 1000 to 5000 ppm, these fluorescences may be comparable in signal strength
to Raman scattering from major constituents.
Raman §cattering_
Unlike fluorescence, Raman scattering from particulates is spectrally specific
and will not pose a problem unless the fundamental frequencies of the particulate
molecules coincide with those of the particular gas species under investigation.
Reference 8l contains Raman shifts and cross sections for a wide variety of particu-
lates. With the general exception of the sulfates, most particulates (classes of
oxides, sulfides, halides) have Raman shifts below 700 cm"1. The sulfate bands are
grouped in three regions: ^00-500 cm"1; 600-700 cm"1; and 950-1200 cm"1. Carbon
has Raman bands at 1360, 1580 and 21^0 cm"1 (Ref. 83) although the third band is
only seen from sputtered carbon and may not exist in soot. In carbon black, the
bands at 1360 and 1580 cm"1 are quite broad (hundred to several hundred cm"1) and
merge together. In comparison with other sources of noise from particulates, i.e.,
background luminosity, fluorescence and laser modulated incandescence, Raman
scattering from the particulates is not anticipated to be a major problem and will
not be belabored further.
Las_er_ Jtodulated Particulate_ In£andes£ence_
Laser modulated particulate incandescence occurs when the already incandescent
soot particles absorb the incident light scattering laser radiation, heat to
temperatures far above the ambient flame temperature and emit greatly increased
37
-------
quantities of blackbody radiation. This phenomenon has been studied in some detail
(Refs. 8U, 88) and represents a very serious source of noise in laser light
scattering diagnostics. This is particularly true for weak processes such as sponta-
neous Raman as will be apparent in a later section. For example, in an air sustained
laminar propane diffusion flame, the No Raman signal to laser modulated particulate
incandescence noise ratio is below 10~^ for ^00 kW laser excitation at 5900 A. Being
broadband, the laser modulated particulate incandescence is not easily avoided. Most
solution approaches to this problem yield some improvement in signal/noise, perhaps
two orders of magnitude, but the resultant signal/noise remains low generally
necessitating signal averaging. As mentioned previously, for turbulent environments,
this can lead to ambiguous data interpretation. Space does not permit a detailed
exposition of laser modulated particulate incandescence here. Suffice it to say
that depending on the laser flux, the irradiated soot particles are generally driven
to or slightly above carbon vaporization temperatures as seen in Fig. 5- There the
dashed curves are analytical predictions of particle surface temperature as a
function of laser flux. It is quite apparent that at flame temperatures where the
gaseous mean free path exceeds the soot particle diameter that heat conduction is
insufficient to restrain the particle surface temperature from reaching the vapori-
zation point. Consequently vaporization is the dominant heat transfer mechanism
and the surface temperature displays a weak dependence on laser flux. Also shown
are measured laser modulated soot temperatures (points) in an air-sustained laminar
propane diffusion flame (Ref. 88). As seen the experimental results are in fair
agreement with the theory and approximately 10-25 percent higher. The absolute amount
of incandescence (noise), of course, depends not only on the temperatures to which
the soot is driven but also on the soot number density which determines the number
of particles irradiated. Signal to noise calculations for the various diagnostic
techniques under consideration will be presented in their respective sections.
In addition to broadband incandescence, spectrally specific molecular emisssions
may also be present. In studies of laser modulated particulate incandescence,
Swan emissions at 5165 A from laser vaporized C2 were inferred to be present. In
fact, the oscillator strength of the Swan system has been measured from studies of
laser irradiated graphite (Ref. 89). There are other cases in the literature where
C2 Swan band radiation has been excited by ruby laser irradiated graphite (Refs. 90,
91). Besides incandescence, then, Swan (C2) and other Cn interferences may thus also
be present. In Table VIII, potential Swan and Comet Head (C?) interferences in the
N2 Raman bands (typically used for thermometry) using various fixed frequency laser
sources are shown.
Only the bandheads are listed. The Swan bands degrade to the violet, the
Comet Head to the red. With the advantage of tunability, these specific emissions
can be avoided vis-a-vis the Raman scattering with a dye laser appropriately tuned.
38
-------
LASER IRRADIATED PARTICLE TEMPERATURES
DUUU
5000
| 4000
UJ
c/)
Ul
Ul
oc
o
vo Q 3000
1
UJ
cc.
r>
QC
Ul
o.
ul 2000
1-
1000
A
100,000 I 10,000 j 1000 j [100 s>"r
o ' I I ' o "' s'
- PARTICLE DIAMETER (A) I 1 d>2000A S ^ '
II 1 ^ -
| 1 1 ' s* S*
1 ' ' •' ....«• ^ ^
1 I 1 t . S- +^~*
< 1 •'/••^' ^
II • ^ "^ *^*
» . f ____• -^-^ ' • ^ VAPORIZATION
' -/^'7^ -*-'/'"
--r' ' L-'
~-~ /_ -^"^/ /
^ ~--r / ' /
~~~ / / / /
/ / / f HEAT CONDUCTION
/ / /
/ / / /
— / / / ^
X S ^ ^
-*'--^' ~-'
INCIDENT WAVELENGTH 5900 A
AMBIENT FLAME TEMPERATURE 1500°K
1 ~
1 1 1 1 1 1
103 104 105 106 107 108 109 1010 -n
LASER FLUX - WATTS/CM2 P
01
-------
TABLE VIII
POTENTIAL LASER VAPORIZED Cn INTERFERENCES (Ref. U2)
Laser, wavelength
Angstroms
Ruby, 69^3
2x Neodymium, 5320
2x Ruby, 3472
WP, 3371
Dye, 5877
N2 Raman Q, Branch
Wavelength, Angstroms
8281+
5976
6073
4733
3777
3212
3658
3125
6810
5169
Band
C2 Swan
Swan
6004.9 (3,5)
5958.7 (4,6)
6122.1 (1,3)
6059-7 (2,4)
4737-1 (1,0)
o Comet-Head 3793-5
Comet-Head, 3657
Co Swan
5165.2 (0,0)
It is important to note that not all particles will pose a problem in light
scattering diagnostics. For example, alumina possesses an imaginary refractive
index component of 10"" in the visible (Ref. 88), so that the visible light absorp-
tion coefficient varies from 10"? -to 10"3 times the geometric cross section for
alumina particles in the 0.1 to 10.Op, range respectively. Consequently, very little
incident laser energy is absorbed by an alumina particle and little heating occurs
unlike the situation with carbonaceous particles (soot). Furthermore, the
emissivity of alumina is a factor of two to three lower than that for carbon
leading to reduced radiative output for whatever heating does occur. Actually,
alumina particles appear to be an excellent seed for simultaneous LDV (laser Doppler
velocimetry) - laser Raman work since laser induced alumina incandescent noise
should be quite small. Thus, in regard to laser modulated particulate incandescence,
not only are the number density and size of the particles important, but their
chemical composition as well.
Mie_ Scattering_
Particles can also elastically scatter the incident laser radiation and do so
with cross sections much larger than those associated with fluorescence or Raman
scatter as shown in Fig. 6. There scattering cross sections are displayed as a
function of particle circumference to laser wavelength ratio and were calculated
-------
FIG. 6
PARTICLE SCATTERING AND ABSORPTION CROSS SECTIONS
10
CM
O
UU
to
CO
CO
O
a:
o
REFRACTIVE INDEX
1.56-0.461
10
10
10
,-13
Ul
-------
using the UTRC Mie scattering code. The extinction cross sections which are the
sum of the scattering and the absorption cross sections will be discussed in a
later section. As can be seen, the cross section for scattering from a 0.1 p.
diameter particle is about twenty orders of magnitude greater than the Ng Raman
cross section. For a particle number density of 10° cm~3, the N2 number density
in a flame would be about ten orders of magnitude higher. Hence the Mie scattering
would be about 10 orders of magnitude greater than the N£ Raman signal. Nominally
this is not a problem when detecting inelastic scattering well shifted spectrally
from the incident laser line. It is a problem, however, if the spectrally
selective instrument being used does not have a high enough rejection outside the
passband. Single monochromators have rejection ratios in the range of 10^ to 10 .
If such an instrument were employed with no other prefiltering, the unrejected
Mie signal would greatly exceed the Raman signal present. Consequently, care must
be taken in the design of a light scattering experiment to ensure adequate
rejection outside the passband region. Clearly such scattering precludes the diagnostic
viewing of unshifted resonance fluorescence and can be problematical for rotational
Raman scattering if a double or triple monochronator is not used.
Window Fluorescence
As seen previously, coaxial scampling approaches, i.e., 180° or backscattering,
are preferable to right angle schemes from a signal to background luminosity noise
standpoint. In experiments at UTRC on a model combustor, window fluorescence
proved to be a problem with coaxial viewing for dye laser fluxes on the order of
10° W/cm2 at 5900 A. The fluorescence from the quartz window was approximately
equal to the Raman Stokes signal from high temperature nitrogen in the combustor.
The fluorescence prevented utilization of coaxial sampling and right angle viewing
was instead attempted. However, the very high levels of background luminosity
prevented successful diagnosis. Window fluorescence is a potential problem for laser
Raman and laser fluorescence measurements; it should pose no difficulties for CARS
however,
One solution to this problem involves the use of compound windows with opaque
baffling to prevent fluorescence from entering the section of window used to view
the scattering. Such a window is yet to be demonstrated on high temperature com-
bustors and may prove either impractical or too expensive to implement.
Spuriously Scattered Laser Light
For weak signal processes, particularly Raman, the laser beam must be trapped
with a very high capture efficiency after passing through the measurement location.
If permitted to reflect diffusely and specularly in a random fashion in the
combustor, very large unshifted radiations are likely to be incident on the spectral
instrument used to detect the scattering. Very large rejection ratios would be
required to preclude the detection of such spuriously scattered laser radiation.
Worse yet such radiations may cause various optical elements, e.g., interference
-------
filters, to fluoresce and incandesce in the spectral passbands of interest. Thus,
in general, high efficiency beam traps should be an integral part of the measurement
approach. These may range from highly absorbing spheres with an off-axis entrance,
heavily baffled cylinders with absorbing glass endwalls oriented at Brewster's
angle, Rayleigh horns, etc. A discussion of diffuse reflectivities and beam
trapping is provided in Reference 92.
'Perturbations
Although laser light scattering techniques are generally touted to be unobtrusive
and nonperturbing this is not always the case. In this section, three potential
perturbations, namely medium heating, stimulated Raman scattering, and optical break-
down will be considered.
Medium Heating
In the absence of participates, most combustion media of interest are transparent
to the incident laser radiation even when electronic resonances are being probed.
Soot particulates, however, are highly absorbing over a wide spectral range and, in
sufficient quantity, can absorb substantial fractions of the incident radiation. Of
concern here is the thermal perturbation of the medium as heat is transferred from
the particulates to the gas. The characteristic time for heat to be transferred a
distance, L, within the medium is approximately
_
P k
• (7)
a
where kg_ is the medium thermal conductivity; pa, the mass density of the medium; and
ca, its specific heat. For the medium to be perturbed, L must be of the order of
half of the interparticle spacing, i.e., ~ 0.5 np"1/^ where rip is the particulate
number density. The above will apply as long as the time, TC, for heat conduction
from the particle to the medium to become effective is less than Tp. TC may be
expressed as (Ref. 88)
c
a2pscs (l+GK)
where p is the individual mass density of the particulates; cg, the particulate
specific heat; G, a geometry dependent parameter; and K, the Knudsen number. The
Knudsen number, i.e., the ratio of mean free path to particle diameter, enters since
for small particles in high temperature flames, the gaseous mean free path (about
5000A @ 1 atm, 2000°K) exceeds the particle size and continuum heat transfer is no
longer applicable. In Fig. 7, Tp and TG are tabulated for 2000°K, 1 atm pressure air
for a soot dispersion of mass density 10-7
-------
PARTICLE CHARACTERISTIC HEAT TRANSFER TIMES AND ABSORPTION COEFFICIENT
10
-2
10
-3
10'
TO--
UJ
in
I
10
-6
10
-7
10
-8
10
ABSORPTION COEFFICIENT ( 1 0~7 GRAMS/CM3 )
|_ /
/
/
/
/
DYE
(FLASHLAMP)
LASER PULSE LENGTHS
SO LID STATE
DYE (LASER)
,-9
0.01
100
I
III I
10
FIG. 7
-2
10-3
I
u
10-4
10-
0.1 MICRONS 1
1000 ANGSTROMS 10,000
PARTICLE DIAMETER
10
100,000
-------
For laser pulses of 10-6 seconds or less in duration, large particles (
pose no perturbation threat. For short laser pulses, i.e., — 10"" seconds, no per-
turbation of the medium will occur. For intermediate length pulses of several hundred
nanoseconds, typical of flashlamp -pumped dye lasers, perturbation of the medium with
small particulates dispersed throughout could occur. Whether the medium will actually
be perturbed depends on the amount of energy absorbed from the laser beam.
The incident laser beam will lose energy as it propagates through the combustor
volume in accordance with the relation
where IQ is the input intensity and l(x) that after traveling a small distance, x.
Assuming the absorption coefficient o?a to be small, the energy lost in traveling a
small distance Ax is
AE = aaE0Ax . (10)
The absorption coefficient, o-a, may be expressed as
> 6
(11)
2
n a , =nna a > 6
p abs p
P a
= n na^ - a < 5
P 6
where
-------
Stimulated Raman Scattering
At high laser intensities, stimulated Raman scattering may occur (Refs. 16 and 17).
By promoting molecules from the ground to the first vibrational state at a high rate,
the species being probed may be perturbed resulting in erroneous density and tempera-
ture measurements. A Stokes input intensity of Ig(0) will be amplified by stimulated
Raman scattering according to the relation (Ref. 93)
I U) = I (0) exp (gILJ>) (13)
s s
where I U) is the amplified Stokes intensity after a distance, £', IL, the laser
intensity; and g, the Raman gain factor which on line center is
2 2
i6tr c NA
where c is the speed of light; N, number density; A, the fractional population dif-
ference between the lower and upper states; ba/bfj, the Raman cross section; ft » h/2rr
where h is Planck's constant; ois, the Stokes ra,dian frequency; n, the index of
refraction which is nearly unity in gases; and r» the Raman line-width. At 1500°K
in N2 the maximum population resides in J = 16 and A can be shown to be O.dk. Assum-
ing r - 0.1 cm"1, g can be evaluated for a.laser wavelength of 5320A and is found to
be 5-9^ (lO"-^) cm/Watt. For a laser intensity of lcP-0 Watts/cm2 and a 1 cm path-
length, the stimulated Raman gain is miniscule. This would also be true of 300°K,
atmospheric pressure No- In Ref. 93, a gain of only 1.2 was found over a 10 meter
path for a laser intensity of about 10° Watts/cm2. Thus it may be concluded that
stimulated Raman scattering is unlikely to perturb the populations being probed for
typical combustor operating regimes, vis. pressures less than 100 atmospheres and
spatial resolutions of a few centimeters.
Optical Breakdown
With the application of intense electric fields from high intensity laser
radiation, the medium under examination may break down, i.e., become fully ionized.
With plasma formation the medium is substantially altered, thus precluding diagnostic
interrogation. A comprehensive review of laser radiation induced gas breakdown is
presented in Ref. 9**« Most work to date has been concerned with breakdown at 10.6,
1.06 or 0.69^3|J. where the breakdown thresholds roughly scale according to 1/X^ as
predicted by cascade ionization models. However, in the visible and, particularly,
in the uv, multiphoton processes become important and the breakdown thresholds begin
to decrease with decreasing wavelength. For example in Ref. 95, in examining air
breakdown between 6500 and 5500A, the threshold increased from ~ 1.5 (1011) W/cm2
at 6500 % to a peak value of SClCr1) W/cm2 at 5500 X. In Ref. 96, similar peaking
-------
effects were observed in noble gas breakdown studies. In attempting to establish a
breakdown threshold for a practical combustion device, the effects of particulates
and number density must also be accounted for. Large particulates (i.e., greater than
several microns in diameter) decrease clean air thresholds by about two orders of mag-
nitude in general (Refs. 97 and 98). Smaller particulates generally have no effect
due to very high electron diffusion losses. The pressure (i.e., density) dependence
on the breakdown threshold is approximately inverse, i.e., 1/p. In an atmospheric
pressure flame at temperatures on the order of 1500-2000°K, the breakdown threshold
should be approximately 5-7 times higher than the clean air 1 atmosphere breakdown
thresholds. Gas temperatures up to 2000-3000°K are not expected to affect the thres-
hold values.
For an atmospheric pressure combustor operating at temperatures near 2000°K,
breakdown will be assumed to occur at about lO-^^ W/cm2 at 5000A. To obtain this
estimate the 10^- W/cm2 atmosphere density value (Ref. 93) has been increased by an
order of magnitude to account for density decreases at high temperature and reduced
by about two orders of magnitude to account for particulates. The pessimistic
assumption will be made that in a hydrocarbon fueled diffusion flame there will
always be a few large particles, i.e., > few microns diameter, present in the laser
focal volume. At shorter wavelengths, the threshold will decrease (Ref. 9M and
breakdown will be taken to occur at 109 W/cm2 at 2000 A and 5 (109) W/cm2 at 3500A.
These values then represent the maximum focal fluxes tolerable for any diagnostic
approach.
Laser/Signal Transmission
To perform spatially resolved measurements at a given location in the combustor,
the laser beam must be transmitted reproducibly and with high efficiency to the desired
measurement point. There are a number of factors which can influence the energy,
intensity and even the actual measurement location pertaining in a given situation.
Some of these considerations will be explored in this section.
Optical Component Damage
Experiments in the laboratory are often performed on flames devoid of enclosures
and optical ports. This is generally not the case with practical device probing
where the phenomenon under investigation is viewed through a window, often of limited
aperture. With the device operating, the window is likely to become coated with
particulates over a period of time. Quartz is commonly used for optical probing of
combustors due to its high temperature capabilities. In Ref. 99» the optical damage
threshold for bulk quartz at 69^-SA for a single mode laser was found to be 28 +
5x(lo9) W/cm2. Surface damage thresholds are generally lower than bulk values. In
Ref. 100, a front surface damage threshold of 20.2 (1C>9) W/cm2 was reported at 69^3 A for
X-cut crystal quartz. Exit damage thresholds are generally lower than entrance values
due to Fresnel reflections; for glass with a refractive index of 1.55, the exit damage
threshold is about 33 percent lower (Ref. 101). Furthermore cracks, pores, etc.
-------
reduce the damage threshold between 2-5 for low index materials such as quartz (Ref.
1C2). Based on the foregoing, quartz may be assumed capable of transmitting fluxes
on order of a few gigawatts/cm^. If the optical surfaces become contaminated with
dirt/soot, the threshold will be even lower. It should be noted that due to temporal
variations in pulse shape and spatial variations in intensity, actual peak intensities
in laser pulses may be a factor of five to ten higher than the calculated average flux
level.
To minimize the probability of damage in optical materials, the laser flux
should be kept as small as possible passing through the window. One way of achieving
this is to place lenses as close to the window as possible. This then maximizes the
distance between the laser focal point, the region of highest flux and the window.
Another approach, of course, is to beam expand to decrease the laser intensity prior
to transmission through the optical port. To avoid particulate deposition on ports,
gas purging of the surface may be necessary. Measurements near a window , i.e., at
the device periphery may be precluded, however, by optical damage.
Soot Extinction
As the laser beam propagates through the combustor, particulate matter, e.g.,
soot, will attenuate the beam due to scattering and absorption. The latter, of course,
results in the laser modulated particulate incandescence phenomenon previously dis-
cussed. In Fig. 6, extinction and scattering cross sections are displayed for car-
bonaceous particles as a function of rrD/X. The difference between the extinction and
scattering curves is due to particle absorption. Radiation propagating through such
a dispersion will be attenuated as exp (-n^7ei) where npis the soot density,
-------
For the previously examined soot dispersion of 10^ cm" 3, i^QOA diameter particles
there would only be a beam attenuation of about 1.5 percent over a 50 cm pathlength.
From Table IX it is clear that participate extinction over a 50 cm path would become
significant for small particles at mass densities above a few times 10~® gm/cm^.
Hence, only at the highest background luminosities previously displayed in Fig. 3
might the potential for significant extinction be present.
Beam Steering/Defocussing
Turbulence and thermal gradient effects in the combustion medium may cause
the incident laser beam to be defocused or steered due to refractive index
gradients. This is a difficult phenomenon to analyze without detailed turbulence
and temperature models. For small combustion devices operating at or near
atmospheric pressure, it is not believed to be a serious problem. This is based
upon steering experiments conducted at UTRC on the 12 cm dia. combustor described
in Ref. 77 and experiments on the EPA Rainbow furnace described in Ref. 7^- In
the latter set of experiments, two laser beams were crossed in the furnace to
produce an interference fringe pattern. The beams upon exiting the device were
then imaged to form a second fringe pattern which could be probed with a tungsten
whisker. Operation of the furnace produced no change in the fringe pattern.
LDV measurements were also performed successfully. In LDV work at UTRC on the
12 cm dia. combustor previously mentioned, there is an interrupted data rate;
whether the interruption occurs due to turbulence effects or lack of a scattering
particle in the sample volume is not clear. Nevertheless LDV measurements have
been successfully performed. In brief, then, it is believed that combustion
turbulence in devices of small diameter (< 100cm) operating at atmospheric pressure
will not be a serious problem. Whether it is a problem in large scale, high
pressure devices is probably best determined via a series of relatively simple
experiments.
Particulate induced thermal blooming of the incident laser beam (Ref. 103)
is also anticipated to be unimportant for short laser pulse lengths. These
effects would become important only on a time scale on the order of T (Fig. 7)
which is long compared to the pulse length of most high energy pulsedplasers.
For long laser pulse lengths, convection effects would minimize blooming.
Signal Averaging
In instances where the single pulse signal to noise ratio is not sufficiently
high to permit accurate measurements, signal averaging in conjunction with a noise
sampling and subtraction approach, will be required to enhance signal to noise
prior to further data treatment. In certain circumstances depending on the
magnitude and correlation in medium property fluctuations, signal averaging may
result in an accumulation of averages over these fluctuations. These residual
terms cloud interpretation of the signal averages and introduce errors into the
-------
measurements if the standard data reduction approaches are applied. Since each
measurement technique differes in its functional dependences on density and
temperature, more detailed assessments of signal averaging will be deferred to
those sectionsin which each diagnostic approach is separately discussed. Suffice
it to say here, that in general, signal averaging in temporally fluctuating media
is not straightforward and should be carefully scrutinized.
Summary
In Table X, the various practical considerations discussed in this section
are summarized. Many of the effects discussed can be dismissed as being unlikely,
too weak or avoidable by proper design approaches. Those likely to be serious
problems will be treated in the later sections in which each diagnostic approach
is separately reviewed.
TABLE X
SUMMARY OF PRACTICAL CONSIDERATIONS
Item
Comment
Sources of Noise
Background Luminosity
Laser induced particulate fluorescence
Particulate Raman scattering
Laser modulated particulate incandescence
Mie scattering
Window Fluorescence
Spurious laser scattering
Perturbations
Medium heating
Stimulated Raman Scattering
Optical Breakdown
Laser/Signal Transmission
Optical Component Damage
Soot Extinction
Steering/Defocussing
Signal Averaging
50
potentially serious interference
potentially serious interference
interference unlikely
potentially serious interference
avoidable with high rejection
avoidable with compound window, or
right angle viewing
avoidable with beam trapping
generally unlikely
very little liklihood
maintain focal flux below 10-10W/cm
maintain window flux below 10°W/cm
problematical in large (> 1 m dia),
highly sooting combustors
unlikely in small (< 1 m dia) devices
with caution, only after analysis
-------
RAMAN SCATTERING
Introduction
Laser Raman techniques offer a number of advantages for combustion and other
diagnostics as described in detail in Refs, 8, 104, and 105. In brief, only a single
laser is required to monitor all of the species of interest. The laser can operate
at any wavelength without the necessity of being tuned to resonances of the molecule
being probed. This is not true for near-resonant Raman scattering, whose discussion
will be deferred to the end of this section. Here only spontaneous Raman scattering
will be considered. Visible wavelengths are favored, however, because of the scaling
of the Raman cross sections as X^ , where Xp, is the Raman scattering wavelength.
With proper detection, several species can be monitored simultaneously. Quite impor-
tantly, the Raman scattered intensities are unaffected by quenching. Furthermore,
absolute calibration is readily achieved by comparing the scattered signal from the
species of interest with that of nitrogen. Unfortunately, spontaneous Raman scat-
tering is very weak. Typical vibrational Raman cross sections (Table V) are on the
order of 10~30 cm^/sr. It is the weakness of the process, despite all of its other
advantages, that makes spontaneous Raman scattering very difficult to apply to
practical combustion devices, as will be shown later.
Most of the work on species measurements in flames utilizing Raman scattering
has been directed toward detection of majority species such as N2 (Refs. 106, 107, -^
and 109), 02 (Refs. 106, 107, and 108), C02 (Refs. 104, 106, and 1C?), CO (Ref. 107),
H20 (Refs. 107, 108, and 109), and H2 (Refs. 29, 109, and 110) to name a few. Leonard
(Ref. 78) successfully monitored 02 and C02 in a T53 engine exhaust, but was pre-
vented from detecting NO because of hydrocarbon fluorescence interferences as men-
tioned before. CO and N02 detection were not attempted due to anticipated strong
interferences from N2 and COo, respectively. Much of the work on remote detection
of pollutants carried out to date has been based on Raman scattering, although
differential absorption backscatter is receiving much attention. Inaba and Kobayasi
(Ref. 69) summarize much of the work to 1972. Of particular note (Ref. 6l) is the
detection of H20 (ICr ppm), C02 (310 ppm) and S02 (30 ppm), the latter from a range
of 200 meters.
Thermometry has been performed by a number of investigators generally from
analysis of the scattering from a dominant molecular constituent such as N2. Raman
temperature measurements have been made in flames (Refs. 1C^, 108, 109, 110, 111,
11? and 113), air in the atmosphere, wind tunnels, or shock tubes (Refs. 114 - 121),
and electric discharges (Refs. ^7, 122, and 123).
51
-------
Most of the above referenced studies have "been performed under relatively benign
instrumentation circumstances, i.e., low background luminosity, particulate free
environments. Spontaneous Raman scattering, despite its weak signal strengths, is
ideally suited for diagnosis of such environments. Interpretation of the Raman
spectra is relatively straightforward and for the most part free of spectral inter-
ferences (Table VI). However, for practical combustor diagnosis, the many sources
of "noise" previously reviewed pose a formidable obstacle to successful implementa-
tion. In this section, the princples of Raman scattering will be briefly reviewed
and its application to density and temperature measurements discussed. Its measure-
ment capabilities in clean flames will be discussed and illustrated by sample cal-
culations. Then, signal/noise calculations will be performed for various state-of-
the-art laser sources for both background luminosity and laser modulated particulate
incandescence. The effects of signal averaging Raman data in a turbulent medium
will be reviewed. Costs and probability of success, i.e., risk, for practical
applicability of Raman scattering will be discussed. Wear-resonant Raman scattering
will be examined at the conclusion of this section.
Theory
Raman scattering is the phenomenon of inelastic collision processes between
photons of light and molecules in either solid, liquid, or gaseous phases. The
effect was theoretically predicted by Smekal in 1923? but subsequently named in
honor of its experimental discoverer, C. V. Raman, who first published his observa-
tions in 1928. Although the discovery of the effect is nearly fifty years old,
its application to gas phase diagnostics awaited availability of powerful monochro-
matic light sources. With the advent of high power visible laser sources, Raman
scattering is now being widely exploited for a variety of gas phase diagnostics
studies as the foregoing references clearly indicate. Raman scattering has been
physically understood for some time and detailed theoretical treatments are to be
found in Refs. 8, 23, 1214-, and 125. For diagnostic purposes it suffices to know that
the Raman scattered power is proportional to the incident light power and the number
density of molecules in the appropriate initial quantum states for the scattering to
be observed.
Photons of light colliding with molecules may either lose energy to or gain
energy from the target molecules as shown in Fig. 8. In the former event, termed
Stokes scattering, the molecule becomes excited, and, in the latter, termed anti-
Stokes, the molecule is deexcited providing, of course, that it was in an excited
state prior to the collision. The energy exchanges which occur are quantized in
accordance with the allowable energy levels of the molecule, thusly,
hv + N(v,j) -» hV + N(v',J')
h(v - v«) - E(v«, J') - E(v,j)
52
-------
RAMAN SCATTERING PROCESSES
u>
V +1
1
0
Q S O
RAYLEIGH STOKES ANTI-STOKES
ROTA-TIONA
Q S O
VIBRATIONAL STOKES
VIBRATIONAL ANTI-STOKES
P
00
-------
where h is Planck's constant; v, the frequency of incident photons; N(v,j), the
quantum energy state characterized by a vibrational quantum number, v, and rotational
number, J; and E, the state energy. Primes denote the above quantities after the
collision. Here v,J represent the totality of quantum numbers, dependent on the
polyatomicity of the molecule. Since each molecular species possesses a character-
istic set of energy states, the spectral distribution of Raman scattering is uniquely
determined by the incident laser wavelength and the species from which scattering
occurs. If no change in vibrational quantum .number occurs, the scattering is termed
rotational Raman, otherwise it is termed vibrational-rotational or vibrational for
short. The allowed changes in quantum number are governed by certain selection
rules for the process. For diatomic molecules vibrational quantum number changes are
restricted to 0, -I while rotational numbers changes of 0, -2 are permitted. If no •:
change in rotational quantum number occurs, the Raman scattering is termed Q branch,
while for ±2 it is termed S and 0. The scattering may be either upshifted (anti-
Stokes) or downshifted (stokes) in frequency depending on whether the state (v',Jf)
resides below or above (v,j), respectively in energy.
S
Density measurements derive from the fact that the Stokes power, P . scales
directly with incident power, Pj_, and number density, n, as (rewriting Eq. (l))
Psr = ks Pinfs(T) (16)
fs(T) is termed the bandwidth factor and is a temperature dependent term which
accounts for the fraction of scattering species in the appropriate initial quantum
states for scattering to be observed. fs(T) depends on the spectral location, shape
and bandwidth of the spectrometer or interference filters employed and on the laser
"line" profile and bandwidth. It can be easily calculated employing detailed Raman
codes (Refs. 109 and 113). ks is a factor dependent on Raman cross section, wave-
length, geometry, and optical collection efficiency and usually determined accurately
by calibration. Having so determined ks, and knowing or measuring P^ and T, n can
be determined from the measured Raman scattering. To eliminate the requirement on
temperature information in order to make density measurements, fs(T) can be made
constant over a wide temperature range as shown in Fig. 9 by proper selection of
bandwidth. Unfortunately the bandwidths required are large which decreases the S/N
in the presence of spectrally broad sources of noise. In Fig. 9 bandwidth factors
are displayed for varying bandwidths for Raman scattering from T^ employing a 5320 A
laser source (e.g., frequency doubled neodymium) with infintesimally thin linewidth
using a Raman code described in Ref. 113 • Similar calculations have been performed,
for example, in Ref. 109 with similar findings.
Because the spectral distribution of Raman scattering is essentially a display
of state populations, temperature measurements can be performed in a number of ways,
e.g., spectral band contours (Refs. 10Q, 110 and 112), peak height ratios (Refs. Ill,
113 and 119 ), peak height shifts. A common technique is to ratio the anti-Stokes to
Stokes vibrational scattering produced by a single pulse, i.e., from Eq. (16)
-------
FIG.9
TEMPERATURE VARIATION OF STOKES BANDWIDTH FACTOR
LASER LINE 5320 A
N2SCATTER ING
FILTER CENTER AT 6073 A
GC
O
0
I
h-
Q
m
CO
LLJ
to
STOKES FILTER BANDWIDTH (A) 100
500
1000 1500 2000
TEMPERATURE-DEC KELVIN
2500
3000
-------
Pa o A
r _ h* fa(T)
pj kS fS(T)
Note that the ratio is independent of the laser power and most importantly
number density and solely dependent on temperature. In Fig. 10, anti-Stokes to
Stokes bandwidth ratios are displayed for the previously illustrated case of an
infinitesimally thin linewidth laser source at 5320 X. In practice the factor ka/
ks is obtained via calibration, e.g., from a tungsten filament lamp (Ref. 8^ ).
Preferred Raman Approaches
Referring to Eq. (l) it is seen that the Raman scattered power scales as the
product of the incident laser power, Raman cross section and molecular number den-
sity in the appropriate initial quantum states for scattering to be observed. With
this in mind, preferred approaches to the implementation of Raman scattering diagno-
sis can be examined.
Raman Band Selection
Cross sections for rotational and vibrational-rotational scattering have been
summarized in Table V. Of note is that only small differences exist in the scat-
tering cross sections of the various molecules. This means that calculations per-
formed for one species are fairly well exemplary of what can be expected for any
other species. There is a substantial difference, however, between cross sections
for pure rotational scattering and for vibrational/rotational scattering. For
example, the cross section for a single line, J = 6 -» J1 = 8, in the rotational
spectrum of N2 is nearly an order of magnitude greater than the entire vibrational
Q, branch cross section. This advantage is offset at high temperatures by the
smearing of rotational level populations so that only a few percent of the mole-
cules reside in the level from which scattering originates. Another problem with
rotational scattering is that the energy exchanges involved are very small leading
to small spectral displacements of the rotational Raman lines from the exciting
laser line. The spectral displacement is given by:
„ 2B(2J-1) 0 branch
A'v = t (~*\
-2B(2J+3) S branch U°J
Since B for most molecules is only a few cm"1, the rotational spectra from the
various molecules overlap and interfere with one another. In addition discrimination
against the nearby and much stronger Rayleigh , Mie and/or spurious laser scattering
is very difficult.
56
-------
FIG. 10
BANDWIDTH FACTOR RATIO VARIATION WITH TEMPERATURE
500
1000
1500 2000
TEMPERATURE-DEG KELVIN
2500
3000
57
-------
Some of these difficulties are overcome by the detection scheme devised by
Smith (Ref. 126) in which a Fabry-Perot etalon with a free spectral range equal to
the rotational Raman line spacing (^Bo) is employed. Properly tuned and with high
finesse such an etalon simultaneously transmits all the rotational Raman lines of
a particular molecule while discriminating against other molecules. However a
Fabry-Perot etalon possesses a discrimination ratio of 1CF to 1XX at most, so that
some light will be transmitted even though not resonant with the filter. Conse-
quently, it would be extremely difficult to detect trace concentrations of species
accurately due to incomplete discrimination of the rotational Raman scattering from
major flame ; constituents, of the Rayleigh scattering and of the Mie scattering when
particulates are present. In this light it is not surprising that rotational Raman
has not been widely used in flames or multicomponent mixtures.
Despite the weakness of the cross section, vibrational Raman bands are well
displaced spectrally from the exciting line, typically by 1000 cm'1 or more, and
interferences between vibrational Raman spectra in flames are rare (Table VI).
Furthermore for Q branch transitions, the scattering arising from the entire popu-
lation of a given vibrational state can be monitored, partially offsetting the vibra-
tional cross section disadvantage. Consequently, only vibrational Raman scattering
will be considered in these diagnostic evaluations.
Continuous Wave or Pulsed Laser Excitation
Although many Raman studies have been conducted with continuous wave lasers in
clean flames, it will be shown here that cw lasers are unacceptable for practical
combustion device diagnostics. This will be done by considering the Raman signal/
noise ratio in a luminous background. Combining Eqs. (1) through (3), the Raman
signal to background luminosity noise ratio may be expressed as
(19)
Consider the situation for Raman scattering from N2 using a 10 watt argon ion laser
at 51^5 A. The Stokes scattering will reside at 58^6 A and the cross section (Ref.
12?) appropriately scaled is U.31 (lO""^1) cm2/sr. For a 2000°K flame the number
density of molecules in the ground vibration state, no is 2.38 (lO1^) cm~3. pOr a
10 A5 bandwidth, f ^ 0.5. F8 collection optics will be assumed typical of most mono-
chromator acceptance solid angles. The sampling extent will be taken as 1 mm,
chosen small to increase the S/N ratio. The calculated S/TT are summarized in Table
XI below as a function of the radiation energy density.
-------
TABLE XI
CONTINUOUS WAVE LASER RAMAN/ BACKGROUND LUMINOSITY NOISE RATIO
(Powers of Ten in Parentheses)
it is clear that with a high peak power pulsed laser
that the Raman signal to luminosity noise ratio will be considerably improved. For
example with a pulsed laser with a peak power of 10 Watts, the foregoing S/N ratio
will be increased by about seven orders of magnitude possibly permitting majority
species studies in highly luminous environments.
Trace species detection is difficult, however, regardless of background con-
siderations due to the smallness of the Raman cross sections. As mentioned earlier,
because the Raman Q-branch cross sections are all nearly the same, detectability
limits for one specie will be exemplary of the sensitivity levels that may be gen-
erally achieved. In the following, the detection limits for NO will be examined.
The Raman scattered energy in the Stokes Q-branch, 0^ induced by a pulsed laser
with energy, Qin, is given by (rewriting Eq. (l))
0
(20)
where nNO (v=0) is the ground state number density. For simplicity the detector
bandwidth is assumed broad enough so that the bandwidth factor is unity. The Q
branch NO cross section appropriately scaled is 2.1 (10~3!) cm2/sr. F5 collection
optics corresponding to a 3.1 (10~^) sr solid angle will be assumed; for a 1 meter
diameter furnace, a 10 cm optical port would be required. The collection efficiency
will be assumed to be 10 percent. The amount of ground state NO is given by
nNO(v=0) = (1 - e )nC (21)
where E(l)-E(0) is the energy difference between the first and ground vibrational
state, 1977 cm'1; n, the total number density; and c, the fractional NO concentration.
Assuming the scattering is induced by a pulsed, frequency-doubled, neodymium laser
at 5320 8, the center of the NO Stokes Q branch will reside at 5910 A. Dividing
59
-------
the Raman scattered energy by the individual photon energy yields the number of
collected Raman photons, np. Ignoring background for this illustration, the S/N
is limited by photocathode statistics (Ref. 128) and is given by
S/N =y (22)
where T| is the photocathode quantum efficiency, assumed to be 0.1. Assuming the
detectability limit to be a single pulse S/N of unity, the minimum detectable con-
centration can be calculated. The accuracy of the measurement when shot noise
limited can be improved by signal averaging. For example, averaging the above over
100 shots would provide a measurement accuracy of - 10 percent. In Fig. 11, pulsed
laser Raman detectability limits for NO are displayed as a function of laser pulse
energy with gas temperature and spatial resolution shown parametrically. For a 1
Joule laser pulse at a high flame temperature, 2000°K and a 1 cm sampling extent,
measurements are not possible below about 2000 ppm. Note that a 1 Joule laser pulse
with a typical pulse length of 10~^ sec and focused to a 1mm spot size, corresponds
to an average focal flux of 1010 W/cm2. Higher energies would most likely lead to
gas breakdown as seen earlier. Although a 10 cm length lowers the sensitivity an
order of magnitude, this hardly constitutes a "point" measurement. 10 cm can in
effect be obtained with a 1 cm extent in a multipass cell with a gain of 10. Multi-
pass cells have been successfully demonstrated in Raman studies using diffraction
limited gas lasers on small burners (Ref. 129). Their applicability to poor beam
quality pulsed lasers on a real furnace is highly doubtful however. The foregoing
calculations are intended to illustrate that even in the absence of background noise
effects, Raman detection of species in trace quantities is very limited even with
high energy/pulse lasers and poor spatial resolution.
Pulsed Laser Raman Signal to Noise Calculations
In the preceding section, continuous wave lasers were shown to be incapable of
Raman combustion studies except in very low luminosity environments. It was also
indicated that pulsed lasers may lead to sufficiently high S/N ratios for majority
species determinations in luminous environments. In this section, this conclusion
will be more closely examined for a variety of pulsed laser systems. In addition
to considering noise from background luminosity, laser modulated particulate incan-
descence effects need also be considered as described previously.
Laser Source Selection
Four state-of-the-art laser sources will be considered for the signal/noise
calculations. These will include: (l) a 1 Joule per pulse frequency-doubled neo-
dymium laser at 5320 X with a 10 nanosecond pulsewidth; (2) a 0.5 Joule dye laser
at 5900 & with a 0.5 u-sec pulsewidth; (3) a 1 Joule, 30 nanosecond pulsed ruby laser
60
-------
FIG. 11
10
10-
0.01
PULSED RAMAN NO DETECTABILITY LIMITS
ONE ATMOSPHERE PRESSURE
10% COLLECTION EFFICIENCY
10% QUANTUM EFFICIENCY
F5 OPTICS
LASER ENERGY-JOULES
61
-------
at 691+3 S and (k) the aforementioned ruby laser frequency doubled to 3^72 A with
50 percent doubling efficiency. Low energy pulsed N2 lasers have been excluded
from consideration since their Raman photon yields are generally quite low. With
the high pulse energy lasers selected, adequately large numbers of Raman photons
are collected, thus minimizing shot noise fluctuation effects and permitting single
pulse thermometry in principle (Ref. 113)-
Background Luminosity
First, "noise" from background luminosity will be treated. The calculations
will be performed utilizing Eq. (19) for the following conditions: an atmospheric
pressure, 2000°K flame; Raman scattering from N^ assumed to constitute 70 percent
of the combustion gas mixture; a 10 A bandwidth and F5 optics. The radiation energy
density will be assumed to be 130 (10~9) watts/cm^ sr X corresponding to the parti-
culate dispersion of 10® cm~3, UOO X soot particles (Fig. 3). In Table XII, the
calculated S/N are displayed.
TABLE XII
N2 RAMAN SIGNAL/BACKGROUND LUMINOSITY NOISE RATIOS
flame:
parti culates:
2000K, 1 atm
10®
cm~3,
Laser Power (w) Wavelength (g) N£ Raman (A*
Sampling Extent
i em 1 mm
2X Nd
dye
ruby
2X ruby
10U
106
3.3 (10?)
1.7 (107)
5320
5900
69^3
3^72
6073
6840
828U
3778
U.3
.013
.086
600
U30
1.3
8.6
60,000
.. *
In each case the scaling of the Raman cross section (A^ ) and blackbody distribution
(Fig. 3) with wavelength has been taken into account. From the Table, it is seen
that the high peak power solid state lasers give good S/N at high spatial resolu-
tion. However in a more luminous situation, i.e., liquid fuel, where the luminosity
is as much as a factor of thirty larger (Fig. 3) only the doubled neodymium or
doubled ruby appear feasible. A similar conclusion in regard to the 2X ruby laser
is the presence of intense background was reached in Ref. 105.
Although ruby lasers with tens of joules of energy per pulse exist, they have
not been seriously considered in the above due to gas breakdown considerations. With
the 1 Joule, 10 nanosecond doubled neodymium laser, breakdown may pose a problem.
If the laser were focused to a 1 mm beam diameter, the average focal flux would be
62
-------
on the order of 10 ° Watts/cm . Due to spatial (intensity) and temporal (pulse shape)
variations, the peak flux is probably a factor of four or more higher making gas
breakdown a likely possibility. Consequently higher energy pulses than those selec-
ted have not been considered. If the neodymium pulse were stretched to decrease the
intensity (say to 50 nsec) the peak power and, hence S/N, would be correspondingly
decreased by a factor of five. Hence with proper laser selection it would appear
that even the most intense background luminosity measured in the Rainbow furnace could
be overcome. Of course this applies only to Raman scattering from the dominant molecu-
lar constituent and is not true of trace species concentrations, i.e., below 1000 ppm.
For example, in attempting detection of a trace constituent at 1000 ppm in the highest
luminosity case shown in Fig. 3> all the lasers listed would produce S/N ratios less
than unity with the exception of the 2X ruby which would yield a S/W of about three.
Actually for trace concentration levels and the high resolution (l mm) required for
good S/N, the photon yields would be extremely small as seen in Fig. 11.
Laser Modulated Particulate Incandescence
It has just been shown that with proper laser selection, background luminosity
can be overcome by the spontaneous Raman scattering from a major flame constituent.
Yet to be considered is the laser pulse particulate interaction which can lead to the
variety of noise effects previously noted. Fluorescent interferences for laser wave-
lengths below 5000 A appear to be of the same order as the Raman scattering from a
. dominant molecular constituent for hydrocarbon concentrations in the 1000-5000 ppm
(as CHlj.) range. Fluorescent interferences are difficult to predict quantitatively
a priori without knowledge of the specific hydrocarbon species involved. Here only
the distinctive liklihood of fluorescence interferences for laser excitation below
5000 A will be noted.
Laser modulated particulate incandescence occurs when the already incandescent
soot particles absorb the incident light scattering laser radiation, heat to tempera-
tures far above the ambient flame temperature and, thereby, emit greatly increased
amounts of blackbody radiation as described earlier. Unlike the situation with
background luminosity where the Raman volume and total sampling volume can differ,
laser modulated incandescence can occur only from the irradiated (i.e., Raman)
volume. Consider the situation for the previously examined lasers when focused to
a beam diameter of 1 mm. Assuming gas breakdown does not occur, the temperature to
which the soot particles are heated can be found from Fig. 5 once the flux has been
calculated. Using the Planck radiation expression, the single particle radiation
per unit bandwidth per unit solid angle can be calculated. For a 1 mm Raman sampling
extent, the irradiated and viewed volume will be 0.79 ™^« Knowing the particulate
number density, the total laser modulated incandescence can be calculated. For the
Q o . O O
previously examined soot dispersion, namely 10 cm'0, 400 A dia, and assuming a 10 A
bandwidth and a bandwidth factor of 0.5, the 2000°K N2 Raman signal to laser modu-
lated soot incandescence noise ratio has been calculated and is summarized below in
Table XIII.
63
-------
TABLE XIII
N2 RAMAN SIGNAL/LASER MODULATED SOOT INCANDESCENCE NOISE RATIO
Particle
Laser Flux (W/cm2) Temperature (°K) S/N
2X Nd 1010 6000 1.6
dye 108 1+500 0.037
ruby 3.3(109) 5500 0.33
2X ruby 1.6(109) 5300 U.2
Compared with the 1 mm sampling extent results in Table XII it is clear that laser
modulated particulate incandescence is a more serious problem than background luminosity.
Despite fewer particulates being viewed relative to the normal background case, the
noise increases significantly due to the high temperatures to which the particles are
driven. Furthermore, due to the shift in the blackbody spectral distribution with
temperature, the frequency doubled ruby laser is now only slightly better than the
frequency doubled neodymium laser in contrast to the case of background luminosity.
It should also be pointed out that these S/N ratios are about the best which can be
expected since it was demonstrated in Ref. Qh that the Raman signal to laser
modulated incandescence noise ratio increases with increasing focal flux.
Clearly, the S/N actually obtained will depend strongly on the properties of
the soot dispersion present. As an example, in Fig. 12 (Raman) signal to (laser
modulated particulate incandescence) noise ratio contours are mapped out over soot
dispersion space. These contours were calculated for the previously examined case
of the 1J frequency-doubled neodymium laser inducing Raman scattering from flame
N£ at 2000°K and atmospheric pressure. Also shown are soot dispersions characteristics
of practical devices and sooting flames. Note that for a given mass density of soot,
the calculated S/N increases linearly with particle size. This is due to the scaling
of the particle surface area/volume ratio inversely with particle diameter. For
larger size particles and a constant soot mass density, there is less total surface
area available to radiate. Thus for a given soot mass density, distributions skewed
toward larger particle sizes are less troublesome and lead to higher S/N ratios.
However, a given radiation energy density, R , (Fig. 3) requires that the soot mass
density increase linearly with particle diameter, again due to surface area/volume
considerations. Thus for a certain level of radiation energy density, one finds the
Raman signal to laser modulated soot incandescence noise ratio to be independent
of particle size. Thus contours of constant S/N are contours of constant radiation
energy density. This means that the S/N ratios calculated in Table XIII are valid
independent of the specific soot dispersion characteristics assumed and would result
for the calculated radiation energy density shown in Fig. 3, namely any dispersion
producing an R of 130 (lO"9) Watts/cm^ A sr at 6000$l. For radiation energy densities
an order of magnitude larger, e.g. liquid fuels (Fig. 3), the laser modulated soot
incandescence would exceed the ^ Raman signal in all of the laser cases examined.
These calculations illustrate the serious noise problems facing spontaneous Raman
diagnostics even for scattering from major species constituents. Thermometric
6k
-------
RAMAN S/N MAP OVER SOOT DISPERSION CHARACTERISTICS FOR LASER
MODULATED PARTICULATE INCANDENSENCE
FIG. 12
REFERENCE
87-COMBUSTOR, JP-4
76-CH4: O2. PREMIXED FLAT FLAME
86-BUTANE DIFFUSION FLAME
BONCZYK, UTRC-COMBUSTOR, C3Hg(g)
LASER: IJ, 5320A. 10~8 sec
RAMAN: N2, 2000°K, 1 atm
SOOT MASS DENSITY- g/Cm3
10*
0.01
100
10.0
100,000
PARTICLE DIAMETER
65
-------
investigations from major species may be possible with proper laser selection but,
probably, only at modest radiation energy densities, e.g. < 10 (10~9) Watts/cm A
sr at 6000A. Successful detection of minor species definitely appears unlikely.
At very high focal fluxes, some decreases in noise may occur during the laser pulse
due to particle shrinkage (Ref. 88). Such effects are not anticipated to greatly
improve the S/N ratio, however.
Required S/W and Signal .Averaging
The foregoing S/N ratios can be increased using a noise sampling and subtraction
technique ''Ref. 8U) if the Raman photon count is high enough. In such an approach,
the "noise" is sampled in a spectral region adjacent to the Raman bands simultaneously
with the signal and then subtracted from the signal. In the following, the accuracy
to which this can be done will be briefly explored. It will be assumed that both the
"signal" and "noise" channels can be accurately calibrated relative to one another.
The signals and relative errors on both the "signal" and "noise" channels can be
written for photomultipliers with Poisson Statistics (Ref. 128) as
where T] is the detector quantum efficiency; ns, the number of signal photons; and nn,
the number of noise photons. The shot noise will actually vary from shot to shot;
the relative error quantities shown correspond to the variance in the signal over a
large number of shots and are taken to be representative of the error on any one
shot. The subtraction can be performed to yield the true signal %s, with a resul-
tant signal to noise (S/N)* of
/7]ns(S/N)
' 5
where S/N is the average single pulse S/N ratio, n^/r^. In Fig. 13, the signal to
noise ratio after subtraction (S/N)* is displayed for various initial S/N ratios
as a function of single pulse photon yield for photomultipliers exhibiting a 20 per-
cent quantum efficiency. Note that, depending on the initial S/N and the photon yield,
subtraction may actually decrease the signal to noise ratio! In regions where this
can occur, the curves in Fig. 13 are shown dotted. A 1 joule pulsed laser will typi-
cally produce a Raman yield in the range of KP to 1(A photons/pulse depending on
collection solid angle and collection efficiency from 2000°K, atmospheric pressure
flame N2« Since two channels need to be ratioed to make a temperature measurement
(i.e., the respective relative error will double) a signal/noise after subtraction
on the order of 30-50 would be required for temperature measurements to an accuracy
66
-------
SINGLE PULSE S/N ENHANCEMENT VIA NOISE SAMPLING AND SUBTRACTION
1000
a\
100 -
g
§
QC
I-
m
QC
LJJ
<
z
(/}
10
QUANTUM EFFICIENCY 20%
SHOT NOISE LIMITED DETECTORS
SINGLE PULSE S/N 100
102
103 104
RAMAN PHOTON YIELD
105
to6
P
CO
-------
of about ± k percent. This would require a minimum single pulse signal/noise on the
order of 10. For density measurements to an accuracy of ± 10 percent, a S/N of unity
would -be tolerable since subtraction results in a large signal to noise improvement
for photon yields on the order of several thousand. Thus for typical Raman photon
yields, a minimum single pulse S/N in the range of from 1 to 10 is required for
medium measurements with each pulse.
With signal averaging, the shot noise fluctuations can be averaged out completely
in stationary media (Ref. 8U) permitting measurements to be made. The effect of signal
averaging is to increase the Raman photon count in essence permitting considerable
enhancement in signal/noise as seen from Fig. 13- For example if a typical Raman yield
was KP photons, averaging over 100 pulses at a per pulse S/N of .01 would increase
the S/N after subtraction from 0.7 to 7.
If the medium is fluctuating, however, averaging leads to an accumulation of
terms involving the magnitude and correlation of fluctuations in density and tempera-
ture as demonstrated in Refs. 8U, 109. In Appendix II, an analysis is presented
which details the consequences of ensemble averaging pulsed laser Raman data from
a temporally fluctuating medium. Average density measurements can still be performed
if the Stokes bandwidth factor is made independent of temperature. Fairly wide band-
widths (Fig. 9) a^e required to eliminate the temperature dependence of the bandwidth
factor, leading to lower S/N ratios than those previously calculated for narrow
bandwidth. Temperature measurements are obscured however by averaging, and the data
is no longer amenable to unambiguous interpretation. In this situation temperature
measurements must be performed accurately with each laser pulse. Most practical
combustion devices, of course, are highly turbulent to promote mixing of the fuel/air
mixture. In summary then, for temperature measurements in turbulent media, individual
channel Raman signal/noise ratios of at least ten appear required. For temperature
measurements in stationary media and for density measurements in any situation,
lower S/N are tolerable, generally above 0.01, but signal averaging over many pulses
(generally more than one hundred) is required.
Practical Combustion Device Applicability
It is difficult to be categorical about the utility of spontaneous Raman
scattering in regard to practical combustor diagnosis. There are undoubtedly measure-
ment situations to which spontaneous Raman scattering can be successfully applied.
For example, in exhaust regions and some secondary combustion zones where particu-
late loadings may be substantially lower than in the primary zone, Raman measure-
ments are potentially possible. What has been attempted in the foregoing sections
are Raman S/N calculations for both background luminosity and laser modulated soot
incandescence employing a common value of radiation energy density typical of a
hydrocarbon-fueled primary combustion zone. Recall that the Raman/laser modulated
soot incandescence S/N ratio is independent of the specific dispersion characteristics
for a given radiation energy density. The S/N calculations were made at favorably
68
-------
high peak powers and focal fluxes. The latter were somewhat speculative in regards
to gas breakdown, whose occurrence, of course, would obviate any measurement. For
single pulse thermometry or detection of minority species quantities, laser modulated
soot incandescence led to unacceptably low S/N ratios. For frequency doubled ruby
lasers, fluorescent interferences are probable as well but more difficult to predict
a priori without experimental investigation. The S/N ratio can be improved somewhat
by noise sampling and subtraction and enhanced considerably by signal averaging.
Signal averaging in turbulent, fluctuating media appears permissible only for density
determinations, but, for low concentration species detection, an inordinate number
of pulses would need be averaged over.
In regard to cost and probability of success, the following comments may be
offered. The dye laser considered is the least expensive approach (~ $10 K) but is
faced with very low S/N. Experience at UTRC with such a laser confirms this conclu-
sion. A 1 Joule frequency-doubled neodyraium laser is quite expensive ($1*4-0 K, Ref.
130), yields fairly good major constituent S/N in some but not all situations and
can be operated at good repetition rates for diagnostics (10-20 pps). One Joule ruby
lasers are cheaper ($20-50 K , depending on mode quality desired) but are generally
limited to a pulse/second at best. In the cases considered here, they were less
attractive than 2X Wd. If frequency doubled, the 2X ruby appears slightly better
than 2X Nd re particulate incandescence, may be worse vis-a-vis fluorescence and
suffers, of course, from lower repetition rates. Furthermore, 2X ruby laser gas
breakdown thresholds may be considerably lower than those for 2X Nd due to multipho-
ton ionization phenomena (2X ruby has a 3.6 ev photon energy). In summary, the costs
for these potentially successful lasers are high, and the probability of success for
spontaneous Raman scattering in these environments even for thermometry from majority
species appears fair at best. For trace species measurements (i.e. < 1000 ppm), the
probability of success is poor over a broad range of combustor operating conditions.
Thus spontaneous Raman appears to be a high risk approach for practical device diagnos-
tics.
Clean Flame Diagnostics
Previously it was shown that trace species detectivity was quite limited even
with high energy pulsed lasers- and poor spatial resolution. For clean flames, the
high peak Raman powers produced by pulsed lasers are of no special diagnostic advan-
tage, except for turbulence studies where time resolved measurements are desired.
From a collected Raman photon standpoint, there is no difference between a 10 pps,
1 Joule pulsed laser and a 10 Watt continuous wave laser. However cw lasers do possess
the general advantages of lower cost, increased operational reliability, better line-
width and better beam quality, cw gas lasers are generally diffraction-limited per-
mitting the use of multipass optical scattering cells to expediate photon collection.
For conditions similar to the pulsed laser detectability limit calculations presented
earlier, calculations of photon counting time versus NO concentration were made and
are summarized in Fig. Ik. Shown parametrically is gas temperature, measurement
69
-------
CW LASER RAMAN NO COUNT TIMES
FIG. 14
106
105
CO
Q
LU
CO
LU
z
I
10*
103
ONE ATMOSPHERE PRESSURE
P8 OPTICS
10% COLLECTION EFFICIENCY
10% QUANTUM EFFICIENCY
102
10
10
~6
10"4 10~3 10~2
NO CONCENTRATION
10-1
70
-------
accuracy as determined by shot noise considerations, and laser power times pathlength
product. For example, 10 Won may correspond to a 10 Watt laser over a 1 cm spatial
resolution, one Watt over 10 cm, one Watt over 1 cm multipassed 10 times, etc. These
calculations were made assuming unity bandwidth factor. From Fig. 13 it is seen that
in a flame at 2000°K, species concentration measurements to 10 ppm with 10 percent
accuracy could be made with a 5 watt argon ion laser, multipassed over a 1 cm path
with a gain of 20 in about 7 minutes. Without a multipass approach or for measure-
ments to greater accuracy, considerably longer times are required. Species concen-
tration measurements much below 10 ppm would require inordinately long measurement
periods and do not appear feasible.
Near-Resonant Raman Scattering
Review
Near-resonant Raman scattering, in principle, could lead to a substantial
increase in the Raman cross sections, and, concomitantly, to great increases in the
Raman intensities. In near-resonant Raman scattering, the laser frequency is tuned
near an electronic resonance in the molecule being probed (see Fig. l). Formerly
resonance fluorescence and resonant Raman scattering were treated as separate physi-
cal processes. Current theories (Refs. 131, 132) hold that they are essentially the
same physical process distinguished by the frequency difference between the absorp-
tion and laser lines. As the frequency difference, AUJ, becomes small, the state
liftetime (1/Aco) becomes long, i.e., if energy is not conserved in the transition to
the excited state by an amount 4^, then via an uncertainty relationship, the lifetime
of the molecule in the excited state is limited to 1/Atu. Hence as the detuning dw
decreases, the "scattering" changes from a nearly instantanous Raman-like process to
a longer lived fluorescence emission process exactly on resonance. Although resonance
Raman is a commonly used term, the nomenclature of Ref. 133? namely near-resonant
Raman scattering, will be used here. That near resonance leads to greatly enhanced
scattering is illustrated by the fact that the intensity of scattering for the induced
transition n -» m is given by (Ref. 9)
'k p 2 (26)
nm
where v is the incident laser frequency and v^, the frequency corresponding to the
transition n -» m. Pnm is the induced electric moment matrix element given by
where E is the electric vector of the incident light; r denotes any level of the
complete set of the unperturbed molecule ; vri, the frequency corresponding to the
frequency difference of states r and i; and M^, the corresponding transition moment
71
-------
Clearly when vo lies near a particular real absorption frequency vrn, the intensity
of scattering will be significantly enhanced and so-called near-resonance Raman
scattering is observed.
In liquid solutions, substantial increases, on the order of 10°, in the Raman
intensities have been reported in certain instances (Ref. 9). Until recently, rela-
tively little had been done on-near-resonant Raman scattering in gases. Many studies
have concentrated only on spectral (Refs. 13^, 135 and 136) and/or lifetime (Ref.
131) observations. Penney (Ref. 132), Robrish et al (Ref. 137) and Fouche and Chang
(Ref. 138) have examined the degree of resonant enhancement attainable. Fouche and
Chang, tuning across the 511+5 A* argon ion laser line, report a ratio of the near-
resonant Raman l£ cross section to the ordinary Raman cross section of N2 of 2.6(10 ),
an enhancement of six orders of magnitude. It is interesting to note that the
resonance fluorescence was three orders of magnitude stronger than the near-resonant
Raman. It should also be pointed out that Williams et al (Ref. 131) showed that the
change from a longer-lived fluorescence process to a short-lived Raman process occurred
in just 2.3 GHz, which at 51^5 A corresponds to a detuning of only 0.02 A. Robrish
(Ref. 137) reports a resonantly enhanced l£ cross section at 5^66.36 A in atmospheric
pressure N2, U(lO°) greater than the No spontaneous Raman cross section. In N02 they
report a cross section of 5.6(10~27)cnr/sr at ^5^7.8 A, resonantly enhanced by about
three orders of magnitude over those reported in Table V. Clearly, very narrow laser
linewidths and very good laser frequency stability are required to avoid exciting
potentially stronger fluorescence interferences. In high temperature flames with
high water vapor concentrations, this may be less of a problem due to severe quenching
of the fluorescence.
Whether such large enhancements can be expected in all cases is not clear. For
example, Penney (Ref. 132) performed a calculation for the near-resonant enhancement
of NO tuning into the y(0,0) band at 2265 A and estimated a factor of only forty
enhancement. In a similar calculation, Robrish et. al. estimated a near-resonant
enhancement of 1,6(10°) (Ref. 139). There has not yet been an experimental examina-
tion of near-resonant Raman in NO. Enhancement is a strong function of band strength
and six orders of magnitude enhancement certainly may not be typical, e.g., NOo. One
additional advantage of tuning near strong bands, as Penney points out, is that it may
permit operation at larger detuning, relaxing requirements on laser linewidth and
stability. Penney points out another difficulty with molecular near-resonant Raman
in contrast to atomic work. Namely, and this is particularly true at high flame
temperatures, the fraction of molecules in the appropriate initial state can be very
small. A similar situation is encountered in laser fluorescence diagnostics. Unlike
Q branch Raman scattering, where the entire rotational ensemble can be sampled with
appropriate detector bandwidth, in near-resonant Raman only a single transition is
probed. Several lines could be simultaneously excited presumably but the degree of
near-resonant enhancement would not be uniform, leading to unacceptable diagnostic
nonlinearities.
72
-------
Practical Applicability
Recall that in practical combustor flames, spontaneous Raman scattering appeared
tenuous for the probing of even majority constituents. Near-resonant enhancement of
several orders of magnitude would certainly alter this view. Unfortunately, the major
species of interest such as N2, Og, CO and C02 possess strong absorption bands only
at or below 2000 A (see Tables III, IV) making them inaccessible to near-resonant
enhancement. Wear-resonant enhancement of minority species Raman cross sections is
mitigated by three factors. First, by definition the low number densities associated
with minority species offset the potential gains in cross sections so at best, enhanced
minority species signals might be comparable to spontaneous Raman signals from major
constituents. Second, the enhanced minority species signal is reduced by the laser
energy compromises which result from the very narrow linewidth and spectral selec-
tivity requirements of the laser source. Third, the requirement to probe a selected
vibrational-rotational state as opposed to the entire band further decreases the
generated signal. Thus, it is concluded that near-resonant enhancement of minority
species Raman cross sections will not produce signal levels comparable to the spon-
taneous Raman signals from major species which were previously found lacking. Thus
for the remote probing of practical combustion devices (high background luminosity,
particulates) near-resonant Raman scattering does not appear particularly feasible.
Potential Applicability
In clean flames, near-resonant Raman scattering could permit probing of some
molecules for which fluorescence is precluded or expedite photon collection in other
cases. For example, in H02 where fluorescence is severely quenched under typical
flame conditions (Ref. 55), near-resonant Raman may offer signal advantages over
spontaneous Raman scattering. In molecules which dissociate upon absorption of light
and, hence do not fluoresce, near-resonant Raman scattering may possibly be employed.
In 12 for example, near-resonance Raman was first observed at photon energies beyond
the dissociation limit (Ref. 13*0 before it was observed below the limit (Ref. 138).
In instances where photo-dissociation occurs, it is argued that, because of its
extremely short lifetime, near-resonant Raman can be observed prior to molecular
dissociation. Photon collecticn will only be expedited, of course, if the near-
resonant enhancement achieved overcomes the sacrifices in laser energy and restricted
state populations necessary to produce the effect.
73
-------
LASER FLUORESCENCE
Introduction
Laser-induced fluorescence is a process, illustrated in Fig. 15, in which
the laser wavelength is tuned to coincide with a molecular absorption, thereby
causing the molecule to make a transition to an excited electronic state. Following
absorption of the radiation, the excited molecule then returns to the ground state
with emission of radiation. This fluorescence may be at the same wavelength as
that of the exciting radiation, termed resonance fluorescence, or may be shifted in
wavelength. In this latter case, the molecule returns to a vibrational state
other than that from which it originated.
Laser-induced fluorescence has received considerable attention recently as a
potential method of species concentration measurement. The technique is of interest
both with regard to atmospheric and flame environments. Baardsen and Terhune
(Ref. 37) and Wang and Davis (Ref. 38) have applied laser-induced fluorescence to
detect OH in the atmosphere. In flames, the technique has been applied to CN by-
Jackson (Ref. 28), to CH by Barnes, et al (Ref. 27) and to C2 by Jones and Mackie
(Ref. 2U) and Baronavski and McDonald (Ref . 25). The results of these latter works
reflect the fact that the technique is still in its early stages of development
with respect to flame and atmospheric probing. In particular, the flame measure-
ments referred to are seen to be in fact demonstrations of feasibility. Up to the
present time, concentrations have not been determined with good accuracy at ppm
levels. Some of the specific problems associated with probing a turbulent reactive
flow characteristic of a combustor have been discussed by Wang (Ref. ll+O). Wang
reviews several different laser diagnostic techniques including laser- induced fluo-
rescence. In regards to fluorescence, Wang concludes that low number density measure-
ments are feasible, in principle, but that it may be difficult in practice to
implement the technique for a complex chemical system owing to the spectroscopic
and quenching data which are needed. Quenching corrections have always been a major
problem in fluorescence diagnostics. Here the view is adopted that analytic quenching
corrections to fluorescence data are feasible only in very well characterized flames,
where temperature and major quenching species concentrations are known. In less
well characterized, turbulent combustion media, such analytic corrections would,
most likely, be very inaccurate. Accordingly, approaches are discussed herein,
which obviate the difficulties and uncertainties associated with the need for
quenching data and corrections. These approaches involve saturated laser- induced
fluorescence whose importance with regard to species measurement was first realized
by Piepmeier (Ref. l^l) and more recently by Daily (Ref.
There are several basic criteria which must be satisfied if fluorescence
measurements are to be performed on a given molecule. The first of these is that
the molecule must have a known emission spectrum. This is not always the case
-------
MOLECULAR ABSORPTION/FLUORESCENCE
VJl
(a) ABSORPTION
V
(b) FLUORESCENCE
P
~*
O1
-------
since a molecule when excited to a given state may dissociate prior to the
emission of a photon. Specific examples of this are given in Tables III and
IV. In some cases assigning the absence of emission to predissociation is
necessarily speculative since it may be difficult to rule out the presence of
emission which is very weak and difficult to observe. Second, the molecule must
have an absorption wavelength which is accessible to a tunable laser source. At
the present time, the spectral range covered by tunable dye laser sources is roughly
the interval from 2000 A to 1.5 microns. In the case of the near UV wavelengths
it is often necessary to frequency double the visible laser output to achieve the
desired UV wavelengths. Several atoms and molecules, which are not amenable to
laser-induced fluorescence techniques since the absorption occurs at wavelengths
less than 2000 X are listed in Table VII. A third requirement is that the rate of
radiative decay of the excited state be known. This is simply due to the fact
that the fluorescence power is proportional to this rate. Fourth, if other mole-
cules are present, the excited state loss rate may be increased considerably over
the radiative rate due to collisions involving the excited state and other mole-
cules. The increase in total decay rate due to collisions is known as quenching.
Historically, it is the requirement to correct the measured fluorescence power for
quenching,prior to obtaining the species number density from the measurements,which
has limited the applicability of the technique. The quenching correction involves
knowing the partial pressures of all species present other than the one of interest,
as well as the rates for deactivation of the excited state of the species of interest
by all others present. In addition to this is the requirement that the dependence
of these rate constants on temperature be known. Suffice it to say that all of this
information is difficult if not impossible to obtain.
There are ways by which the difficulties associated with quenching may possibly
be circumvented. These relate to saturation of the absorbing transition, achieved
through the use of pulsed lasers with high spectral intensity. Saturation may be
thought of as a condition for which a sizeable,equilibrium population in the
excited state is achieved. Daily (Refs. 1U2-1UU) has discussed saturation for the
case of full saturation whereby the fluorescence power may be shown to be complete^.-/
independent of quenching and incident laser spectral intensity. If full saturation
is achieved, it is not necessary to know the partial pressures of other species pre-
sent, nor is it necessary even that these.be identified. A somewhat different
approach has been taken by Baronavski and McDonald (Ref. 25). In this case, the
requirement is for near saturation of the absorption. It may be shown that a
measurement of fluorescence power versus laser spectral intensity yields the total
quenching rate and number density provided that appreciable (but not complete) sat-
uration is achieved. This is an important distinction in practice, since complete
saturation may require unattainable laser spectral intensity.
The technique of partially saturated laser fluorescence is not without its
difficulties. This technique involves measurement of fluorescence power as a functior
of laser spectral intensity. Accordingly, species concentration may not be determinec
76
-------
from a single laser pulse. This is of concern for measurements in a highly
turbulent medium wherein temporal fluctuations of temperature and species concen-
tration occur. At best then, a time-averaged concentration may be determined.
Analysis is yet required to address the effects of signal averaging and to
determine preferred measurement approaches. Measurement of the average species
concentration also depends on knowing the flame temperature. This follows since
the fluorescence power is representative only of the population of the particular
vibration-rotation level of the molecule which absorbs the radiation. To compute
the total population of the ground level of the molecule by use of an appropriate
Boltzmann factor requires that temperature be known. Another potential difficulty
with the saturation technique involves the multi-rotational level nature of mole-
cules. Molecules with many rotational degrees of freedom are more difficult to
saturate when collisional relaxation among rotational levels takes place in a time
which is short compared with the time for relaxation of the excited state. For
this reason it may be very difficult to saturate transitions in molecules such
as RHp and N02.
Fluorescence Theory
Piepmeier's Approach
Tiree
The three-level system which is treated in detail below is illustrated in
Fig. 1.6. The analysis given follows Piepmeier (Ref . lUl) closely. This system is
appropriate, for example, to a case in which level 3 is near level 1 and collisional
cross-relaxation occurs between them. The rate equations in this case are given by
dt
Q13) + N3(Q31 + A31)
and
(28c)
where 1^, N2, and N are the populations of levels 1, 2, and 3; A^y A^ and A21, the
rates for radiative decay between the subscripted levels; Q-, Qo» Q and
_ 2l
the rates for collisional relaxation; and b , b__ , rates associated with stimulated
absorption and emission, respectively. Theiineshape is introduced in b-^ through
b!2 = 0B2q^F " VL^' where p ls the laser energy density; B^, the Einstein
77
-------
FIG. 16
LASER-INDUCED FLUORESCENCE FOR THREE-LEVEL SYSTEM
A
i Q23'A23
b2VA21'°21
°31'A3V
78
-------
coefficient for stimulated absorption of radiation; q(v - v ) the lineshape
factor. For the lineshape factor a Lorentzian profile is assumed hence
q( v - v ) = _
(29)
where v is the molecular frequency; v , the laser frequency; Q, , a net rate for
all collision processes which interrupt stimulated emission. Omitting substantial
algebraic detail, it may be shown that in the presence of the laser the fraction of
molecules present in level 2 in the steady-state (dN /dt = dN /dt = dN /dt = 0) is
given by
N2 D p Bi2/(l+L)
ITT B^} (30)
In Eq. (30), the parameters K, L, and D are given by K = (^ + Q^V^i +
L = Qi3/(Qo;j_ + A3i); D = (^21 + ^cV(-A2i + ^23 + ^3)' Next account is taken of
the thermal motion of the molecules in the gas, i.e., Doppler effect. It is
assumed that despite the presence of the laser, the total population retains its
Maxwell-Boltzmann distribution of velocities. The function which describes the
Doppler-broadened frequency distribution is given by
(3D
where N is the total population appropriate to all frequencies, vj Av tne
width associated with the molecular frequency, v . It follows then that the fraction
of molecules in level 2 with inclusion of the Doppler effect is given by
HP DPB!2 fT exp [-(2(v-vp)/Avn) In2] dy _
= (32)
Dp B +
The procedure for evaluation of the integral in Eq. (32) is known (Ref. 1^5 )•
the case VL = v » the fraction of excited molecules is
(33a)
79
-------
In Eq. (33a), the parameters F(a,R), a and R are given by
i 1. a 1
F(a,R) = n2 a(l+R)2 exp [a (l+R)J erfc [a(l+R)2j (33b)
(330)
and •
1+K
B .
B12>
The parameters g., and g in Eq. (33a) are the degeneracies of levels 1 and 2,
respectively. The term erfc in Eq. (33b) refers to the "error function". Tabula-
tions of this function for various values of its argument are readily available
(Ref. 1^5). The parameters a and R have a precise significance. The parameter a
gives the ratio of the homogeneous to the Doppler width and, hence, characterizes
the absorption lineshape. The parameter R is a saturation parameter. It gives
the ratio of the rate for stimulated emission to the rate appropriate to de-
excitation of the molecular excited state owing to radiative decay and collisions.
The quantity F(a,R) approaches a value of unity for a and/or R large. Consequently,
the more homogeneous the lineshape and/or the more intense the laser the less
important is the factor F(a,R). In order to demonstrate the sensitivity of the
factor F(a,R) to laser .intensity, the quantity [R/(l+R)] F(a,R) is plotted as a
function of R in Fig. 17, for the case of homogeneous broadening (a > l). The
theory, as given by Piepmeier, is applicable to the case of strong homogeneous
broadening. The parameter R is proportional to laser intensity, 31. The fraction
of molecules in the excited state may be obtained from Fig. 17 after multiplication
of ordinate values by {(l+L)[(g1/g2) + (l+K)/(l+L)]]~1. The latter factor is the
limiting value of (Np/N^) in the case of R very large. This corresponds to full
saturation of the molecular transition. It is worthwhile noting that in evaluating
(Np/N^) the fluorescence power is also evaluated since it is proportional to Np.
The fluorescence power is given by
A21 , W2 n
SF = h^F^ "cVc (^>N°>
where Q is the light collection solid angle; V , the sample volume; and h,
Planck's constant. The exact shape of the curve in Fig. 17 is dependent on the
magnitude of a. The practical implication of this is that the shape may be
different for different temperature flame zones. If full saturation of the trans-
ition is not achieved, determination of species concentration by measurement of
the fluorescence power requires knowing the Doppler and homogeneous widths of the
transition as well, as the rate constants. Even if full saturation is achieved and
80
-------
FIG. 17
SATURATION FOR HOMOGENEOUS BROADENING
DC
ti
tr
+
10-1
10
-2
10
-1
j
Ft
10
102
81
-------
[R/(l+R)3 F(a,R) -» 1, the rate constants still enter through the parameters K and L.
Therefore, for a three-level system full saturation does not obviate quenching cor-
rections if only fluorescence at v is measured. In view of the above, the presence
of an active third level is viewed as seriously complicating species measurements.
A specific example, where effects such as these could be important, is for CIT.
Here it is known that, in addition to emission from the excited state B £ to the
ground level X2^, emission from B2£ to A2n has also been observed (Ref. U2). A
second example involves the OH molecule where fluorescence occurs via £ (v1 = l)
-» 2n(v" = l) °r 2Z+(v' = 0) .» 2n(v" = 0), whereas the excitation corresponds to
2n(v" = 0) + V(v' = 1) (Ref. 39).
Two Levels
It is desirable to apply the above analysis to a two-level system. The
reasons for this are as follows: (l) It is important to know whether the satura-
tion behavior of a two-level system differs from that of a three-level system. If
so this would provide a means of detecting the influence of a third level. (2) By
performing a two-level analysis with inclusion of lineshape factors, a more ready
comparison may be made between these results and the two-level results of Daily
(Refs. lUs-lUU) and Baronavski and McDonald (Ref. 25) which are discussed below.
(3) The two-level model is the model one would.hope to apply to species determina-
tion. The reason for this resides in the relative simplicity of the model, and the
more direct interpretation of experimental results.
For a two-level system, the appropriate rate-equations are
—-^ = -N b +N(A +Q +b )
dt VIS 2V 21 ^21 °21; (35a)
and
= Nb - N (A + Q +b).
dt 1 12 2^ 21 *21 2l' (35b)
If a steady-state is assumed, it is readily shown that
; (c)2 + Dp(B 3 , (36a)
2 ' KV 12 21'
where
82 •
-------
If this result is compared with that given in Eq. (30) above, it is apparent that
the two-level result may be inferred from the three-level result by setting L=K=0
and defining a new D as given in Eq.. (36b). Accordingly, for a two-level system
with lineshape analysis included, it follows that
x '" (37a)
in which
Dp
R
,A21-H3C.2 (37b)
The parameter a retains its earlier definition. It is apparent that there are
not any significant differences between a two-level and a three-level system as
regards the dependence of Hp/N on a and R. When R is large the limiting value
of (N2/N°) for a three-level system is (l+L)[(g1/g )+ (L-HC)/(l+L)]~^» whereas for a
two-level system it is [(g-j/gg) + l]"1- The ratio of degeneracies (g-j_/g2) is
generally known. Consequently, if one succeeds in fully saturating a two-level
system the details of the lineshape are not relevant and the fluorescence power is
completely independent of quenching. As is shown in Eq. (3^)j the fluorescence
power depends on k^ and ^. Accordingly, N° may be determined without quenching
corrections provided that Ap, is known, which is often, but not always, the case.
Daily's Proposals
Two .Levels
Daily has made two proposals for the measurement of species concentration via
laser-induced fluorescence methods (Refs. 1^2-l^U). These are related in that, in
both cases, saturation of the absorbing transition is shown to eliminate the need
for quenching corrections to the fluorescence yield. The first proposal involves
observing the temporal behavior of the fluorescence, while the second involves time-
averaged measurement of the fluorescence power.
For the case in which the temporal behavior of fluorescence is monitored,
Daily suggested excitation of the molecule with a laser pulse, abrupt turn-off of
the pulse after equilibrium saturation is achieved, and temporal measurement of the
subsequent fluorescent decay. In such a case, the fluorescence power may be shown
to be given by
(38)
83
-------
where S is the fluorescence power at time t; SF(t=0), the power at the time of
laser cut-off. Accordingly, if the laser is turned-off abruptly, the time con-
stant of the fluorescence decay gives (Q, + A2^) and, hence, the quenching rate Q
provided that Ag^ is known. In this way, the total quenching due to all other
species present is determined directly, and reference to individual rates and
partial pressures of other molecules is not required. If the absorption is fully
saturated the number of molecules in the upper level may be seen to have a very
simple relationship to the number in the lower level. This relationship is given
n
Iff — f U /ft! J.U \ ~11\T ^
"fe - ^/'^ %!>»! (39)
It may be shown then that the number of molecules in the absorbing level is given
n,° = [(8i/fo) + J'-r^ ,r-7T^ r Sy(t) at, (to)
where \_ is the fluorescence wavelength. The significance of this result may be
summarized as follows: If the laser intensity is large so that Eq. (39) is valid
and the temporal behavior of the fluorescence power is measurable, the number
density N.. may be determined from one trace of fluorescence versus time provided
that g, , g and A^, are known. The number density is the area under the curve
of SF(t). The quenching term Q is derived from the decay of the fluorescence.
It is important to remember that determination of the total number density of
molecules in the ground level from N-, is possible provided only that the gas tem-
perature is known. This temperature must be measured separately. Further, A-,, is
not always known precisely. A practical difficulty, which one may encounter in a
flame at 1 atm pressure, is that Q is large and hence, the decay so rapid that it
is not possible to shut off the laser pulse abruptly enough to time-resolve the
fluorescence. It is known that quenched excited molecular lifetimes in a flame
can be as short as 10"12 sec (Ref. 25). In principle, a Pockels cell can function
as a shutter with about a 500 picosecond response time, but this represents its limit
of operation. Moreover, photomultipliers have response times which are typically
tenths -of -nanoseconds at best. Accordingly, time resolving picosecond decay times
is a formidable task.
Daily's second proposal deals with time-averaged measurement of the fluorescence
power. In this case, the fluorescence power is given by Eq. (3*0. This is equiv-
alent to measurement of the number of fluorescence photons emitted without reference
to time resolution of the excited-state decay process. In the limit of small laser
-------
spectral intensity I. , i.e., laser intensity per unit bandwidth, IL/CAVT» it may
be shown that N2^l) = N^jgl, /(Q^ + A21), whereas in the limit of large I ,
N \2) = [i + (g-j/gg)]"1 N£ 7 In the former case, the fluorescence is ^
S(l) Hfc.
Sp -Kc/T'l^
Here it is apparent that Sj. ' depends on IT and quenching Qpn through the factor
^21' (^21 + ^21^> which is commonly referred to as the fluorescence yield or Stern-
Vollmer (Ref. 1^6) factor. This factor may be very small; it is not unusual for
it to be of order 10~" (Ref. 25), thereby severely limiting the fluorescence power.
In the limit of large IT , however, use of N^' yields
S (2) hf
sp =n(
In this case, EL., is independent of quenching and laser spectral intensity.
Accordingly, the sought for N^ may be determined by measurement of Sp without
any reference to quenching. This result is identical to that of Piepmeier for
two-levels in the case that R » 1.
A practical difficulty is whether I, can be made large enough that Eq. (Ulb)
applies. This is discussed in detail further in the text. However, it is con-
cluded that it is very difficult to saturate a transition fully such that Eq. (Ulb)
may be used directly to infer N,°. This is due to practical limitations con-
cerning achievable spectral intensities. A way around this difficulty has been
suggested by Baronavski and McDonald (Ref. 25).
Three Levels
The preceding discussion was confined to a two-level system. Daily has con-
sidered a three-level system as well (Ref. 1^3). The principle conclusion is that
species concentrations may be determined without reference to quenching in the three
level case as well, providing that the absorbing transition is fully saturated and
that measurements of fluorescent intensities at two wavelengths are made. Daily
points out that this procedure is applicable to more complex systems although the
separation of the increased number of fluorescence intensities may be more diffi-
cult. Again there remains the uncertainty as to whether it is possible to saturate
the absorbing transition fully.
-------
Baronavski-McDonald Approach to Species Measurements
Baronavski and McDonald have made use of Daily's proposals regarding saturated
fluorescence (Ref. 25). A difference in their approach involves the recognition
that it may be very difficult in practice to saturate a transition completely.
Accordingly, their analysis is appropriate to a condition for which the degree of
saturation is high but not complete, a condition more common in practice. The
analysis applies to a two-level system. The fluorescence power in exact form is
given by
i N1°B12
SF = hCc/AJCA^/Mn v. ^ (U2)
They then expand S about (I ) in a Taylor series. This results in an approxi-
mate expression for SF given oy
)(A21/8rr)n V
c c
0
,
(B,, + B
From Eq. (Us), it is evident that SF has a linear dependence on (I ) In a
plot of SF versus (IT ) , the intercept of the resulting straight line is
essentially N-^0, while the slope of the line depends on the quantity of fn " '
from which the quenching rate can be determined. The accuracy of the N, measure-
ment depends on knowing \F, QC, V and Ap,. The former three parameters can be
obtained through suitable calibration. Uncertainty in the determination of N,
then depends on the uncertainty in
Baronavski and McDonald applied the preceding method of analysis to the
determination of C~ concentration in an oxy-acetylene flame. A concentration of
10 cm~3 was determined with a factor of 3 uncertainty. This latter uncertainty
was due to lack of precise values for the apparatus parameters fi and V . Inclusion
of the uncertainty in A21 would result in still larger error in N-,°. In determining
the Cg concentration, a value of 10~° was obtained for the fluorescence yield factor
This emphasizes the extreme importance of quenching in
influencing the fluorescence intensity for a case in which the laser spectral
intensity is far less than that required for saturation. The maximum laser power
appropriate to the G£ measurements above was about 1CH Watts . This was achieved
with a flashlamp-pumped dye laser. The laser was focused to a spot size of 0.1 mm,
corresponding to an intensity of 1.3 x 10^ Watts/cm2. The beam divergence of such
lasers is typically 1 milliradian at best. For measurement in a 1 meter diameter
furnace, where the focusing lens could be as much as 50 cm removed from the sample
86
-------
volume, the focal spot size would be about 0.5 mm, corresponding to an intensity
of 5.2 x 105 Watts/cm2. This would not suffice to saturate the C2 transition
sufficiently to permit implementation of the Baronavski-McDonald analysis procedure.
For such furnace measurements to be feasible, laser powers on the order of 2? (lO-~)
Watts would be required.
Lineshape
The preceding discussions of the saturation properties of the fluorescence
power are not applicable to arbitrary values of the laser spectral width AVT
relative to the molecular linewidth. The molecular linewidth is determined by con-
tributions from collisional and Doppler broadening. If the pressure is high and
temperature low, the lineshape is homogeneous. If the gas temperature is high and
pressure low, the Doppler effect predominates and the lineshape is inhomogeneous.
Cases occur wherein the two effects contribute almost equally to the linewidth.
Figure 18 displays the homogeneous and inhomogeneous broadened linewidths for NO,
where collisions of WO with water molecules primarily determine the homogeneous
width, Av. It is seen that for the temperature range 1000°K < T < 2000°K, AVTT >
Av for PTT > 10 torr. The Piepmeier analysis is appropriate to the case in which
homogeneous broadening is present and the molecular linewidth exceeds the laser
spectral width. Daily and Baronavski-McDonald treat the case where the laser
spectral width exceeds the molecular linewidth. More detailed discussions of these
subtleties are given by Greenstein (Ref. ll*7) and Killinger, Wang and Hanabusa
(Ref. 39). Here discussion will be limited to pointing out the differences which
occur for the two cases with regard to the manner in which the quenching influences
the saturation of a two-level system.
If the laser spectral width exceeds the molecular linewidth, it is not difficult
to show from the preceding discussions that
WP
-0 - ±— I —1 (UUa)
Hl
where
R!=_JZ 21 "v . (UUb)
(02!
In Eq. (UVb), ]L = IL/(CAV ) and Rf is seen to be inversely proportional to the
product (Qp + A-" ) (cAv ) , It may be shown that for a two-level treatment following
"Piepmeier the saturation parameter is
IL
R = - — ' (U5)
-------
FIG.18
DOPPLER AND HOMOGENEOUS LINEWIDTHS FOR NO
o
I
Q
Q
I
162
103
TEMPERATURE - DEC KELVIN
10
102
(TORR)
103
-------
2
and R is seen to be inversely proportional to (Q~ + A ) . In general then, the
two cases differ in the way the saturation parameter is defined, and for the case
of ^iepmeier the term F(a,R) is present. If the molecular lineshape is strongly
homogeneous, F(a,R) is nearly unity in value and, hence, this distinction vanishes.
However, even for a homogeneous lineshape the distinction exists between R and R1.
Of course, should the intensity of the laser be so high that both [R/(l+R)] and
[R'/Cl+lR')] have values of approximately unity, then all reference to lineshape
and quenching becomes unimportant, and the two approaches agree as regards (Ng/N, ).
Hence, in applying a two-level model to species determination, it is apparent
that not one model applies to all cases. The model selected must satisfy the
existing relationships between the laser spectral width, homogeneous and
inhomogeneous molecular width.
Molti-Level Saturation
The preceding models are strictly appropriate to systems where only two or
three levels are present. If such models are applied to estimate the laser spectral
intensity required to saturate a molecular transition, where many closely-spaced
rotational levels are present, the saturation intensities estimated will be low.
Multi-level saturation has been discussed by Christensen, Freed and Haus (Ref. 1^8)
with reference to the CCU molecule and depends on rapid cross-relaxation among the
rotational levels within the time of electronic deactivation of the molecule. In
this way, the effective relaxation rate can be shown to be increased by the weighted
relaxation rates of all the other tightly-coupled rotational levels. If there are
M rotational levels populated at the gas temperature, the effective rate is Qeff =
MQ,, thus resulting in an increase in the laser intensity required to achieve satura-
tion. For a diatomic molecule, it is a straightforward matter to estimate M, which
is the inverse of the number of molecules in a given J-state in relation to the
total number of molecules present in a given vibrational state. Specifically, the
parameter M is given by (Ref. 23)
f /hcB \ I."1
M = (Wj/N°) = -) (2J+1) exp -[j(J+l)hcB /M] (U6)
I \ kT / J
where B is the rotational constant; k, Boltzmann's constant; T, the gas temperature; and
J, the rotational quantum number of the excited level. An evaluation of M for a
selected group of molecules is given in Table XIV. The J value is that which
corresponds to maximum population in the Boltzmann distribution for 2600 K.
Two-Photon Spectroscopy
Attention has been given by others to species measurement via two-photon
absorption of radiation (Ref. 1^9) which eliminates the need for frequency-doubling
to achieve near UV wavelengths. A single visible source may be used. This
technique is not given consideration here in that perturber concentrations and
individual quenching rates are required. This requirement arises, since with
89
-------
TABLE XIV
EFFECTIVE NUMBER OF ROTATIONAL LEVELS
(2600°K)
Molecule JM/\v (Maximum Population) M
MAJv
CH 7 13
CN 21 36
NH 7 12
OH 6 11
NO 22 38
available laser sources, it is not possible to saturate a two-photon absorption
with severe excited state quenching present. The two-photon absorption rate would
have to be comparable to the single-photon rate required for saturation. This,
however, is unlikely in the presence^of quenching since the two-photon absorption
cross-sections are approximately 10" - 10~ of the single-photon cross-sections.
Signal to Noise Estimates
Signal Strength Calculations
Signal strength estimates are made for the molecules CH, CN, NH, OH and NO.
These molecules have known emission spectra, absorption wavelengths accessible to
tunable dye lasers and known lifetimes for radiative decay. The existence of quenching
information concerning these molecules is, in principle, not relevant since quenching
corrections may be determined experimentally using the Baronavski and McDonald approach.
Attention is not given to the molecules N02 and NE^. The molecule N02 has a relatively
long lifetime for radiative decay of (2 x 10"5) sec. Since the saturation parameter
is inversely proportional to this lifetime, it is unlikely that it is possible to
saturate the N02 transition at Xp(N02) = kOOO A. The molecule NH2 has a shorter
lifetime for radiative decay of (5 x 10-7) sec and a relatively long fluorescence
wavelength, XF(NH2) = 5700 A which makes it more favorable than N02 vis-a-vis satura-
tion. The difficulty with NH2 is analytic; namely, it is a strongly asymmetric mole-
cule and this makes it difficult to compute M. For this reason detailed estimates
for NH2 are not made. However, it appears to be a molecule worthy of experimental
study in order to determine if saturation can be achieved since X^M^) = 5700 A
which is a favorable wavelength regime for high power tunable dye lasers.
90
-------
The saturation fluorescence analysis given by Baronavski and McDonald is
applicable for the case in which AvL>AvH as previously stated. For the diatomic
molecules above, the absorption is homogeneously broadened in a flame environment
and A\JH is determined by the electronic deactivation of the excited molecular
state by collision with water vapor molecules. Water is taken here as the dominant
broadening species in a flame due to its relatively high partial pressure and its
efficiency as a quencher. In the case pf the NO y-bands for example, the homo-
geneous width, AVH is O.U3 cm"1 computed using a quenching rate of 6.8U x 10^ sec'1
Torr"1 (Ref. 150) and a water vapor partial pressure of 120 Torr (Ref. 151). For
the laser spectral width, a value of Avj, = 2.5 cm'1 is used in the computations;
this value is consistent with the spectral width achieved recently with a flash-
lamp-pumped dye laser (Ref. 152). Accordingly, the ratio of linewidths in this
case is AVL/AVJJ = 5«8 so that Av^ > AVJJ is satisfied. In the case of the y-bands
of NO and a temperature of 2600°K, it is readily shown that Avj) = 0.15 cm"1 or
The expression which is used to evaluate the fluorescence signal power is
given by (Ref. 25)
where the saturation parameter may be shown to be given by
The expression for SF is equivalent to that given previously in Eq. (U2). The
degeneracies g, and g2 in this case are assumed to be approximately equal. This is
an adequate approximation for transitions involving moderately high vales of J.
For the signal estimates, an F/8 lens system for light collection is assumed
corresponding to an ncof 0.012 sr. For a 90° sampling geometry and unity magni-
fication optical transfer (Fig. U), Lc is equal to the aperture diameter A, here
assumed to be 1mm in diameter. Assuming a laser beam divergence of Imilliradian
and a 50 cm focal length lens, the cross sectional area, AC, of the focused laser
beam is rr/U (.05 cm)2 or 1.96 (10~3) cm2. Hence the sample volume Vc is 1.96
*) cm3.
The evaluation of the saturation parameter R would be straightforward were
it not for the uncertainty regarding Q for the molecules CH, CH and NH. For these
molecules, rates for electronic quenching by water vapor are unknown. The situa-
tion is somewhat better, however, for the molecules WO and OH. In the case of
quenching of excited NO 2£+ , the rate is 6.8U x 108 sec'1 Torr'1 (Ref. 150). This
rate was measured at 300° K. The rate which corresponds to a temperature of 26dO°K
91
-------
is expected to be larger, but data at this or nearby temperatures are not available
and calculation of the rate at 2600°K from first principles is difficult if not
impossible (Ref. 153). In the case of OH, the rate for quenching of the 2£+ excited
state is 1.1+5 x 10? sec~l Torr"1 (Ref. 15^), a value considerably smaller than that
for NO. Again, in the case of OH the rate is known only at the temperature of 300°K.
The reason for the smaller rate in the case of OH is probably due to the fact that
the dipole moment of OH is 0.95 Debye whereas for NO the dipole moment is much
larger and eq.ua! to 7.U? Debye (l Debye = lO'1^ esu-cm). Thus, despite similar
electronic structure of the excited state, the forces acting between NO and H20
in a collision exceed those between OH and, H^O. In view of the lack of data and in
order not to;underestimate the intensity required to saturate transitions in CH, CN
and NH, the procedure adopted here is to use, for the quenching rate in these cases,
the larger of the two values above, namely the quenching rate for NO. Even this
value may be too large however. In the work of Basco, Callear and Norrish, (Ref. 150),
a value of 6l6(A)2 is given for the collision cross section for electronic relaxa-
tion of NO (A2£+) by NO (X2I). In the subsequent work of Callear and Pilling
(Ref. 155), a value of 35(A)2 is given. No reference is made to theoearlier work.
The value of Callear and Pilling is in reasonable agreement with 25(A)2 and l8(A)2
as measured by Melton and Klemperer (Ref. 156) and Broida and Carrington (Ref. 36),
respectively. This raises serious doubt concerning the correctness of the value
given by Basco, Callear and Norrish. In addition, this may imply that the cross
section given by these latter authors for relaxation by ^0 is also much too large,
which would lower significantly the laser spectral intensity required for satura-
tion of CH, CN, NH and NO. It is tempting to take a less pessimistic view and
assume the rates associated with CH and NH are the smaller OH value since CH, NH
and OH have comparable dipole moments. This is not done. However, it is important
to keep in mind that estimates made below of laser spectral intensities required
to saturate transitions in NH and CH may be high, and the resolution of this
uncertainty resides in performing NH and CH saturation measurements.
In Table XV, the quantity [R/(l+R)] is evaluated. The parameter M is intro-
duced to account for an increase in Q to MQ due to the presence of M rotational
levels in the excited electronic state. Accordingly, [R/(l+R)] is calculated
using Eq. (Vfb) except that Q, is replaced by (QM). If (QM)"1 is evaluated for NO,
the result is (Ojyf)"1 = (3 x lO^S) sec. This appears at first sight to be a very
short time; however, Baronavski and McDonald have measured quenched lifetimes on
the order of 10"12 sec for C2 molecules in an oxy-acetylene flame. Accordingly,
the present estimate of (QM)"1 for NO may not be unrealistic.
In Table XV, the transition is completely saturated in the case that [R/(l+R)]
-• 1. It is apparent from the Table that for the laser intensity and spectral width
given, substantial saturation is achieved for all molecules except NO. The reason
for this is that R is proportional to \j,3 and A^ and for NQj these parameters are
small relative to other cases. This leads to the conclusion that despite its
importance in combustion processes it may be difficult to measure NO in the manner
described herein owing to difficulty in saturating the transition.
92
-------
TABLE XV
SATURATION TERM DJ FLUORESCENCE INTENSITY
IL = 108 watts/cm2, AvL = 2.5 cm"1, T = 2600°K
Molecule MA) M I [R/(1+R)]
CH ^315 13 0.82 0.45
CN 3883 36 1.8 0.64
NH 3360 12 0.46 0.32
OH 3064 n 8.0 0.89
N0 2270 38 0.10 0.09
In order to compute SF from Eq. (4?a), it is necessary first to evaluate NI°
This latter number density is distinct from the total number density of molecules
N° present at 1 atm pressure and at 2600°K. It is well known that N^ is given by
NI = ifif^fJ, where fv and ar are evaluated from appropriate vibrational and rota-
tional partition functions (Ref. 23). For 2600°K, 1 atm pressure and a species
concentration of 1 ppm, it follows that N° = (2.84 x 1012)/cm3. The product fvfJ
for the molecules of interest is given in Table XVI along with the number density,
N]_0. The calculation is done for excitation from the level v = 0 and J = J(MAX).
TABLE XVI
NUMBER DENSITY OF ABSORBING MOLECULES
Concentration = 1 ppm @ 1 atm total pressure, T = 2600°K
Molecule (*v=o)(fJ=JMAx) Hj^cm-S)
CH 6.2 x 10~2 1.8 x 1011
CN 1.9 x lO'2 5-5 x 1010
NH 7.0 x lO-2 2.0 x 1011
OH 7.7 x 10"2 2.2 x 1011
10
NO 1.7 x iO'2 4.9 x 10'
It is now possible to evaluate SF in Eq.. (47a) for the five molecules. Values
of SF are given for CN, OH and NO in Fig. 19- From these curves, it is possible to
determine the minimum value of Ij^ required to saturate the transitions to an extent
which permits evaluation of N]_0 as described in preceding discussions. These values
are given in Table XVII and are appropriate to R ± 1 for each molecule. Values are
given in Table XVII for 12 Torr of ^0 as well, in order to stress that less water
93
-------
FIG. 19
FLUORESCENCE POWER VERSUS SPECTRAL INTENSITY
10-7
106
107
(WATTS/CM2 CM-1)
109
1010
-------
vapor lowers the threshold for saturation correspondingly. If a plot of SF versus
1^ is made for a molecule such as CN at a temperature lower than 2600°K, namely
at SAT°1K' the T^6 °f ^ \iS n0t chan«ed markedly. In the case of CN at 1000°K,
ILV = 1 x 10 watts/cm2 cm'1. Accordingly, calculations are presented in Fig.
19, only for the one temperature of 2600°K.
TABLE XVII
SATURATION LASER SPECTRAL INTENSITY
(T = 2600°K)
ILVSAT %SAT
Molecule XF(A) (12 Tor* HgO) (120 Torr H£0)
CH 4315 4 x 10^ Watts/cm2 cm"1 4 x 107 Watts/cm2 cm"1
CW 3883 3 x 106 3 x 10?
NH 3360 1 x 107 1 x 108
OH 3064 6 x 105 6 x 10°
WO 2270 4 x 107 k- x 10°
It is important to realize that for a molecule the fluorescence can occur in
a large bandwidth. This is due to fast cross-relaxation among rotational levels
which establishes rotational equilibrium in a time which is generally short com-
pared to the electronic deactivation time. The emission occurs in a width influenced
by B and T. As an approximate method of estimating this bandwidth, k\F, the separa-
tion of the P- and R-branch maxima for a diatomic molecule is taken to be A\p which
is equal to 2.36 JBeT (Ref. 23). Values of A\F for the 5 molecules are given in
Table XVIII. These are important for the estimates below of species detection
limits.
TABLE XVIII
FLUORESCENCE EMISSION BANDWIDTH
(T = 2600°K)
Molecule Xp(A) AXr(A)
CH U315 85
CW 3883 25
NH 3360 56
OH 3064 49
NO 2270 8
95
-------
Species Detection Limits
In order to set detection limits in ppm for the species, it is necessary to
make estimates of the signal-to-noise ratio (S/N). This requires taking into
account the various sources of noise. In this regard, three sources of noise
are considered. The first of these is elastic scattering of the laser radiation by
the particulates in the flame, namely Mie scattering. Mie scattering cross sections
are given in Fig. 6. The second is the radiation energy density which is given in
Fig. 3. The third source of noise is laser -modulated particulate incandescence.
The background due to Mie scattering depends on particulate properties, namely
the number of particulates present, their size and refractive index. The Mie power
occurs at the same wavelength as that of the incident radiation and may be estimated
by use of
PM = (da/dn)(npVc)ncIL
where dcr/dQ is the differential cross section; np, the particulate number density.
For kOO A particles, 5000 2 laser radiation and 90° viewing, it may be shown that
da/dQ = (U x lO"1^) cm2/steradian. If np = 108/cm3, IL = 10? Watts/cm2, and Vc and
Oc are as given earlier, the Mie power is calculated to be PM = 1.1 (10""5) Watts.
The very large Mie power precludes observation of the fluorescence exactly at the
wavelength of the exciting radiation. Fortunately this does not constitute an unre-
solvable difficulty since fluorescence is emitted in a broad spectrum. Spectrometers
with good discrimination are available and it is possible to observe shifted fluores-
cence.
For the radiant energy density a value is taken from Fig. 3 typical of that
measured in the Rainbow furnace. For wavelengths of ^OOOA or less, a region of
particular interest in view of the fact that Xp £ 14-315A for the given molecules, a
conservative value for the radiation energy density of 100 (10~9) watts/cm3 A
steradian is assumed. For a detection bandwidth of 10A, and the previously assumed
vieving parameters, the background power is calculated to be 1.6(10-10) watts. In
the discussion which follows concerning laser -modulated particulate incandescence,
this radiant power is seen to be small.
It may be shown that the noise power due to laser modulated particulate incan-
descence is 6.9(10-9) Watts for a 10A bandwidth, Vc and nc as above and X = 6073A.
This value is appropriate to l+OOA particles in a concentration of 10^/cm3, and was
scaled from earlier calculations. Comparing it with the radiant power, it is appar-
ent that the laser modulated incandescence is more than an order of magnitude more
important than the background luminosity. The former is therefore used in the S/N
calculations. The laser -modulated particulate incandescence wavelength dependence
is determined by the black-body distribution function, namely X~5 [exp(hc/XkT) - I]"1.
Table XIX gives noise powers for the wavelengths of interest inferred from the
value above at 6073A using the black-body distribution function.
-------
TABLE XIX
LASER MODULATED PARTICULAR INCANDESCENCE NOISE POWER LEVELS
AX = 10A, ftc = 0.012 ster, Vc = 1.96 (10"M cm3
Molecule XF(A) Noise Power (Watts)
7.5(10-9)
CN 3883 6.9(10-9)
NH 3360 5.5(10-9)
OH 306U 4.^(10-9)
NO 2270 1.2(10-9)
With the values given in Table XIX, it is possible to compute S/N ratios for given
species concentrations. An example of this is given in Fig. 20 for CN. In Fig. 20
a spectrometer efficiency of 30 percent and a 10 sec laser pulse width are
assumed. Species detection limits are summarized in Table XX. In practical flames,
the lower limit on species concentration is taken as that concentration which
yields S/N a 10. Limits are also given for the case of a clean flame. In this
case, the view is adopted that the limit of sensitivity is set by the available
number of photons. The values given correspond to about 150 photons at the cathode
of a photomultiplier tube. This may be shown to yield about a 1 mV signal at the
photomultiplier anode for a reasonable choice of gain, capacitance and quantum
efficiency.
TABLE XX
DETECTION LIMITS FOR SPECIES MEASUREMENT
Practical Flame Clean Flame
Molecule ppm # photons ppm # photons
CH 80 U.7 (loj|) .26 150
CN 10 3.1 (104) .05 150
NH 25 3.1 (10M .13 150
OH 35 1.6 (10^) .32 150
NO 1 3.1 (103) .05 150
From Table XX, it is apparent that saturated laser fluorescence appears capable
of quite sensitive trace species detection for the molecules to which it is applic-
able. This is true even in practical flame situations. For example, if the S/N
requirement is relaxed to unity, measurements below 10 ppm may be possible for all
the species listed.
97
-------
SIGNAL-TO-NOISE ESTIMATE FOR CN
FIG. 20
100
10-1
1 10
CN CONCENTRATION - PPM
98
-------
Apparatus Calibration
In order to determine a number density from a measurement of the fluorescence
power, values for a number of parameters related to the measurement are required
•which are exclusive of the fluorescence power itseLf. Aside from fundamental con-
stants, the following are required: (l) XF, fluorescence wavelength; (2) Ag^,
radiative decay rate; (3) nc, light collection solid angle; (k) Vc, sample volume;
(5) ILV (implies knowing laser intensity in watts, focused area in cm2 and spectral
width in cm"1; and (6) e, light collection efficiency. Quantities which lend them-
selves to measurement with some precision are Xp- and ITV, although there may be
some difficulty in determining the focused area precisely. For Agj., the usual
procedure is to use the best value available in the published literature. For
flc, Vc and e, the uncertainty in these values may be large; that is, these uncer-
tainties are likely to be more significant than those for X^,, ITV and AO-, . For
the preceding reasons, it is important to have a calibration procedure in order to
be able to determine eflcVc. A calibration procedure which does not require detuning
X-^ away from X-p is most desirable. One such procedure which fits these requirements
very well is spontaneous Raman scattering from room air nitrogen. Since this latter
process is non-resonant, it may be used at any wavelength corresponding to the mole-
cule chosen. Therefore, resonance-fluorescence and spontaneous Raman emission may
be observed at Xp. This calibration procedure has been used successfully by Wang
and Davis to measure OH concentration in air (Ref. ^0 ). Indeed, in this latter case the
spectrum of scattered light displayed Raman scattering from Ng, 0% and water. The
only requirement of this approach is that the Raman cross-section be known which it
is to fairly good accuracy.
Required Temperature Measurements
In order to determine the total species population of interest, once the
population of the initial level excited is determined from the fluorescence measure-
ments, it is necessary to know the flame temperature. Since it may be necessary
to pulse average the fluorescence measurements, and since fluctuations of tempera-
ture in a turbulent medium cause population changes, it is desirable to select a
particular initial J-level for measurement which is least sensitive to changes in
population due to temperature fluctuations. If this is possible, an average
temperature, as determined, for example by CARS, may be used to compute the species
concentration from the measured fluorescence power. This then would eliminate the
need for simultaneous and instantaneous temperature measurements.
The particular J-value which achieves this end is determined by evaluating
dfj/ST and equating the result to zero, fj is the fraction of molecules in the
state J and is given by (Ref. 23)
(2J+1) exp - [BeJ(J+l) he AT].
99
-------
If this is done, the rotational level meeting this requirement is determined from
J*2 + J* - (k/Behc)T . o, (50)
where T is an average flame temperature. This is a quadratic equation with real
roots and is trivial to evaluate. If J* is evaluated for the CN molecule and for
T = 2000°K, the result when rounded to the nearest integer is J* = 27. This contrasts
with the state of rotation associated with a population maximum of 2000 K which is
JMAX = *9' In FiS- 21 » fj* and fjMAx f^6 Plotted versus temperature for average
temperatures of 2000°K and lUOO°K. For T = ,lUOO°K, fj* - 22 and fj^ = l6' In
both cases, it is evident that f,-* is signincantly less sensitive to temperature
excursions about T than f^y Indeed, for 20$ fluctuations in temperature for the
case T = 2000°K, f * changes by no more than 3-5$ while fjMAY can vary up to 10$.
In view of the above, it is important to select for excitation the level J . Thus,
despite temperature fluctuations it may be possible to determine reliably a con-
centration even for the case in which averaging of pulses is required by using the
average temperature.
Summary
The significant conclusions of this section are: (l) Of all the molecules of
interest in combustion processes, only a few are amenable to detection by laser
fluorescence. (2) The laser spectral intensities which are required to saturate
the molecular transitions are of order (10-10°) Watts/cur cm" . In the case of
OH the estimated spectral intensity is probably reliable. In the case of CH, CN,
NH and NO the estimated saturation intensities may or may not be too high depending
on the correctness of assumptions made concerning the relevant quenching rates. For
these latter molecules, it is desirable to make laboratory measurements in order to
determine the saturation laser intensities. (3) Laser modulated particulate incan-
descence is the principal background noise source, (k) The lower limits of detection
sensitivity are determined by laser modulated particulate incandescence for practical
flames and by photon considerations in clean flames. (5) Calibration of the
fluorescence apparatus is best done by measurement of spontaneous Raman scattering
from N2 in air. (6) By proper choice of excitation level, it appears possible to
employ an average temperature to avoid simultaneous temperature measurements and
which might make averaging possible. (7) If saturation is achieved, detection
limits are typically in the tens of ppm for the molecules considered in practical
flames.
Practical implementation and systems considerations are discussed in a sub-
sequent section.
100
-------
FIG. 21
CN FRACTIONAL POPULATION VARIATION WITH TEMPERATURE
4.0 -
1000 1200 1400 1600 1800 2000 2200
TEMPERATURE - DEC KELVIN
2400
2600
2800
101
-------
COHERENT ANTI-STOKES RAMAN SCATTERING (CARS)
Introduction
CARS techniques have recently come to prominance for combustion diagnostics
based upon the investigations of Taran and his coworkers (Refs. 19, 157-160) at
ONSRA in France. The effect was originally discovered in the early sixties by Maker
and Terhune (Ref. l6l) and essentially remained in the province of nonlinear optics
investigations until Taranfs application of it for gas phase diagnostics. In the
United States, Harvey and his coworkers (Refs. 162-165) have conducted numerous inves-
tigations into the technique. Barrett has demonstrated both CW CARS generation
(Ref. U5) and pure rotational CARS (Ref. 166). Broadband CARS generation in a single
pulse has also been obtained (Ref. 16?). Publications describing investigations into
the technique are appearing at an ever increasing rate and the technique apparently
will have a major impact in molecular structure and biological studies. The technique
has also been described as four wave mixing or three wave mixing, but use of the
acronym CARS seems to be gaining broad acceptance.
Review
CARS is probably best understood by reference to Fig. 22 The explanations
outlined in Refs. 160 and 162 will be followed. Incident pump photons at frequency
o)-j_ interact with photons at mg (often termed the Stokes beam) through the third order
nonlinear susceptibility x'3) (-u> , uu, uu, -uuo) to generate a polarization component
which produces radiation at the anti-Stokes frequency ouq = 2uu_ -2 is close to the vibrational
frequency of a Raman active resonance, the magnitude of the signal generated becomes
very large as will be seen. Because of the requirement to conserve linear momentum,
the anti-Stokes signal emerges as a diffraction-limited beam at an angle, 9', as
shown in Fig. 22 . Consequently all of the CARS radiation can be collected. Contrast
this with the situation pertaining in the normal Raman process where photons are
scattered over UTT sr and are collected only over a limited solid angle, n. Further-
more, since CARS can be collected in an extremely small solid angle, discrimination
against background luminosity and laser induced particulate effects is greatly facil-
itated. In actuality, the pump (uu-|_) and Stokes (0)2) beams need not be precisely
aligned as shown in Fig. 22 since a certain amount of phase mismatch is tolerable,
namely,
JLC = TT (51)
where |Ak| is the magnitude of the vector
Ak = 2^ - kg - k^ (52)
102
-------
COHERENT ANTI-STOKES RAMAN SCATTERING (CARS)
(a) ENERGY LEVEL DIAGRAM
FIRST EXCITED ELECTRONIC STATE
STIMULATED STOKES EMISSION
s
U>
VIRTUAL STATE
CO,
VIRTUAL STATE
ICARS)W3
STIMULATED ANTI-STOKES
EMISSION
GROUND STATE
(b) PHASE-MATCHING DIAGRAM
2k
REF. BEGLEY. ET AL. APPL. . HYS. LETT., 25, 387 (1974)
-------
where k is the wave vector, 2n/X and Jt,c is the coherence length between u^ and u)2.
I depends on the frequencies and the dispersion of the medium. For most gases in
the visible the coherence length is on the order of tens of centimeters (Ref. 159)
permitting colinear alignment of the pump and Stokes beams, while still satisfying
the phase matching requirements.
The CARS intensity Io at uJo is expressible as
0 0 o
*i % M2*2 (53)
where 1^ is the intensity at frequency uj*; x, the third order nonlinear susceptibility,
and z, the distance over which the phase matched interaction occurs. The suscepti-
bility can be written in terms of a resonant and nonresonant part, X111',
X = X' + i X" + X™7 . (5U)
X111" is the contribution from electrons and remote resonances. The resonant suscepti-
bility associated with a homogeneously broadened Raman transition, j, is
X' + i X" = N A g -2 - -, - - 7—7 - r (55)
< - - - i -
where fi is Planck's constant divided by 2-rr; N, the total species number density;
AJ, the population difference between the levels involved in the transition; g-,
strength factor and equal to (v. + 1) for a Q, line; (6
-------
where f is the focussing lens focal length; D, the beam diameter at the lens; and X,
the pump laser wavelength. The foregoing correspond to a diffraction angle, k/-n (\/V)
of 0.07 milliradians at 5320 A and D = 1 cm. In actuality, most pulsed solid state
lasers used for gas phase CARS work are not diffraction limited, but possess diver-
gence angles on the order of 1 milliradian. Due to the cubic dependence on intensity
of the CARS signal, the CARS signal generated for a given focal length lens will
vary inversely as the sixth power of the divergence angle. In the example above this
could lead to an overestimation of the CA&S signal intensity by a factor of nearly
seven orders of magnitude. Furthermore, with colinear beams the region over which
the CARS is generated may exceed the desired spatial resolution. For example, in
Table XXI below, the diffraction limited geometric parameters are displayed for vary-
ing focal length lenses.
TABLE XXI
Focal length (cml
10
100
1000
CARS PROBE VOLUME
Diameter (cm)
6.11 (-M
6.11 (-3)
6.11 (-2)
Length (cm)
1.22 (-2)
1.22
122
As can be seen with a one meter focal length lens which may be necessary in some
measurement situations, the resolution would be about 1.2 cm and may exceed the
resolution desired. In the signal estimates to be made here, the intensity formula
tions will be employed to show explicitly the spatial resolution and focal lengths
employed.
CARS Signal Strength and S/W Calculations
Signal Magnitudes
If the detuning frequency, AUJ . = uu . -
susceptability may be expressed as
- tu2) is introduced, the resonant
(58)
where
,u
U2
105
-------
On resonance Auo. » 0, and |x| = K.. Assuming the CARS beam to have the same cross
sectional area as the Stokes beam, the CARS power is
22 (60)
Consider an atmospheric pressure flame at 2000°K. For W , the rotational
distribution peaks at J = 18 and A. can be shown to be 0.029. Since the line
strengths of the individual Q, branch lines have only a weak dependence on J (i.e.,
most of the scattering arises from the trace of the polarizibility tensor, Ref. 9)»
the cross section for Q (18) is assumed to be the unresolved Q branch cross section.
Assuming
-------
to a temperature of 6000°K over a 20 cm extent. Actually, due to the gradient in
focal flux along the laser beams, the particles will not all reach 6000°K. The 20 cm
extent corresponds to 2FA (Fig. k) for an aperture of 0.05 cm and F = 200. For the
2(10-5) sr viewing solid angle, and a 1 A bandwidth, the collected laser modulated
incandescence is calculated to be 1.5^ (10"11) Watts, nearly an order of magnitude
below the 100 ppm signal level. For an order of magnitude increase in number density,
corresponding to the highest luminosity displayed in Fig. 3, the laser modulated
incandescence would be comparable to the 100 ppm signal level for the conditions
assumed. It appears then that both background luminosity and laser modulated soot
incandescence should not pose serious noise problems for carefully designed CARS
diagnostics.
Population Perturbations
Taran (Ref. 160) describes two potential perturbations in CARS diagnostics. The
first is stimulated Raman gain wherein,because of too high an intensity at u)-^, the
Stokes wave at u^ experiences gain and ?2 is no longer the initial power introduced.
This effect is generally weak as the previous examination of stimulated Raman scat-
tering demonstrated. The second effect involves a perturbation in A^ expressible as
- 2
\ «(!)„=- / -.1 \ nu ; t
j
on line center. Clearly, since A*(t) = A,-(0) exp (-t/T ), for the population
distributions to be unperturbed, T. » T., where T. is the laser pulse duration.
Evaluating Eq. (6l) for the previously assumed parameters in the signal strength
calculations, i.e., I-^Ig - 2.6(1017) W2/cmL|', T is found to 750 (10""9) sec, much
larger than the laser pulse duration of 10 (10-9) sec so that no perturbation occurs.
For laser and Stokes focal flux products of 2(10^°) W^/cm , a 10 percent population
change will occur. Consequently the product of the laser and Stokes beam intensities
should not exceed this value.
Medium Property Measurements
In this section some of the problems and limitations of the CARS technique
will be examined. These will include interference effects which complicate the CARS
spectrum and nonresonant contributions which limit species detection sensitivity.
Interferences
2
From Eq. (51*) and noting that P- ~ |x| , the square of the absolute value of
the susceptibility is given by
107
-------
x
2 - x'2 + 2x'xnr H- x^ + x"2 (62)
X' and X" have a functional dependence on the detuning frequency, AUJ = ^ - (u^-u^),
similar to the real and imaginary parts of the refractive index about resonance as
illustrated in Fig. 23 . X" exhibits line shape behavior and X' derivative behavior,
i.e., Xf is positive or negative depending on the sign of AUJ. In the absence of the
nonresonant background, X111", [x|2 is equal to X'2 + X1'2 and the CARS spectrum exhibits
line shape behavior as the detuning is scanned through the resonance. However, in
the presence of nonresonant background, the CARS spectrum will exhibit "anti-
resonance" behavior when the Ex'X"1" term is negative. Far from resonance the CARS
signal will be proportional to X111" • As resonance is approached the signal will
fall below this value as illustrated in Fig. 23 and then exceed this level when X'
becomes positive.
In the presence of multiple resonances, for example when probing a vibrational-
rotational distribution with small rotational spacing, the susceptibility must be
written as, recasting Eq. (58),
(63)
J J
Consider the case of two adjacent resonances, 1 and 2, when one is tuned to the
first resonance, then X-j = 0 and
[x|2 = x^2 + 2X'2 x" + x1^2 + xf + 2 x^ H- xf
lip nr-2
Hence, on line center of the first resonance, in addition to X^ + X1^ which
would constitute the signal from a single resonance, there are additional "contri-
butions" to the signal from the nearby resonance. The term 2XoXnr may be a positive
or negative contribution depending on the relative orientation of the two resonances.
Thus unlike the Raman spectrum which, for the most part, mirrors the distribution of
state populations, the CARS spectrum is much more complicated as evidenced by the
distributions displayed in Ref. l60.
Thermometry
Temperature measurements have been performed from CARS measurements of flame
W2 by Taran (Ref. l6o) from the rotational distribution of the Q branch under high
resolution, and from the ratio of the CARS peaks from the ground and first vibratior.al
states. The first technique gives greater accuracy, since, for high J values, there
is little line overlap, the resonant susceptability is much larger than the nonresonar/:
contributions and interference effects are small. This permits a straightforward
temperature determination from the rotational population distribution. The second
108
-------
CARS SPECTRA
WEAK LINE
STRONG LINE
I
Aw = 0
T]
p
KJ
OJ
-------
technique is less accurate since, at high temperature, the high J valued Q branches
from the ground vibrational state interfere with the first vibrational state signal.
Because of the complex nature of the CARS process, signal averaging in temporally
fluctuating media will certainly obscure interpretation of the CARS spectrum leading
to temperature measurement errors. In such cases, measurements will have to be per-
formed with each laser pulse. This can be done with a device such as a multichannel
spectrum analyzer (Ref. 168) or a pair of interference filters appropriately placed.
In the case of the spectrum analyzer, considerable improvement in the state-of-the-art
will be required before high resolution spectra can be captured accurately from a
molecule such as Kg. To date the technique has been demonstrated only in CH|^ and K-,
(Ref. 167), where in the latter case, due to the very large rotational constant, i.e.,
B0 ss 60 cm™1, the CARS Q branch is well dispersed. The use of interference filters
will require an elaborate CARS computer program with accurate linewidth, filter
function, etc., input; this remains to be experimentally demonstrated.
Despite these spectral complications, CARS appears to be the best approach for
thermometry in practical combustion devices. With moderately powerful, pulsed laser
sources, collected CARS signal strengths significantly greater than background
luminosity and laser modulated soot incandescence can be generated. However, inter-
ference free CARS generation has yet to be demonstrated in sooting flames. Of pos-
sible jeopardy in this regard are potential, nonlinear particulate interactions which
shall be discussed later.
Species Concentration Measurements
For simplicity consider the case of a single resonance belonging to the species
of interest immersed in a background diluent, e.g., Nj in air fed combustors. Then
Eq. (6k) applies and on resonance may be written as
. .2 2 *"2 2 *nr2
|x| = Ns XS + \\ (65)
where NS is the species density of interest; N , the diluent or majority species
density; and the caret notation on the susceptibilities indicates the per molecule
susceptibility. From Eq. (65) it is clear that when the background contribution
begins to dominate the susceptibility, species detection and measurement will be
precluded. The nonresonant third order susceptibility has been measured for a number
of gases (Ref. 169) and for atmospheric pressure N2 is 1.35 (1CT11) cm^/J. Recall
that the previously calculated resonant susceptibility for the Q(l8) line of Wo at
20CO°K was 2.l4.8(lO'10) cm3/J. On a per molecule basis one finds xg1" « 5(10-3!) cm^/J
and Xg «s 8.8(10~29) cm°/J. Assuming the resonant susceptibility calculated for N2
to be representative of any diatomic minority species, Eq. (55), the minority species
resonant and nitrogen background nonresonant contributions are equivalent for a
110
-------
minority species concentration of about 6000 ppm assuming N2 to constitute the
background. Actually, the foregoing illustration is greatly oversimplified and among
other things neglects other Q, line contributions to the total signal. Also for weak
lines in a strong background, the CARS signal does not maximize at resonance; the
CARS peak is actually shifted off resonance. For weak lines, the CARS spectrum
resembles the real part of the resonant susceptibility as it in effect "modulates"
the nonresonant background (Fig. 23). Nevertheless, the foregoing approach illus-
trates the fundamental limitation on minority species detectivity in the presence
of other gases using CARS techniques. Namely, for very low minority species concen-
trations, the resonant susceptibility contribution from the species of interest
(i.e., the signal) is masked by the nonresonant contribution of the background gases.
Without going into the details of the derivation, a more rigorous approach
(Ref. 160) yields the minimum detectable species density as
k
f> ID- !"•
" nr
where a is the peak to peak fluctuation in the relative CARS signal magnitude, and
n, the number of pulses averaged over. Using Eq. (66), a detailed calculation was
performed for the case of CO detection. For a typical or of 0.3 (Ref. 160) and a
single shot (i.e., n = 1) the minimum detectable CO concentration in a 2000°K flame
was calculated to be 9^ ppm. With the exception of light molecules such as Hp_,
typical minimum detectivities for heavier molecules using CARS are generally about
1000 ppm. As Taran points out, these must be considered order of magnitude estimates.
For Hp where the large rotational spacing leads to large values for AJ, and due to the
narrow linewidths, detectivities to 10 ppm appear possible. Experimentally, Taran was
able to detect H^ in No *° about 100 PI™ (Ref. 159)• However, for most molecules of
interest in combustion situations, CARS species detectability limits appear to be on
the order of 1000 ppm. However, several variations of conventional CARS have been
proposed to reduce or eliminate these background interferences and will be examined
briefly in the next section.
CARS Variants
Variations of the CARS technique previously described have been proposed in an
attempt to eliminate or suppress the nonresonant contributions of background gases.
Most of the techniques to be outlined have only been demonstrated in liquids. Their
application for combustion diagnostics has to be considered speculative at this point
until such time that they are successfully demonstrated. Furthermore, they generally
represent additional sophistication and, hence, additional complexity to an already
complex technique.
Ill
-------
Resonance Enhancement
The third order susceptibility has the form (Ref. 162)
X3 ~ (u^-uj (u^-u^-u; j + ir-jMaw-L-ujg-iDb)" (67)
where ui and uu are electronic transition frequencies. Note that x displays
resonant enhancement as the input laser pump frequency, o^, or the anti-Stokes
frequency, uu^ = 2u>i-u>p, approaches an electronic transition in the same manner that
spontaneous Raman scattering shows near-resonant enhancement. By analogy with near-
resonant Raman scattering, detectivities in the ppm range are anticipated (Ref. 170)
but yet to be demonstrated. Besides the obvious difficulty of tuning to an elec-
tronic resonance (if accessible) there are fundamental questions as to whether the
nonresonant background may not also be enhanced. Certainly the cross terms between
the real part of the resonant susceptibility and nonresonant background will be
enhanced.
Double Resonance CARS
In this approach demonstrated in liquids (Refs. 171 and 172) three beams at
O)Q, ULL and (Dg are introduced into the medium under observation, u;^ and uig are tuned
as in the usual CARS arrangement to the resonance of interest. CUQ is tuned in such
a way that u>Q-u>p approaches a resonance from another constituent. For example, in
a combustion application one might tune near fig. Writing the susceptibility as X =
X, + Xp + X*1^ where the subscript 1 refers to the resonance being probed and 2 to the
resonance being exploited, the square of the absolute value of the susceptibility is
|X2 = X2 + 2X + 2X.xnr + X2 4- 2X*nr + ^ + 2X + X (68)
* ' nr
If '-"Q-^O are tune
-------
CARS experiment that background contributions can be eliminated resulting in
undistorted line shapes. This approach is similar to double resonance in that three
beams are employed, U)Q, w^t and but only u--uu need be tuned to the resonance
under investigation. In a polarization orientation approach termed "asterisk",
because the properly aligned polarization directions resemble a star, no detectable
background was found for detection of 3 percent benzene in carbon disulfide. For
conventional CARS, orthogonally oriented laser and Stokes beams are preferable with
the CARS viewed parallel to the laser beam. However, this technique does not suppress
background to the extent "asterisk" does.
Background Subtraction
Background subtraction techniques have been investigated using reference
nonresonant samples (Ref. 175) but the noise reductions were more modest (factor
of three) than expected. One could consider doing in-situ background subtraction
using a three beam approach where ^Q-^O is not tuned to a second resonance. Such
an approach however cannot eliminate interference effects between the resonant and
nonresonant susceptibilities, but might improve species detectivity accuracy depending
on the photon levels involved. The subtraction accuracy or signal/noise improvement
would be comparable to that calculated in Fig. 13. As before, subtraction accuracy
on a single pulse is limited by photomultiplier tube shot noise effects.
Preferred Variant
Of all of the foregoing approaches, the polarization techniques appear most
promising for near term investigations in terms of simplicity and potential benefit.
These approaches have not been demonstrated as yet in gases and one can only conjec-
ture as to what the improvement in species detectivity might be. One to two orders
of magnitude may be possible, potentially permitting CARS species measurements in
the 10 to 100 ppm range. Also of potential importance is the elimination of the
anti-resonance effects leading to "clean" spectra which would facilitate simpler and
more straightforward data reduction approaches, particularly, in regards to
thermometry.
Practical Applicability
Based upon the preceeding considerations, CARS appears to possess high potential
for successful application to practical combustion device probing. The calculated
signal levels appear to be well in excess of the collected noise levels, such as
background luminosity and laser modulated soot incandescence. These signal levels
were produced by laser and Stokes intensities well below population perturbation,
gas breakdown and stimulated Raman scattering thresholds. Potential jeopardies
include phase mismatching induced by turbulence and nonlinear interferences generated
113
-------
by interactions with particulates. The former effect is not anticipated to be
serious in general. This conclusion is based upon the fact that LDV is performed
rather routinely in modest sized turbulent combustors, and from the interference
fringe examinations by Farmer in the EPA Rainbow furnace (Ref. 71)-). At worst,
occasional interruptions in the CARS data rate might be anticipated. Analogous to
the nonresonant majority species background interferences, nonresonant CARS genera-
tion from the soot particulates and the soot vaporization products could be problem-
atical. With the laser intensities used in CARS, it is clear from earlier discus-
sions of laser-soot interactions, that significant soot vaporization will occur
during the time of the pulse (Ref. 88). Due to the density squared scaling of the
CARS signal, the high pressure soot vapor species may produce serious nonlinear,
nonresonant interference. CARS techniques have yet to be demonstrated in sooting
flames; this represents an area in which further investigation is required to
address this potential problem. In general the jeopardies appear modest.
The probability of successful thermometry appears to be high although data
reduction may be more complex relative to Raman processes. Species concentration
measurements appear likely with good chance of success to about the 1000 ppm level.
Potential improvements in detectibility appear possible using polarization approaches
or double resonance with probability of success for measurements in the 10-100 ppm
range assessed as fair. For low density flame work, high peak power laser sources
are absolutely required. Pump laser selection narrows quickly to either ruby or
frequency doubled neodymium. From a systems standpoint the latter, although gener-
ally more expensive, appears preferable. 2X Nd lasers can be operated at a repeti-
tion rate generally an order of magnitude higher than ruby, at least 10 pps versus
1 pps. If a portion of the pump laser is split off to pump the Stokes beam dye
laser, 2X Nd lasers at 5320 A can pump very efficient dyes in the 5500-6500 A
region, while ruby lasers must work on lower efficiency near ir dyes. Furthermore,
the coherent anti-Stokes radiation from 2X Nd resides in regions of higher photo-
multiplier tube quantum efficiencies than do those generated by ruby. These systems
aspects will be addressed in more detail in the section on systems considerations.
-------
SYSTEMS CONSIDERATIONS
To this point, attention has been addressed, separately for the most part, to
the various aspects of the in-situ, point, combustion diagnostics problem, i.e.,
species spectroscopy, potential sources of noise, and the physics/capabilities of
the various approaches under review. In this section, preferred measurement
approaches employing the various scattering techniques previously reviewed will be
described. An assessment of systems costs and the probability of success will be
attempted. Some of the material has already been discussed in previous sections;
it will be briefly summarized here for completeness as required. Areas of additional
research/development to improve device performance and address technical uncertain-
ties will also be described. Possible systems integration of the various tech-
niques will also be discussed.
Raman Scattering
Spontaneous Raman
From a systems standpoint, spontaneous Raman scattering is the most attractive
diagnostic technique for multiple species and temperature determinations since only
a single, nonspecific wavelength laser is required. Data on a variety of molecular
species of interest can be obtained simultaneously without the requirement to tune
to a resonance as required in near-resonant Raman, CARS and laser fluorescence.
Unfortunately, because of its inherent weakness, it is the technique least likely
to succeed in most practical combustion systems. As previously discussed, for
minority species measurements in practical combustors, its probability for success
is perceived to be very poor. For majority species measurements and for thermometry,
the probability of successful application ranges from fair to poor depending on the
hostility of the particular combustor and combustion zone being probed. Therefore,
in examining the systems aspects of spontaneous Raman scattering, attention will be
directed toward major constituent measurements.
In Fig. 2k, a laser Raman system for combustion diagnostics is displayed. Two
possible optical routings of the laser beam are shown. In the scheme emphasized,
coaxial scattering is shown. This has the advantage of permitting radial traverses
at a given axial location in the combustor simply by translating the focusing lens,
FL and collecting lens, CL in tandem. In the alternate routing, namely right angle
viewing, measurements would typically be constrained to the center line regions
without elaborate modification of the combustor housing. In coaxial viewing a port
opposite the viewing window would be required for a suitable beam trap. Also the
inlet window would have to be of a compound design to prevent collection of window
fluorescence. By obscuring the central part of the collecting lens with a disk, 0,
115
-------
SPONTANEOUS RAMAN SCATTERING COMBUSTION DIAGNOSTIC SYSTEM
COMBUSTOR
RAMAN SPECTROMETER
OPTIONAL RIGHT ANGLE
ROUTING
CALORIMETER
MULTICHANNEL
SIGNAL
AVERAGER
T
COMPUTER
-------
spatial resolution can be considerably enhanced as described in Ref. 176. The
collected scattering is focused through the aperture A and recollimated. It passes
through an optional polarization filter and is spectrally separated by a series of
dichroic's D and passed through a series of blocking and narrow-band interference
filters which isolate selected portions of the Raman spectrum. In Fig. 2k, only
four channels are displayed for simplicity, more or less could be present as desired.
At least two channels would be employed for thermometry, ratioing the anti-Stokes
to Stokes intensity bands from nitrogen, a commonly used technique (Refs. 112, 113,
119). Four channels may be used for thermometry if noise sampling and subtraction
are necessary. Other channels would monitor Stokes bands from molecules whose
number density is desired. Preferably, the filter bandpasses are made broad enough
so that there is no bandwidth factor Variation with temperature. If not, tempera-
ture corrections to the Raman density datk would be required. Broad bandpasses lead,
of course, to much lower S/N ratios. If the laser pulse energy stability is poor,
the laser energy would be monitored on each pulse and used as a normalization factor
for the density measurements. For thermometry, where band ratios are employed, this
would not be necessary since the pulse energy divides out in forming the ratio.
Calibration for thermometry is performed using a tungsten filament lamp whose tem-
perature is known (standard source) or measured. Calibration for density measure-
ments of Np or Oo could be performed in room air. For gases such as CCL or CO,
calibration would be performed from sample cells containing the gases at known
pressure.
For an end use measurement system, a monochromator offers no advantage, since
only a single constituent could be examined at a time. Although other constituents
could be probed sequentially, this approach is rather inefficient since much infor-
mation is lost (i.e., those spectral regions not being examined) with each pulse.
A spectrograph could be employed together with a multichannel spectral analyzer,
such as that used in Refs. 168, 177 or commercially available Ref. 178. Such an
approach would be considerably more expensive than the use of multilayer dielectric
filters and does not appear to possess any particular advantage.
Signal processing can range over an extended spectrum of cost and sophistica-
tion depending on the degree of automation and speed of data reduction required.
Little or no information is gained by following the Raman scattering on a fast time
scale (tens of nanoseconds or less) since this is considerably faster than the char-
acteristic time for small scale turbulent fluctuations. Furthermore, real time
photon statistics may preclude such dynamic measurements even if desired. Thus, the
Raman scattering can be integrated in time using gated detection techniques and fed
to an appropriate multichannel signal averager. For measurements employing just a
few channels, commercially available boxcar averagers may be used. From there the
averaged data can be received and reduced, or digitized and computer processed.
Recall that signal averaging may not be tolerable in fluctuating media depending on
the magnitude of the fluctuations and the parameter range of interest (Appendix II).
Density measurements can be designed to avoid such averaging errors as discussed
earlier, but problems may be encountered in thermometry.
117
-------
The jeopardies to successful Implementation of spontaneous Raman scattering
reside primarily, as discussed extensively earlier, in laser induced or naturally
occurring background noise in practical combustors. With the exception of a few
details, the physics of spontaneous Raman scattering is well understood. Present,
and for the most part commercially available, laser sources and instrumentation are
completely adequate for Raman diagnostics of clean flames. For practical diagnos-
tics, high peak power, solid state laser sources will be required, based upon the
previously performed S/N calculations. These lasers, depending on specific types,
are fairly expensive, ranging in price from $20K to $60K for several joule ruby
lasers and several tenths Joule frequency doubled neodymium lasers, (depending on
the mode quality and repetition rate desired, (Ref. 179)) to $lUOK for custom high
energy (1.2 Joules) frequency doubled neodymium (Ref, 130). The Raman spectrometer
may range in price depending on the number of channels from about $5K for an inter-
ference filter type to $25K for a commercial 1-meter double or triple monochromator
inclusive of many desired options. Averagers may run from $3K-$6K for a single or
double channel boxcar to $10-$15K for multiple input averagers. Miscellaneous items
might be on the order of $5-$10K for mirrors, lenses, mounts, doublers, etc. Small
computers, if desired, would add perhaps $15-$20K in capital cost plus peripherals
and engineering for the interfacing. Since such equipment is optional, already
available or present in the form of even larger computational facilities in many
laboratories, costs beyond the averager will not be included in assessments of total
cost. Not including engineering, design, etc., a system may run from a low of $35K
to a high of $190K depending on the speed and number of channels desired. Similar
figures were arrived at in Ref. 2. Note that the laser system is the dominant cost
item.
In Table XXII, the assessment of spontaneous Raman scattering for practical
combustion diagnostics is summarised. Based upon the previous signal/noise calcula-
tions for a variety of high peak power, pulsed laser sources, the probability of
successful temperature and major species concentration measurements varies from fair
to poor depending on fuel type and combustor operating conditions. Minority con-
centration measurements are deemed highly unlikely under most circumstances. Based
upon systems costs of $35K to $190K, the "risk" of spontaneous Raman scattering is,
therefore, perceived to be high. Risk is subjectively assessed and combines systems
costs and probability of success judgments.
Before deciding affirmatively on a spontaneous Raman approach for a given
diagnostic application, the medium to be studied should be well assessed in regard
to the estimated magnitude and spectral character of background radiations, presence
of particulates, turbulence levels and ranges of operation. Some of the above can
be measured fairly inexpensively, and others can be estimated by reference to similar
environments. In this manner, one should be able then to assess a priori the feas-
ibility of a given measurement.
118
-------
TABLE XXII
vo
Technique
Spontaneous Raman
Near-Resonant Raman
Laser Fluorescence
CARS
Temperature
COMBUSTION DIAGNOSTIC SYSTEMS ASSESSMENT
Probability of Success
Major Specie^ Minority Species
System Costs
Perceived Risk
Fair -Poor
Poor
Questionable
Good
Fair-Poor
Not Applicable
Not Applicable,
Good
Very Poor
Poor
Good
Fair- Poor
$35K-$190K
$90K-$190K
$90K-$120K
$80K-$120K
High
High
Moderate
Low-Moderate
-------
Near Resonant Raman
Unlike spontaneous Raman scattering, wavelength specific and narrow linewidth
laser sources are required to perform near-resonant Raman scattering diagnostics.
From a systems standpoint, the approach and equipment required is very similar to
that needed for laser fluorescence. Consequently, systems considerations will be
treated in the fluorescence section.
Here only the probability of successful application -will be reiterated. For
major species measurements and thermometry from major species, the likelihood of
a measurement is very unlikely at the present time due to the unavailability of
high energy laser sources at or below 2000A. For measurement of trace constituents,
the probability of success is very low due to the lack of high energy laser pulses
at the desired wavelengths and linewidth, the near-resonant enhancement achievable,
and the small fraction of molecules in the appropriate initial state. Should the
laser source picture change with advances in existing or with the development of new
laser sources, the situation would have to be reassessed.
Laser Fluorescence
A laser fluorescence combustion diagnostics system is schematically diagramed
in Fig. 25. It is quite similar in regard to major components to the laser Raman
system just described. Unlike the Raman scattering system, however, only a single
molecular species can be probed at a time using a single laser source and detector.
It would be possible to combine a multiplicity of laser beams of different wave-
lengths, which could probe various molecules simultaneously using a multichannel
detection scheme. Such a system would be considerably more complex, however. A
laser is employed to induce fluorescence from the molecule under study. The fluores-
cence is collected either coaxially or at right angles to the incident laser beam
(not shown). As before, coaxial scattering is preferred since it readily permits
radial traverses of the combustor/furnace. The collected fluorescence is focused
upon the entrance slit of a double monochromator. Unless the fluorescence is well
shifted in wavelength, i.e., a hundred Angstroms or more, it is unlikely that iner-
ference filters could be employed to discriminate against the strong Mie/Rayleigh
scattering. Good double monochromators on the other hand can possess as much as
fourteen orders of magnitude rejection within 20 cm of the laser line (Ref. 180).
The fluorescence power incident on the photomultiplier can simply be integrated
through a gate driven by a fast detector which monitors the laser pulse duration.
The integrated signal can be digitized via a dc to frequency converter and read out
on a frequency counter or sent to a computer for storage and/or processing. The
data can also be normalized by the laser pulse energy as required. Other data
treatment schemes, e.g., boxcar averagers, may also be employed. Depending on the
magnitude of the temporal fluctuations, however, signal averaging may or may not
be tolerable as discussed earlier.
120
-------
LASER FLUORESCENCE DIAGNOSTIC SYSTEM
T ^Sr-——
BS,
M.
L,
FO,
DC,
PT,
O,
T,
G,
E,
C,
PD,
BEAMSPLITTER
MIRROR
LENS
FREQUENCY DOUBLER
DYE CELL
PHOTOMULTIPLIER
OBSCURATION
TRAP
GRATING
ETALON
CALORIMETER
FAST DETECTOR
MONOCHROMATOR
GATE
SAMPLE AND HOLD
DC TO FREQUENCY CONVERTER
O
COMPUTER
READOUT
INTERFACE
OPTIONAL
-n
P
NJ
U1
-------
The heart of a fluorescence diagnostic system resides in the laser source
which must be tunable and have sufficient spectral intensity to saturate the mole-
cular trans it ions of interest. For near-resonant Raman scattering which is always
independent of quenching, the spectral power (i.e., power/bandwidth) is of prime
importance. To obtain high spectral intensities, stringent requirements are then
placed on pulse energy, duration, laser spectral width and beam quality. In this
discussion, two general classes of dye lasers will be considered •— flashlamp-
pumped and laser-pumped.
Flashlamp-pumped dye lasers (Ref. l8l) generally deliver large pulse energies
but suffer from relatively long pulse durations, typically several hundred nano-
seconds. Good performance has been reported recently by Butcher and Sherman (Ref.
152) in regards to power and spectral condensation with a flashlamp-pumped dye
laser followed by a flashlamp-pumped, two-pass amplifier. At a wavelength of 5^00 A
and a 1 u.sec pulse width, 0.5 joules pulse energy was obtained with a spectral width
of O.J+A (l.U cm ). The beam divergence was k milliradians. Focusing the output
into an ADP crystal led to a frequency doubling efficiency of 10 percent with a 50
millijoule output at 2700A. For a 50 cm focal length lens, a spectral intensity of
1.2 (107) W/cm2 cnT1 at 5'^OOA and 5.7 (lO5) W/cm2 cnT1 at 2?OOA is calculated. This
performance in terms of spectral intensity exceeds that reported for two commercially
available flashlamp-pumped systems (Refs. 182 and 183) by about an order of magnitude.
The difference in spectral intensity is primarily attributable to lack of an ampli-
fier in the commercial units. Based upon published laser dye energy scaling (Ref.
18U), spectral intensities have been calculated at five other wavelengths corres-
ponding to various absorptions of interest. These are summarized in Table XXIII.
In those cases requiring frequency doubling, a 10 percent doubling efficiency was
assumed, i.e., that achieved by Sherman and Butcher, and a factor of two included
for the associated increase in freqeuncy bandwidth on doubling.
For laser-pumped dye lasers, three different laser source drivers will be con-
sidered, namely, pulsed nitrogen and various harmonics of ruby and neodymium. No-
laser-pumped dye systems are characterized by pulse energies up to 1 millijoule at
^600A for 10 mj of pump energy in a pulse of approximately 5-7 (10~9) sec duration
(Ref. 185). Although this peak power of l.U-2 (lO5) watts is comparable to flash-
lamp-pumped dye lasers, the Ng laser pumped dye laser possesses a lower beam diver-
gence angle, on the order of 1-1.5 milliradian and lower bandwidth, 0.6 cm"1. This
leads, of course, to higher spectral intensities, namely, 1.2 (10°) watts/cm2 cm"-1-
at U600A\ Comparable performance is achieved at both ^315$ (CH) and 3883$ (CW).
In Table XXIII, spectral intensities are also presented for Np laser-pumped dye
lasers. The values listed correspond to what is commercially available, except for
the NO value. In this case, the spectral intensity was achieved by use of two addi-
tional amplifier stages; a 2 percent frequency doubling efficiency was achieved
(Ref. 186). The low spectral intensity values for wavelengths appropriate to NH
and OH are due to low frequency-doubling efficiencies, typically between 1-4 percent.
122
-------
Dye lasers can also be pumped with the second harmonic of ruby at 3472A
(Refs. 187, 188 and 189) or second harmonics of neodymium at 5320A (Refs. 18? and
190). Pumping with the third harmonic of neodymium at 3546A should also be possible.
Conversion efficiencies are typically on the order of 15 to 20 percent. As' in
previous discussions, only neodymium lasers will be considered here because of their
high pulse repetition rates. For the NH and OH wavelengths, the second harmonic
•would pump a dye laser which in turn would be frequency doubled. For CN and CH, the
third harmonic would be used to pump a dye laser directly. For NO, the third har-
monic pumped dye laser would be frequency doubled. A commercially available neo-
dymium oscillator-amplifier system (Ref. 191) with 250 mJ at 5320$ and 70 mj at
35^-6A "will be examined for illustrative purposes. For the molecules CH (4315A) and
CN (3883A), pumping dye lasers with the third harmonic of neodymium at 3546A should
produce spectral intensities in excess of those produced by the 10 mJ N2 laser at
3371A,' since the 3XNd has seven times the energy and peak power as the NO laser
pump. Both systems have comparable be'am quality and pulse duration. Hence1, in
Table XXIII, the spectral intensities are listed as > 1.2 (10 ) W/cm2 cm"1. For
NH (3360) and OH (3064) the spectral intensities were calculated as follows. The
2XNd laser with 0.25 J and pulse duration of 10 sec was assumed to pump a dye
laser in the 6000A to 6600A range with an efficiency of 15 percent. The dye laser
was assumed spectrally condensed to 0.1A (0.3 cm" ) via intracavity dispersive
elements (e.g., prisms, etalons) with 10 percent efficiency. The output was then
frequency doubled using ADP or KDP crystals with 15 percent conversion to the second
harmonic (Ref. 186). The NO spectral intensity value at 2270 was assumed achieved
by frequency doubling via potassium pentaborate (KPB) the third harmonic pumped dye
laser with 1 percent doubling efficiency (Ref. 192).
TABLE XXIII
P 1
LASER SPECTRAL INTENSITIES (Watts/cnr cm" )
50 cm focal length lens
Absorption Flashlamp-Pumped Ng Laser Nd Laser Required to
Molecule Wavelength (%) Dye _ Dye _ Dye Saturate
CH 4315 5-6(6) 1.2(8) > 1.2 (8) 4(7)
CN 3883 2.8 (6) ,1.2 (8) > 1.2 (8) 2 (7) :
NH 3360 5-6 (5)* 6.0 (5)* l.o (8)* l (8)
OH 3064 1.0 (6)* 3.8 (6)* 1.0 (8)* 4 (6)
NO 2270 4.4 (5)* 1.0 (6)* 7.0 (6)* 4 (8)
*Frequency doubling of dye laser output required
123
-------
For Table XXIII several conclusions are apparent. At the large focal distances
required in a practical measurement system, none of the laser systems can provide
a high enough spectral intensity to saturate NO. The neodymium laser system appears
preferable since it is capable of probing CH, CN, NH and OH subject to the assump-
tions made in arriving at the spectral intensity estimates. These were reasonable
but yet to be demonstrated concurrently in an integrated setup. The N laser pumped
dye system is capable of saturating only two of the molecules, the f la shlamp -•pumped
dye laser, none, in a practical situation. In a laboratory situation where shorter
focal length lenses would be tolerable, e.g., 10 cm, both flashlamped -pumped and N
laser pumped dye lasers could saturate all the molecules listed except NO. NO
appears difficult to probe in any flame situation with presently available or rea-
sonably assumed tunable laser systems. This comment applies, of course, to probing
NO via saturated fluorescence only. NO laser-fluorescence has already been examined
in a sample cell at room temperature (Ref.
In terms of cost, the laser fluorescence system using a neodymium laser system
would be as follows. The neodymium driver with second and third harmonic capability
would be about $U5K (Ref. 191)- The dye laser setup including grating, etalons,
prisms, etc. is estimated at $10K. Commercial laser pumped dye systems begin at
about this price, but may run two to three times this depending on accessories,
capabilities, etc. The double monochromator is about $25K. A simple detection
scheme might be about $5K from photomultiplier to readout. With miscellaneous
items totaling $5K, the system would run between $90K and $125K, providing that a
single molecule is probed at a time.
The major jeopardy with laser fluorescence probing is the validity and appli-
cability of two level saturated fluorescence approaches to eliminate the effects of
quenching. If such approaches are correct as reviewed previously, the ability to
saturate the transition in question becomes of paramount importance. The saturation
spectral intensities calculated above are approximate and rely upon low temperature
quenching data. Experimental efforts should be directed toward investigations of
the magnitudes of saturation spectral intensities and the validity of the simplified
analytical approaches. If correct, the possibility of fluorescence measurements of
selected species at ppm levels in practical environments appears to be good. Tem-
perature measurements by spectral scanning are probably precluded in turbulent
environments from consideration of the effects of signal averaging. Major species,
i.e., Ng, CO, C02, 02, are not possible due to the inaccessibility of their respec-
tive absorptions. In view of the lack of experimental confirmation of these ap-
proaches and high costs, they are viewed as being moderate in risk. Clearly, these
assessments should be regarded as being preliminary.
12U
-------
CARS
For CARS diagnostics, a minimum of two laser sources is required as seen
earlier, namely, "pump" and "Stokes" laser beams. For double resonance and/or
polarization orientation approaches which suppress background, three beams are
required. Some investigators have used one laser source and generated the Stokes
beam via stimulated Raman scattering (Ref. 19). This scheme is limited to probing
stable species from which stimulated Raman is readily produced and is not very
versatile. A more flexible and, hence preferable, scheme is to employ a laser,
part of which is split off to drive a tunable dye laser. In some cases, the laser
may pump two dye lasers to produce both the pump and Stokes beams or the Stokes and
the additional beam required in the three beam approaches. For gas phase diagnos-
tics, either ruby or frequency doubled neodymium, because of their very high peak
powers, appear preferable to pulsed nitrogen lasers. From a systems standpoint 2x
Nd appears a better choice than ruby since the pulse repetition rate is generally
an order of magnitude greater, 10 pps vs 1 pps typically, and more efficient laser
dyes can be used with the 2x Nd. 2x Nd may be preferable to 2x ruby since gas
breakdown thresholds are likely to be higher at 5320A than 3^72 A, in addition to
repetition rate considerations.
In Fig. 26, a schematic diagram of a CARS system for diagnostics is displayed.
Although the discussion herein will be specific to neodymium lasers, the approach
would be basically the same for other laser sources. The neodymium laser radiation
at 1.06(0, is frequency doubled to 5320A, the pump beam, and passes through a dichroic.
The undoubled 1.06p, is split off and doubled again and employed to pump a tunable
dye oscillator-amplifier combination. The dye oscillator is broadly tuned with a
grating (or interference filter) and can be spectrally condensed as desired with
etalons. The output from the oscillator-amplifier, the Stokes beam, is recombined
with the pump beam and focused into the medium under observation. This can be done
collinearly if the spatial resolution is satisfactory or at a slight angle for a
more definite probing volume. At the output of the combustor, the laser pump and
Stokes beams are split off by a dichroic or beamsplitter to generate a nonresonant
reference signal in a cell typically containing an inert gas. The CARS signal at
(I), is split off from any remaining pump and Stokes beams by prisms, can be addi-
tionally filtered for noise suppression and sent to a monochromator or spectrograph.
In final applications form, the spectrograph may well be an interference filter
device analogous to the Raman spectrometer previously suggested. The approach just
described is essentially that employed by Harvey for CARS investigations (Ref. 173).
For laminar flames, two approaches are possible. One is to spectrally condense the
Stokes beam and tune it about resonance to generate the spectrum. The other is to
produce a broadband dye spectrum and merely scan the spectrum. In the latter the
signal is reduced since the Stokes intensity per unit spectral bandwidth is reduced.
In turbulent flames, where the CARS data probably cannot be unambigously averaged,
one records portions of the spectrum with interference filters to isolate bands of
interest, or captures the entire spectrum (termed multiplex CARS by Taran) with an
125
-------
CARS SYSTEM SCHEMATIC
COMBUSTOR
LASER
CODE: FD.FREQUENCY DOUBLER
M.MIRROR
D,DICHROIC
P.PRISM
T,LIGHTTRAP
BS.BEAM SPLITTER
FD
FD
E.ETALON
G.GRATING
DC.DYE CELL
PT.PHOTO TUBE
L.LENS
F.FILTER
vy^
D\V\OEB/
MULTIPLEXER/
AVERAGER
MONOCHROMATOR/
SPECTROGRAPH
COMPUTER
•n
01
-------
appropriate vid icon (Ref. 178), or intensified version thereof using the monochromator
as a spectrograph. Because of amplitude and frequency instabilities from shot to
shot, the magnitude of the CARS spectrum will fluctuate. These effects can be
handled by generating a nonresonant reference signal, as shown, for normalization
purposes. For multiplex CARS, the vidicon in the reference leg essestially captures
the Stokes beam spectral distribution. The signals are then sent to appropriate
electrical instrumentation. For steady work, this would include a ratio circuit,
signal averager and recorder. For unsteady media investigations a multiplexer,
divider, and multichannel readout would be used. In a final instrument, the data
would probably be digitized and sent to a computer for data reduction, possibly by
comparison with computer generated spectra.
Frequency doubled neodymium lasers with single transverse mode output at 10 pps
and 0.2-0.3 J/pulse cost between approximately $UOK to $60K depending on exact
specifications and manufacturer (Refs. 191, 193 and 19^). The dye oscillator/
amplifier subassemblies including second doubler, mounts, optics, etc., would cost
between $2K-$5K. The one meter double monochromator is approximately $20-$25K.
The vidicons, depending on intensification required and instrumentation packages,
would vary from $10K to $25K. For estimation purposes only one will be assumed to
be necessary. Miscellaneous optics, filters, mounts and so forth are crudely
estimated at $5K. Total systems cost using commercially available, already devel-
oped equipment, again exclusive of computer and peripherals, total between $80K
and $120K.
For thermometry and majority species detection (> 1000 ppm), the probability of
successful application in practical combustion devices appears good. For minor
species measurements, the probability of success in the 10-1000 ppm range is deemed
fair to poor, until demonstrated otherwise by double resonance or polarization
oriented CARS techniques. Below 10 ppm, the probability of success is seen as very
low, based upon both photon yield and nonlinear background interference considera-
tions. The risk is thus perceived to be low to moderate (due to the high systems
costs) for thermometry and major species detection, high for trace species measure-
ments. Approaches employing interference filters and photomultipliers instead of
double monochromators and multichannel spectrum analyzers are clearly desirable in
regard to greatly reducing costs and should be an objective of future developmental
works.
Jeopardies in the CARS area include potential nonlinear noise interactions with
soot particulates, turbulence dephasing, and complex data reduction in general. For
minority species concentration measurements, the feasibility of double resonance and
polarization orientation CARS techniques is yet to be established for gas phase work.
Future research efforts are required in these areas to assess the seriousness of
these jeopardies. As with spontaneous Raman scattering, little in the way of laser
or instrumentation development appears to be required.
127
-------
Systems Integration
Based upon the systems review of the various diagnostic techniques together
with their perceived probability of success, an integrated CARS-laser fluorescence
measurement system is shown in Fig. 27. Shown is an approach which, in principle,
would permit simultaneous CARS-fluorescence diagnostics. Due to the redundancy in
equipment, considerable expense would be eliminated, however, by sequential or
nonconcurrent measurements using the foregoing measurement approaches. By refer-
ring back to Figs. 25 and 26, the major subsystems of the CARS and laser fluores-
cence systems are readily recognizable. A single neodymium laser is frequency
doubled or tripled to drive dye lasers in either an oscillator or oscillator/
amplifier configuration as required. One dye subsystem generates the CARS Stokes
beam, the other the fluorescence laser source which may or may not be frequency
doubled as required. A multiple beam fluorescence system would be similarly con-
figured. The laser beams are directed into the combustor/furnace as shown. CARS
is, of course, detected and analyzed in the forward direction, while the laser
induced fluorescence is collected coaxially at l80°. Hence, both measurement
approaches could be utilized simultaneously, provided the combined focal flux does
not exceed the combustor gas breakdown threshold. If the measurements are not
performed simultaneously, then only one laser pumped dye subsystem and monochro-
mator would be required. Clearly, if interference filters could ultimately be
employed for spectral separation of the CARS and fluorescence signals, simultaneous
measurements would be more feasible economically. An advantage of concurrent
measurements is that the CARS could provide the correct temperature information
required in the laser fluorescence data reduction. Recall that fluorescence
measures the population only in a selected level of the ground state and tempera-
ture information is required to relate that one single state population to the total
ground state or total species concentration. One must also take care to make sure
that the fluorescence inducing laser beam frequency which is greater than the CARS
pump and Stokes frequencies, is not resonantly separated from the latter. In such
an instance, nonlinear (e.g., CARS) and spurious signals may be induced. In general
this will probably not be a problem, and the integrated system illustrates the fact
that the two diagnostic approaches are concurrently compatible.
128
-------
lo
V£>
INTEGRATED COMBUSTION DIAGNOSTICS SYSTEM
G
E
E
DC TO
FREQUENCY
CONVERTER
COMBUSTOR
FREQUENCY
COUNTER AND
READOUT
COMPUTER
INTERFACE
C_^ L $
REFERENCE] 1 _
CELL M
Ap
F XT N
>^ 1 M
^Cs r^j
1 I LJL
MULTIPLEXER/ A/D
AVERAGER
^
- 1
IT-
—
^T
MONOCHROMATOR/
SPECTROGRAPH
COMPUTER
Tl
O
ro
-------
CONCLUSIONS
On the basis of the foregoing discussions, the following general conclusions
may be drawn.
(l) For most species of combustion interest, at least one of the diagnostic
techniques investigated is applicable for point measurements of that constituent.
The lone exception is the N atom which would have to be probed using either a lamp
source absorption or fluorescence technique. Of course, depending upon which tech-
nique is relevant, sensitivity limits may vary widely, e.g., CARS is much less
sensitive than saturated laser fluorescence.
(2) Practical combustion devices contain flames which are very hostile from
an instrumentation viewpoint. High levels of spurious radiations, either naturally
occurring or laser induced, must be overcome by the signal of interest. These
effects, rather than shot noise, are generally the major determinants of signal/
noise ratios. A host of other practical problems, e.g., gas breakdown, window
damage, large distances to the measurement location, must also be confronted.
Temporal fluctuations may well preclude signal averaging approaches to enhance
signal/noise ratios. These effects should be closely examined in each measurement
situation before a given measurement approach is adopted.
(3) Spontaneous and near-resonant Raman scattering appear generally incapable
of probing hydrocarbon-fueled, primary combustion zones over a broad range of
operating conditions. Application to exhausts and secondary combustion regions may
be possible if particulate levels are not too high. For primary zone diagnostics,
thermometry and major species concentration measurements appear problematical even
with advanced state-of-the-art laser sources. Trace species concentration measurements
are definitely precluded. Due to its advanced state-of-development, spontaneous
Raman scattering should receive much near-term emphasis for fundamental combustion
research in specially selected clean flame investigations.
(k) Saturated laser fluorescence has great potential for the measurement of
selected species in low concentrations (ppm) in both practical and clean flames.
The fluorescence signals will be independent of gas quenching effects if the absorp-
tion resonances can be saturated and if simple two and three level models are
applicable. Considerable fundamental and applied research investigations are re-
quired to address these questions for this potential to be realized or dispelled.
(5) CARS is ideally suited for thermometry and major species concentration
measurements in both practical and clean flame environments. Considerable research
is nevertheless still required. Potential nonlinear laser-soot interaction effects
need be addressed to either dismiss or reckon with them. Turbulence dephasing
effects need to be systematically evaluated. Simplifications in gathering and
treating CARS data are highly desirable. Species sensitivity limits in flames need
130
-------
to be clearly established experimentally. Present estimates indicate sensitivity
to be relatively poor for most molecules, i.e., on the order of 1000 ppm. CARS
variants need to be assessed vis-a-vis their practical utility and capability in
regards to lowering detectivity limits.
(6) Laser diagnostic techniques capable of point, in-situ diagnostic applica-
tion to practical combustion media are quite expensive, generally in the $50K-
$200K range for equipment alone and require skilled personnel for their operation.
Considerable simplification of any diagnostic approach would be desirable to reduce
system costs and personnel skill requirements.
131
-------
REFERENCES
1. Hartley, D. L., Editor: The Role of Physics in Combustion. American Physical
Society Summer Study Report,
2. Goulard, R., Editor: Combustion Measurements in Jet Propulsion Systems.
Project SQUID Workshop Proceedings, December 1975.
3. Selected papers from the conference sessions are summarized in the forthcoming
Measurements in Combustion Research, a volume in AIAA Progress in Aeronautics
and Astronautics Series.
U. Byer, R. L.: Review, Remote Air Pollution Measurement. Opt. Quant. Elec.,
Vol. 7, pp. 3A7-177, (1975).
5. Lapp, M., C. M. Penney and J. A. Asher: Application of Light-Scattering
Techniques for Measurements of Density, Temperature and Velocity in Gasdynamics.
Technical Report prepared under Contract F33615-71-C-1867 for the Air Force
Aerospace Research Laboratores, Dayton, Ohio, January 1973.
6. Harvey, A. B., J. R. McDonald and W. M. Tolles: Analytical Applications of a
New Spectroscopic Tool: Coherent anti-Stokes Raman Spectroscopy (CARS).
Progress in Analytical Chemistry, Plenum Press, to be published.
7. Robben, F. : Comparison of Density and Temperature Measurement Using Raman
and Rayleigh Scattering, pp. 179-195 in Ref. 2.
8. Lapp, M. and C. M. Penney: Laser Raman Gas Diagnostics, Plenum Press, New
York, (197*0. ~
9. Szymanski, H. A.: Raman Spectroscopy, Theory and Practice, Plenum Press,
New York, (1967).
10. Straughan, B. P. and S. Walker, Eds.: Spectroscopy, Vol. 3, Halsted Press,
New York, (1976).
11. Sulzman, K. G. P., J. E. L. Lowder and S. S. Penner: Estimates of Possible
Detection Limits for Combustion Intermediates and Products with Line Center
Absorption and Derivative Spectroscopy Using Tunable Lasers. Comb. Flame,
Vol. 20, pp. 177-191, (1973).
12. McGregor, W. K.: Absorption-Emission Measurements in Jet Engine Flows.
pp. 107-109, in Ref. 2.
132
-------
REFERENCES (Cont'd)
13. Jones, W. J. and B. P. Stoicheff: Inverse Raman Spectra: Induced Absorption
at Optical Frequencies. Phys. Rev. Letts., Vol. 13, pp. 657-659, November
196U.
1^. Lau, A., W. Wernicki, M. Pfeiff'er, K. Lenz, and H. J. Weigmann: Possibilities
and Limits of Inverse Raman Scattering, pp. 39-k2, in J. P. Mathieu, Editor
Advances in Raman Spectroscopy, Vol. I, Heyden and Son. Ltd, London, (1973).
15. Heiman, D., R. W. Hellwarth, M. D. Levenson and G. Martin: Raman-Induced
Kerr Effect. Phys. Rev. Letts., Vol. 36, pp. 189-192, January 1976.
16. Bloembergen, N. : The Stimulated Raman Effect. Amer. J. Phys., Vol. 11,
pp. 989-1023, November 1967.
17. Maier, M.: Applications of Stimulated Raman Scattering. Appl. Phys., Vol. 11,
pp. 209-231 (1976).
18. Verdieck, J. F., S. H. Peterson, C. M. Savage, and P. D. Maker: Hyper-Raman
Spectra of Methane, Ethane and Ethylene. Chem. Phys. Letts., Vol. 7, p. 219,
(1970).
19. Regnier, P. R. and J. P. E. Taran: On the Possibility of Measuring Gas Con-
centrations by Stimulated Anti-Stokes Scattering. Appl. Phys. Letts., Vol. 23,
pp. 2^0-2^2, September 1973.
20. Chabay, I., G. K. Klauminzer and B. S. Hudson: Coherent anti-Stokes Raman
Spectroscopy (CARS): Improved Experimental Design and Observation of New
Higher-Order Processes. Appl. Phys. Letts., Vol. 28, pp. 27-29, January 1976.
21. Schlossberg, H.: Fluorine Atom Probe Techniques for Chemical Lasers. Air
Force Cambridge Research Laboratories Report, AFCRL-TR-75-0522, October 1,
1975.
22. Vriens, L.: Raman Scattering Cross Sections for Indium and Thallium Atoms.
Optics. Commun., Vol. 11, p. 396, (197*0.
23. Herzberg, G.: Molecular Spectra and Molecular Structure. I. Spectra of
Diatomic Molecules, D. Van Nostrand Co., Inc., Princeton, NJ, (1950).
2k, Jones, D. G. and J. C. Mackie: Evaluation of C2 Resonance Fluorescence as a
Technique for Transient Flame Studies. Combustion and Flame, Vol. 27, pp.
, (1976).
133
-------
REFERENCES (Cont'd)
25. Baronavski, A. and J. R. McDonald: The Application of Saturation Spectroscopy
to the Measurement of C2 %u Concentration in Oxy-Acetylene Flames. Submitted
to Appl. Optics.
26. Baronavski, A. P. and J. R. McDonald: Chem. Phys. Lett, in press.
27. Barnes, R. H., C. E. Moeller, J. F. Kirscher and C. M. Verber: Dye-Laser
Excited CH Flame Fluorescence. Appl. Optics, Vol. 12, p. 2531, (1973)-
28. Jackson, W. M.: Laser-Induced Fluorescence from CN Radicals. J. Chem. Phys.,
Vol. 59, p. 960, (1973).
29. Vear, C. J., P. J. Hendra, and J. J. McFarlane: Laser Raman and Resonance
Fluorescence Spectra of Flames. J. Chem. Soc. Chem. Comm., p. 381, (1972).
30. Gaydon, A. G.: The Spectroscopy of Flames. Chapman and Hall Ltd., London,
(1971+).
31. Lee, L. C. and D. L. Judge: CS (A Tl -» T]+) Fluorescence from Photodissocia-
tion of CS2 and OCS. J. Chem. Phys., Vol. 63, p. 2782, (1975).
32. Suchard, S. N.: Spectroscopic Constants for Selected Diatomic Molecules,
Air Force Report No. SAMSO-TR-7^-82, the Aerospace Corp., Los Angeles, CA,
(197*0.
33. See Ref. 30, p. 353-
3U. Zacharias, H., A. Anders, J. P. Halpern and K. H. Welge: Frequency Doubling
in KB^Og-lfflgO and Application to NO A T; Excitation. Optics Comm. Vol.
19, P. 116, (1976).
35. Callear, A. B. and E. W. M. Smith: Fluorescence of Nitric Oxide. Trans.
Far. Soc., Vol. 59, p. 1720, (1963).
36. Broida, H. P. and T. Carrington: Rotational, Vibrational and Electronic
Energy Transfer in the Fluorescence of Nitric Oxide. J. Chem. Phys.
Vol. 38, p. 136, (1963).
37. Baardsen, E. L. and R. W. Terhune: Detection of OH in the Atmosphere Using a
Dye Laser. Appl. Phys. Lett., Vol. 21, p. 209, (1972).
-------
REFERENCES (Cont'd)
38. Wang, C. C and L. I. Davis, Jr.: Measurement of Hydroxyl Concentrations in
Air Using a Tunable UV Laser Beam. Phys. Rev. Lett., Vol. 32, p. 3^9, (1971*).
39* Killingen, D. K., C. C. Wang and M. Hanabusa: Intensity and Pressure Dependence
of Resonance Fluorescence of OH Induced by a Tunable UV Laser. Phys. Rev.
A, Vol. 13, P. 21^5, (1976).
hO. Wang, C. C. and L. I. Davis: Ground State Population Distribution of QH
Determined with a Tunable UV Laser. Appl. Phys. Lett., Vol. 25, p. 3*4-
(197*0.
Ul. Becker, K. H., D. Haaks and T. Tatarczyk: Monitoring of Radicals by a Tunable
Dye Laser. Z. Naturforsch., Vol. 27a, pp. 1520-151 (1972). ;
U2. Pearse, R. W, B. and A. G. Gaydon: The Identification of Molecular Spectra.
Fourth Ed., Chapman and Hall, London (1976). • , *'
h3. Herzberg, G. : Infrared and Raman Spectra of Polyatomic Molecules. D. .Van Nostrand
Co., Inc., Princeton, NJ
kh. Cotton, F. A.: Chemical Applications of Group Theory. Wiley-Interscience,
NY (1963).
ij-5- Barrett, J. J. and R. F. Begley: Low-Power CW Generation of Coherent Anti-
Stokes Raman Radiation in CH^ Gas. Appl. Phys. Lett., Vol. 27, p. 129, (1975).
*
1*6. Weber, A., S. P. S. Porto, L. E. Cheesman, and J. J. Barrett: High -Resolution
Raman Spectroscopy of Gases with CW Laser Excitation. J. Opt. Soc. Am., Vol.
57, p. 19, (1967).
V7. Barrett, J. J. and A. Weber: Pure-Rotational Raman Scattering in a COo
Electric Discharge. J. Opt. Soc. Am., Vol. 60, p. 70 (1970).
lj-8. Becker, K. H., V. Schurath and T. Tatarczyk: Fluorescence Determination of
Low Formaldehyde Concentrations in Air by Dye Laser Excitation: Appl. Optics,
Vol. Ik, p. 310, (1975).
, 'i
49. Bribes, J. L., R. Gaufres, M. Monan, M. Lapp and C. M. Penney: Raman Band
Contours for Water Vapor as a Function of Temperature. Appl. Phys. Lett.,
Vol. 28, p. 336, (1976).
50. Itzkan, I. and D. A. Leonard: Observation of CARS Scattering from Liquid
Water. Appl. Phys. Lett., Vol. 26, p. 106, (1975)-
135
-------
51. Halpern, J. B., G. Hancock, M. Lenzi and K. H. Welge: Laser-Induced
Fluorescence from NH (2A). J. Chem. Phys., Vol. 63, p. U808, (1975).
52. Gelbvachs, J. A., M. Birnbaum, A. W. Tucker, and C. L. Fincher: Fluorescence
Determination of Atmosphere N02. Opto-Electronics, Vol. U, p. 155? (1972).
53. Tucker, A. W. , M. Birnbaum and C. L. Fincher: Atmospheric Determination of
N02 by *4.l42-nm Laser Induced Fluorescence. Appl. Optics, Vol. lU, p. 1*4-18,
(1975).
5*4. Brand, J. C., J. L. Hartwiek, R. J. Pirkle and C. J. Seliskar: The Resonance
Fluorescence and Absorption Spectrum of N02. Can. J. Phys., Vol. 51,
p. 218U, (1973).
55. Agarwal, Y., T. Hadeishi and F. Robben: Measurement of N02 Concentration in
Combustion Using Fluorescence Excited by an Argon-Ion Laser. AIAA Paper No.
76-136. AIAA l*4th Aerospace' Meeting, Washington, D.C., January 26-28, 1976.
56. Okabe, H. , P. L. Splitstone and J. J. Ball: Fluorescence of S02 in Air. J.
Air. Pollut., Control. Assoc., Vol. 23, p. 51*4., (197*0.
57. Fowler, M. C. and P. J. Berger: Feasibility Study of the Use of Resonance
Scattering for the Remote Detection of SC^. Report No. EPA- 6 50/2-7*4-020,
January 197*4-.
58. Zulner, W. , E. Cieplinski and D. Hulm: Pulsed Fluorescent S0p Analyzer.
Thermoelectron Corp. Watham, MA 0215^.
59. Jahnke, J. A., J. L. Cheney and J. B. Homolya: Quenching Effects in S02
Fluorescence Monitoring Instruments. Environ. Sci. Tech., Vol. 10, p. 12*46,
(1976).
60. Wakahara, S., K. Ito, S. Ito, A. Fuke, S. Komatsu, H. Inaba and T. Kobayasi:
Detection of Sulphur Dioxide in Stack Plumes by Laser Raman Radar. Opto-
Electronics, Vol. *4, p. 169, (1972).
6l. Hirschfeld, T., E. R. Schildkraut, H. Tannenbaum and D. Tannenbaum: Remote
Spectroscopic Analysis of ppm- level Air Pollutants by Raman Spectroscopy.
Appl. Phys. Letts. Vol. 22, pp. 38-41, January 1973.
62. Kobayasi, T. and H. Inaba: Spectroscopic Detection of S02 and C02 Molecules i
Polluted Atmosphere by Laser-Raman Radar Technique. Appl. Phys. Lett., Vol.
17, P. 139, (1970).
63. Moore, C. E.: Atomic Energy Levels, National Bureau of Standards, Vol. 1,
(19*19).
136
-------
6k. Anderson, R.: Compilation of Measured Lifetimes of Gaseous Diatomic Molecules.
Atomic Data, Vol. 3, pp. 227-2^0, (1971).
65. Wiese, W. L., M. W. Smith and B. W. Glennon: Atomic Transition Probabilities.
Rational Bureau of Standards, Vol. 1, and Vol. 2, (1966).
66. Herzberg, G.: The Electronic Spectra of Polyatomic Molecules. D. Van Nostrand
Co., In., Princeton, N.J., (1966).
67. Ref. 30, Appendix of Molecular Constants.
68. Ref. k3, Section on Individual Molecules.
69. Inaba, H. and T. Kobayasi: Laser Raman Radar-Laser Raman Scattering Methods
for Remote Detection and Analysis of Atmospheric Pollution. Opto-Electronics,
Vol. k, pp. 101-123, (1972).
70. Calculated from Ref. 69.
71. Penney, C. M., R. L. St. Peters and M. Lapp: Absolute Rotational Raman Cross-
Sections for N2, 02 and C02- J. Opt. Soc. Am., Vol. 6k, p. 712, (197*0•
72. Fenner, W. R., H. A. Hyatt, J. M. Kellam and S. P. S. Porto: Raman Cross
Sections of Some Simple Gases. J. Opt. Soc. Am., Vol. 63, p. 73> (1973).
73. Penney, C. M. and M. Lapp: Raman Scattering Cross-Sections for Water Vapor.
J. Opt. Soc. Am., Vol. 66, p. 14-22, (1976).
Ik. Farmer, V. H. and H. R. Bevis: Observation of Large Flame Characteristics
Relative to the Performance of a Laser Analyzer. Technical Report Under
Contract EPA Fk06-7k-C-OOQk, August 1973.
75. Handbook of Light Measurement Techniques. Gamma Scientific Inc., San Diego, CA,
and W. H. Farmer, Spectron Development Laboratories, Tullahoma, IN, private
communication.
76. D'Alessio, A., A. DiLorenzo, A. F. Sarofim, F. Beretta, S. Masi and
C. Venitozzi: Soot Formation in Methane-Oxygen Flames. Fifteenth Symposium
on Combustion. The Combustion Institute, Pittsburgh, PA, (1975).
77. Eckbreth, A. C.: Laser Raman Thermometry Experiments in Simulated Combustor
Environments. AIAA Paper 76-27, January 1976.
78. Leonard, D. A.: Field Tests of a Laser Raman Measurement System for Aircraft
Engine Exhaust Emissions. Technical Report AFAPL-TR-7^-100, October
137
-------
79- Aeschliman, D. P. and R. E. Setchell: Fluorescence Limitations to Combustion
Studies Using Raman Spectroscopy. Appl. Spec., Vol. 29, pp. k26-k29, (1975).
80. Bailly, R., M. Pealat and J. P. E. Taran: Raman Investigation of a Subsonic
Jet. Opt. Comm., Vol. 17, pp. 68-73, April 1976.
8l. Wright, M. L. and K. S. Krishman: Feasibility Study of In-Situ Source
Monitoring of Particulate Composition by Raman or Fluorescence Scatter. EPA-
R2-73-219, June 1973-
82. Gelbwachs, J. and M. Birnbaum: Fluorescence of Atmospheric Aerosols and Lidar
Implications. Appl. Opt., Vol. 12, pp. 2k^2-2kk7, October 1973-
83. Wakamizo, M., R. Kammereck, and P. L. Walker, Jr.: Laser Raman Studies of
Carbon. Carbon, Vol. 12, pp. 259-267, (197*0.
8k. Eckbreth, A. C.: Applicability of Laser Raman Scattering Diagnostic Techniques
to Practical Combustion Systems. Project SQUID Technical Report UTRC-U-PU,
October 1976.
85. Dalzell, W. H., G. C. Williams and H. C. Hottel: A Light Scattering Method
for Soot Concentration Measurements. Comb, and Flame, Vol. lU, pp. 161-170
(1970).
86. Kunugi, M. and H. Jinno: Determination Of Size and Concentration of Particles
in Diffusion Flames by a Light Scattering Technique. llth Symposium on
Combustion, pp. 251-266 (1966).
87. Pagni, P. J., L. Hughes, and T. Novakov: Smoke Suppressant Additive Effects
on Particulate Emissions From Gas Turbine Combustors. AGARD-CP-125,
pp. 25-1-10, (1973).
88. Eckbreth, A. C.: Laser Modulated Particulate Incandescence. Submitted to the
Journal of Applied Physics.
89. Jeunehomme, M. and R. P. Schwenker: 'Focussed Laser Beam Experiment and the
Oscillator Strength of the Swan System. J. Chem. Phys., Vol. k2, pp. 2^06-
2hOQ, April 1965.
90. Howe, J. A.: Observations on the Maser Induced Graphite Jet. J. Chem. Phys.,
Vol. 39, pp. 1362-1363 September 1963.
91. Mentall, J. E. and R. W. Nicholls: Spectroscopic Temperature Measurements on
Laser Produced Flames. J. Chem. Phys., Vol. U6, pp. 2881-2885, April 1967.
92. Gerry, E. T. and D. J. Rose: Plasma Diagnostics by Thomson Scattering of a
Laser Beam. J. Appl. Phys., Vol. 37, pp. 2715-272U, June 1966.
138
-------
REFERENCES (Cont'd)
93 • Kincaid, B. E. and J. R. Fontana: Raman Cross-Section Determination by Direct
Stimulated Raman Gain Measurements. Appl. Phys, Letts., Vol. 28, pp. 12-lU,
January 1976.
9U. Smith, D. C. and R. G. Meyerand, Jr.: Laser Radiation Induced Gas Breakdown.
Chapter 11 in Principles of Laser Plasmas, G. Bekefi, Editor, Wiley-Interscience,
New York,(19?U).
95. Kato, K.: Laser-Induced Breakdown in Air Using Visible Dye Laser. Jap. J.
Appl. Phys., Vol. lU, pp. 1U09-1U10, (1975).
96. Busher, H. T., R. G. Tomlinson, and E. K. Damon: Frequency Dependence of
Optically Induced Gas Breakdown. Phys. Rev. Letts., Vol. 15, p. 8V7, (1965)-
97. Lencioni, D. E. : Laser-Induced Air Breakdown for 1.06-pji Radiation. Appl. Phys.
Letts., Vol. 25, pp. 15-17, (197*0-
98. Smith, D. C. and R. T. Brown: Aerosol-Induced Air Breakdown with C02 Laser
Radiation. J. Appl. Phys., Vol. k6, pp. 111|6-115U, (1975).
99. Draggoo, V. G., C. Y. She, G. L. McAllister and D. F. Edwards: Effects of Laser
Mode Structure on Damage on Quartz. IEEE J. Quant. Elec., Vol. QE-8, pp. 5^-57,
(1972).
100. Bass, M. and H. H. Barrett: Laser Induced Damage Probability at 1.06 and 0.69pjn.
pp. 58-69 in Laser Induced Damage in Optical Materials; 1972 ASTM Symposium,
Boulder, Colorado, (1972).
101. Glass, A. J. and A. H. Guenther: Laser Induced Damage of Optical Elements - A
Status Report. Appl. Opt., Vol. 12, pp. 637-61+9, (1973).
102. Bloembergen, N. : Role of Cracks, Pores and Absorbing Inclusions on Laser
Induced Damage Threshold at Surfaces of Transparent Dielectrics. Appl. Opt.,
Vol. 12, pp. 661-66k, (1973).
103. Brown, R. T. and D. C. Smith: Aerosol-Induced Thermal Blooming. J. Appl. Phys.,
Vol. U6, pp. J+02-U05, (January 1975).
10k. Lederman, S. : Modern Diagnostics of Combustion. AIAA Paper 76-26, Presented
at the lUth Aerospace Sciences Meeting, Washington, D.C., (1976).
105. Lapp, M. and D. L. Hartley: Raman Scattering Studies of Combustion. Comb. Sci.
and Tech., Vol. 13, pp. 199-210, (1976).
139
-------
REFERENCES (Cont'd)
106. Widhopf, G. F. and S. Lederman: Species Concentration Measurements Utilizing
Raman Scattering of a Laser Beam. AIM J. , Vol. 9, pp. 309-316, February 1971.
107. Arden, W. M., T. B. Hirschfeld, S. M. Klainer and W. A. Mueller: Studies of
Gaseous Flame Combustion Products by Raman Spectroscopy. Appl. Spect., Vol. 28,
PP. 55^-557, (197M.
108. Lapp, M. , T. M. Goldman, and C. M. Penney: Raman Scattering from Flames.
Science, Vol. 75, pp. 1112-1115, March 1972.
109. Setchell, R. E.: Time Averaged Measurements in Turbulent Flames Using Raman
Spectroscopy. AIAA Paper 76-28, AIAA lUth Aerospace Sciences Meeting,
Washington, B.C., January 1976.
110. Drake, M. C. , G. M. Rosenblatt: Flame Temperatures from Raman Scattering.
Chem. Phys. Letts., Vol. kh, pp. 313-316, December 1976.
111. Strieker, W. : Local Temperature Measurements in Flames by Laser Raman
Spectroscopy. Comb, and Flame, Vol. 27, pp. 133-136, (1976).
112. Lapp, M. , C. M. Penney, and R. L. St. Peters: Laser Raman Probe for Flame
Temperature. Project SQUID Technical Report GE-l-PU, April 1973.
113. Eckbreth, A. C. : Laser Raman Gas Thermometry. AIAA Paper 7^-11^, AIAA/SAE
10th Propulsion Conference, San Diego, CA. , October
. Salzman, J. A., W. J. Masica and T. A. Coney: Determination of Gas Temperatures
from Laser Raman Scattering. RASA TND-6336, May 1971.
115. Boiarski, A. A.: Gas Diagnostics Utilizing Laser Induced Raman Scattering.
Aerospace Research Laboratories Report ARL 72-008, January 1972.
Il6. Smith, J. R. : A Rotational Raman Scattering System for Measuring Temperature
and Concentration Profiles in Transient Gas Flows. Sandia Laboratories Report
SAND 75-822U, March 1975-
117. Hickman, R. S. and J. H. Liang: Rotational Temperature Measurements in Nitrogen
Using Raman Spectroscopy. Rev. Sci. Instr., Vol. 1+3, pp. 796-799, May 1972.
118. Salzman, J. A., and T. A. Coney: Remote Measurement of Atmospheric Temperatures
by Raman Lidar. NASA TM X 68250, June 1973.
IkO
-------
REFERENCES (Cont'd)
119. Lederman, S., and J. Bernstein: Specie Concentration and Temperature
Measurements in Flow Fields. Project SQUID Technical Report PIB-31-PU,
March 1973.
120. Bandy, A. R., M. E. Hillard and T. E. Emory: Evaluation of Raman Scattering as
a Sensor of Temperature and Molecular Density. Appl. Spect., Vol. 27, pp. ^21-
U2U, November 1973.
121. Boiarski, A. A.: Shock-Tube Diagnostics Utilizing Laser Rajnan Spectroscopy
Naval Surface Weapons Center Report NSWC/NOL/TR 75-53, April 1975.
122. Nelson, L. Y., A. W. Saunders, Jr., A. B. Harvey, and G. 0. Neely: Detection
of Vibrationally Excited Homonuclear Diatomic Molecules by Raman Spectroscopy.
J. Chem. Phys., Vol. 55, pp. 5127-5128, November 1971.
123. Barrett, J. J. and A. B. Harvey: Vibrational and Rotational - Translational
Temperatures in N2 by Interferometric Measurement of the Pure Rotational Raman
Effect. J. Qpt. Soc. Am., Vol. 65, pp. 392-398, April 1975.
Bhagavantam, S. : Scattering of Light and the Raman Effect. Chemical Publishing
Co., Brooklyn, NY, (19^2).
125. Anderson, A.: The Raman Effect. Marcel Dekker, Inc., New York, (1973).
126. Smith, W. H.: A New Method for the Detection of Raman Scattering from
Atmospheric Pollutants. Opto-Elec., Vol. 4, pp. 161-167, (1972).
127. Penney, C. M., L. M. Goldman and M. Lapp: Raman Scattering Cross Sections.
Nat. Phys. Sci., Vol. 235, pp. 110-111, February 1972.
128. Photomultiplier Manual. RCA Technical Series, PT-61, (1970).
129. Hill, R. A. and D. L. Hartley: Focused Multiple-Pass Cell for Raman Scattering.
Appl. Opt., Vol. 13, pp. 186-192, January
130. Laser Focus, Vol. 12, p. 92, October 1976.
-------
REFERENCES (Cont'd)
131. Williams, P. F. , D. L. Rousseau and S. H. Dworetsky: Resonance Fluorescence
and Resonance Raman Scattering: Lifetimes in Molecular Iodine. Phys. Rev.
Letts., Vol. 32, pp. 196-199, February
132. Penney, C. M. : Light Scattering and Fluorescence in the Approach to Resonance -
Stronger Probing Processes, pp. 191-217, in Ref. 8.
133. Hilborn, R. C. : Theory of the Time and Frequency Dependence of Near-Resonance
Raman Scattering and Quantum Beats. Chem. Phys. Letts., Vol. 32, pp. 76-81,
April 1975.
13^. Holzer, W. , W. F. Murphy and H. J. Bernstein: Resonance Raman Effect and
Resonance Fluorescence in Halogen G^ses. J. Chem. Phys., Vol. 52, pp. 399-^07,
January 1970.
135- Marsden, M. J. and G. R. Bird: Resonance Raman Spectrum of Gaseous Nitrogen
Dioxide (N02). J. Chem. Phys., Vol. 59, pp. 1766-1767, September 1973-
136. Rousseau, D. L. and P. F. Williams: Resonance Raman Scattering of Light From a
Diatomic Molecule. J. Chem. Phys., Vol. 6k, pp. 3519-3537, May 1976.
137. Robrish, P., H. Rosen and 0. Chamberlain: Study of the Quenching of Inelastic
Light Scattering Near An Isolated Resonance in I2 Vapor. Phys. Letts., Vol. 51A,
pp. 1^-436, April 1975-
138. Fouche, D. G. and R. K. Chang: Observation of Resonance Raman Scattering Below
the Dissociation Limit in I2 Vapor. Phys. Rev. Letts., Vol. 29, pp. 536-539,
August 1972.
139- Rosen, H. , P. Robrish and 0. Chamberlain: Remote Detection of Pollutants Using
Resonance Raman Scattering. Appl. Opt., Vol. 1^, pp. 2703-2706, November 1975.
1^0. Wang, C. P.: Laser Applications to Turbulent Reactive Flows; Density Measurement
by Resonance Absorption and Resonance Scattering Techniques. Comb. Sci. and Tech.,
Vol. 13, pp. 211-227, (1976).
lUl. Piepmeier, E. H. : Theory of Laser Saturated Atomic Resonance Fluorescence.
Spectrochimica Acta, Vol. 27B, pp. U31-UU3, (1972).
lU2. Daily, J. W. : Pulsed Resonance Spectroscopy Applied to Turbulent Combustion
Flows. Appl. Opt., Vol. 15, pp. 955-960, April 1976.
-------
REFERENCES (Cont'd)
Daily, J. W. : Laser Induced Fluorescence Applied to Turbulent Reacting Flows.
Presented at the Western States Section Combustion Institute Meeting, (LaJolla,
California, Fall 1976), Paper 76-2U.
Daily, J. W. : Saturation Effect in Laser Induced Fluorescence Spectroscopy.
(To be published).
Abramowitz, A. and I. A. Stegun: Handbook of Mathematical Functions. Dover,
New York, (1965).
Mitchell, A. C. G. and M. W. Zemansky: Resonance Radiation and Excited Atoms.
Cambridge University Press, (1971).
lU7. Greenstein, H. : Line-Width and Tuning Effects in Resonant Excitation. Opt.
Soc., Vol. 65, pp. 33-^0, January 1975.
Christensen, C. P., C. Freed and H. Haus: Gain Saturation and Diffusion in CC2
Lasers. IEEE J. Quant. Elec., Vol. QE- 5, pp. 276-283, June 1969.
Gelbwachs, J. A. and J. E. Wessel: Doppler-Free Two Photon Spectroscopy
Applied to Molecular Electronic Transitions. (To be Published).
150. Basco, W. , A. B. Callear and R. G. W. Norrish: Fluorescence and Vibrational
Relaxation of Nitric Oxide Studied by Kinetic Spectroscopy. Proc. Roy. Soc.
London, Series A, Vol. 2oO, pp. U59-U76, (1961).
151. Fristrom, R. M. and A. A. Westenberg: Flame Structure. McGraw-Hill, New York,
(1965)-
152. Butcher, R. and L. Sherman: Second Harmonic Generation Using a Flashlamp
Pumped Dye Laser. Presented at Laser Institute of America Conference (Electro-
Optics '76), New York, September lU-16, 1976.
153. Polanyi, J. C. and K. B. Woodall: Mechanism of Rotational Relaxation. J. Cheia.
Phys., Vol. 56, pp. 1563-1572, February 1972.
15^- Becker, K. H. and D. Haaks: Measurement of the Natural Lifetimes and Quenching
Rate Constants of OH(2i;+, v - 0,1) and OD(2£+, v = 0,1) Radicals. Zeit. fur
Naturf or s chung, Vol. 28a, pp. 2^9-256, (1973).
155. Callear, A. B. and M. J. Pilling: Fluorescence of Nitric Oxide. Trans. F^aca
Soc., Vol. 66, pp. 1618-1631*, (1970).
-------
REFERENCES (Cont'd)
156. Melton, L. A. and W. Klemperer: Energy Transfer in Monochromatically Excited
Nitric Oxide: A2£+ and B2ir. J. Chem. Hiys., Vol. 59, PP- 1099-1115, (1973).
157. Regnier, P. R. , F. Moya, and J. -P. E. Taran: Gas Concentration Measurement by
Coherent Raman Ant i- Stokes Scattering. AIAA Paper 73-702, AIAA 6th Fluid and
Plasma Dynamics Conference, Palm Springs, CA. , July 1973.
158. Moya, F., S. A. J. Druet and J. P. E. Taran: Gas Spectroscopy and Temperature
Measurement by Coherent Raman Anti-Stokes Scattering. Opt. Comm. , Vol. 13,
pp. 169-174, February 1975.
159. Regnier, P. R. , F. Moya, and J. P*. E. Taran: Gas Concentration Measurement by
Coherent Raman Anti-Stokes Scattering. AIAA J. , Vol. 12, pp. 826-83!, June 1974.
160. Moya, F., S. Druet, M. Pealat, and J. P. Taran: Flame Investigation by Coherent
Anti-Stokes Raman Scattering. AIAA Paper 76-29, AIM l4th Aerospace Sciences
Meeting, Washington, D. C. , January 1976.
161. Maker, P. D. and R. W. Terhune: Study of Optical Effects Due to an Induced
Polarization Third Order in Electric Field Strength. Phys. Rev., Vol. 137,
pp. A801-A818, February 1965.
162. Begley, R. F. , A. B. Harvey, and R. L. Byer: Coherent Anti-Stokes Raman
Spectroscopy. Appl. Phys. Letts., Vol. 25, pp. 387-390, October 1974.
163. Harvey, A. B., J. R. McDonald and W. M. Tolles: Analytical Applications of a
New Spectroscopic Tool: Coherent Anti-Stokes Raman Spectroscopy (CARS) in
Progress in Analytical Chemistry. Plenum Press, in press.
164. Tolles, W. M. , J. W. Nibler, J. R. McDonald and A. B. Harvey: A Review of
the Theory and Application of Coherent Anti-Stokes Raman Spectroscopy (CARS).
Appl;. Spect., to be published.
165. Nibler, J. W. , J. .R. McDonald, and A. B. Harvey: CARS Measurement of Vi
Temperatures in Electric Discharges. Opt. Comm., Vol. 18, pp. 371-373, August
1976.
166. Barrett, J. J. : Generation of Coherent Anti-Stokes Rotational Raman Kadi at i or
in Hydrogen Gas. Appl. Phys. Letts., Vol. 29, pp. 722-724, December 19?6
167. Roh, W. B. , P. W. Schrieber and J. P. E. Taran: Single-Pulse Coherent Anti-
Stokes Raman Scattering. Appl. Phys. Letts., Vol. 29, pp. 174-176, August 1974.
144
-------
REFERENCES (Cont'd)
168. Smith, J. R.; A Rotational Raman Scattering System for Measuring Temperature
and Concentration Profiles in Transient Gas Flows. Sandia Laboratories Report
SAND 75-822U, March 1975.
169. Rado, W. G.: The Nonlinear Third Order Dielectric Susceptability Coefficients
of Gases and Optical Third Harmonic Generation. Appl. Phys. Letts., Vol. 11,
pp. 123-215, August 1967.
170. Druet, S. A. J.: Resonant Coherent Anti-Stokes Scattering in Gases. Proceedings
of the Fifth International Conference on Raman Spectroscopy. pp. 736-737, (1976).
171. Lotem, H., R. T. Lynch, Jr., and N. Bloembergen: Interference Between Raman
Resonances in Four Wave Difference Mixing. Phys. Rev. A., Vol. Ih, pp. 17^8-
1755, November 1976.
172. Lynch, R. T., Jr., S. D. Kramer, H. Lotem, and N. Bloembergen: Double
Resonance Interference in Third-Order Light Mixing. Opt. Comm., Vol. 16,
pp. 372-375, March 1976.
173- Nibler, J. W., J. R. McDonald and A. B. Harvey: Coherent Anti-Stokes Raman
Spectroscopy of Gases. Proceedings of the Fifth International Conference on
Raman Spectroscopy, pp. 717-725, (1976).
17^. Song, J. J., G. L. Eesley and M. D. Levenson: Background Suppression in
Coherent Raman Spectroscopy. Appl. Phys. Letts., Vol. 29, pp. 567-569,
November 1976.
175. Molectron Corporation: Coherent Anti-Stokes Raman Spectroscopy (CARS) - Update.
Applications Note No. 112, August 1976.
176. Eckbreth, A. C. and J. W. Davis: Spatial Resolution Enhancement in Coaxial
Light Scattering Geometries. Appl. Opt., Vol. l6, pp. 80U-806, April 1977.
177. Wilbrandt, R., P. Pagsberg, K. B. Hansen, and C. V. Weisberg: Fast 3.c_., .
Raman Spectroscopy of a Free Radical. Chem. Phys. Letts., Vol. 36, pp. .O-"G.
October 1975.
178. OMA Catalog, T336-20M-7/75-PB. Princeton Applied Research Corporation, Princeton,
N.J. 085UO.
179. 1977 Laser Focus Buyers Guide. Vol. 12, January 1977.
-------
REFERENCES (Cont'd)
180. Instruments SA, Inc., J-Y Optical Systems Div. , Metuchen, N.J. 088^0.
181. Snavely, B. B. : Flashlamp-Excited Organic Dye Lasers. Proc. IEEE, Vol. 57,
pp. 137^-1390, August 1969.
182. Chromatix Corp., Mountain View, CA
183. Electro-Photonics Ltd., Belfast, Northern Ireland BT 17 9HN.
1.8k. Phase-R Company, New Durham, NH 03855.
185. Molectron Corporation, Sunnyvale, CA 9^086.
186. Wallenstein, R. and T. W. Hansch: Powerful Dye Laser Oscillator-Amplifier System
for High Resolution Spectroscopy. Opt. Comm. , Vol. Ik, pp. 353-357, July 1975-
187. McFarland, B. B. : Laser Second Harmonic- Induced Stimulated Emission of Organic
Dyes. Appl. Phys. Letts., Vol. 10, pp. 208-209, April 1067.
188. Bergman, A., R. David, and J. Jortner: A Powerful Broad Band Tunable Dye Laser.
Opt. Comm., Vol. k, pp. k^-k^k, February/March 1972.
189. Deutsch, T. F., and M. Bass: Laser- Pumped Dye Lasers Near UOOOA. IEEE J. Q. E.,
Vol. QE-5, PP. 260-261, May 1969.
190, Wallace, R. W. : Generation of Tunable UV From 2610 to 3150A. Opt. Comm.,
Vol. k, pp. 316-319, December 1971.
191. Quanta-Ray Corporation, Mountain View, CA 9kQk3.
192. Dewey, H. J. : Second Harmonic Generation in HBcOg • kE^O from 217.1 to 315.0 run.
IEEE J. Q. E., Vol. QE-12, pp. 303-306, May 1976.
193. General Photonics Corporation, Santa Clara, CA 95050.
194. International Laser Systems, Orlando, FL 3280U.
1*6
-------
APPENDIX I
RADIOMETRIC MEASUREMENT CONVERSION
Spectral radiance measurements (Ref. I-l) have been made on the EPA "Rainbow"
furnace employing a Gamma Scientific Model 2020-31 radiometer (Ref. 1-2). For
optically thin flames, spectral radiation energy densities are preferable to account
properly for instrument techniques which view some volume of the combustion device
being probed. The spectral radiance in Watts/cm sr A can be converted to a spec-
tral radiation energy density by dividing the former by the depth of field of the
radiometer.
The radiometer consists essentially of a lens, variable aperture and 'detector
as seen in Fig. I-l designed in such a way that the viewing solid angle times source
area product remains constant independent of radiometer to source distance. The
acceptance angle or is fixed, but selectable in various increments. From simple
geometric considerations the linear acceptance angle, or, is given by
tan | = I3- (I-l)
where da is the aperture diameter and q the image distance shown in Fig. I-l.
For fixed acceptance angle, the radiometer is designed with, a constant dg/q ratio.
The source area AS viewed can easily be shown to be
° 4 q (1-2)
The collection solid angle, Q, is
n = Af (1-3)
where A. is the area of the field lens employed. Note that the product of source
area times collection solid angle is
9 a
Agfi = AfTT tan^ ~ (1-4)
™ £_
and is constant, i.e., independent of p, for fixed <*. Thus the radiometer can be
calibrated and used to make spectral radiance measurements directly for any di^a:ici
from the source being measured.
From the lower part of Fig. I-l, the depth of field of the radiometer can oe
found using simple thin lens and geometrical relationships and is given by
2 tan or/2
dof = 2p —-—*- , _.
I-l
-------
RADIOMETER SCHEMATIC
FIELD LENS
VARIABLE
APERTURE
a
DETECTOR
I
ro
O
T1
-------
Note that the depth of field does depend on the radiometer to source distance. The
radiometer employed had a minimum working distance of 1 meter. Since such a working
distance is compatible with measurements from the side of the Rainbow furnace, this
is the radiometer to source distance assumed for the side window measurements. For
the measurements from the rear axial window, the minimum working distance was l^O cm.
The measurements were made with an acceptance angle of 0.1°. The field lens employed
in the radiometer was f/3«5 and 60 mm in diameter. For the side location, the depth
of field was calculated to be 2.9 cm, for the rear axial work, 5-6 cm. The measure-
ments reported in Ref. 1-1 were divided appropriately by these numbers to obtain
the radiation energy density at various locations in the furnace.
1-3
-------
APPENDIX I
References
1-1. W. H. Farmer and H. R. Bevis: "Observation of Large Flame Characteristics
Relative to the Performance of a Laser Analyzer." Technical Report under
Contract EPA F Uo6-7^-C-OOC4 (August 1973).
1-2. "Handbook of Light Measurement Techniques." Gamma Scientific Inc., San Diego,
California.
-------
APPENDIX II
AVERAGING CONSIDERATIONS FOR PULSED, LASER RAMAN
SIGNALS FROM TURBULENT COMBUSTION MEDIA*
Introduction
The magnitude of temporal temperature fluxtuations is of great importance in
the understanding and modeling of turbulent combustion phenomena, particularly in
regards to pollutant formation (Refs. II-l, -2). Fluctuations are also relatable to
the performance of combustors and to the lifetime of downstream turbine components
(Ref. II-3). Thermocouples have been employed to measure fluctuations in turbulent
(Ref. 11-10 or oscillating flames (Ref. II-5). Laser Raman techniques (Ref.,II-6)
are anticipated to see widespread application in this area, particularly where the
absence of a material probe will prove of great advantage, e.g., recirculating flows,
extremely high temperatures. With pulsed lasers of sufficiently short duration,
i.e. < 10 seconds, "instantaneous" temperature and species measurements can be made
(Ref. II-7). By repeating these, measurements a statistically significant number of
times probability distribution functions can be assembled from which property averages
and fluctuation magnitudes can be obtained. < .
In many instances, however, the Raman signal-to-noise (S/N) ratio is limited
due to shot, background or laser induced noise (Ref. II-8) and accurate single pulse
measurements are precluded. Signal averaging is usually then employed to enhance
the S/N in an attempt to obtain time-averaged medium properties. However, such time
averaging can lead to erroneous measurements. In Ref. II-9> Setchell examined the
consequences of time-averaging Raman data generated by a continuous wave laser from
a turbulent medium and identified those instances where averaging errors would arise.
Similarly, an analysis has been presented of the effect of fluctuations on the
accuracy of electron beam diagnostics (Ref. 11-10). In this note the consequences
of ensemble-averaging pulsed laser Raman data in a fluctuating environment will be
treated. As will be shown, averaging can lead to measurement errors in mediun pro-
perties, depending on the magnitudes and correlations of the fluctuations. In the
first portion of the note, the case of averaging pulsed Raman data, exhibiting shot;
noise only, will be considered for both number density and temperature measurements.
Preferred averaging approaches will be illustrated. Then the situation
to averaging Raman data containing other sources of noise will be examined.
*Research supported by Project SQUID under subcontract 8960-20 and the Office
Naval Research under Contract
U-l
-------
Signal Averaging With Shot Noise
The number of Raman photons in the Stokes band, n^s (the superscript a will be
used to denote the anti-Stokes region) generated by the ith laser pulse is given by
nis = ksNifs(Ti)ei (II-1)
where N^ is the number density of the scattering species of interest at instant i;
fs(TjL), the bandwidth factor; and e±, the energy of laser pulse i. The bandwidth
factor is a temperature dependent term which accounts for the fraction of the
scattering species in the appropriate initial quantum states for scattering to be
observed. fS(Ti) depends on the spectral location and bandwidth (hence its name)
of the spectrometer or interference filters employed; these dependences will not be
explicitly denoted. ks is a factor dependent on scattering cross section, geometry
and optical collection efficiency and is constant from pulse to pulse. In Fig. II-l
bandwidth factors are displayed as a function of temperature for the anti-Stokes and
Stokes Raman intensities for Gaussian shaped bandpasses (typical of interference
filters) with bandwidths (FWHM) of 10, 50 and 100 A. These were calculated for a
laser operating at 5320 A (e.g., frequency doubled neodymium) with an infinitesimally
thin linewidth using the analysis described in Ref. 11-11. Similar results would
be obtained for triangular shaped bandpasses typical of monochromator slit functions
(Ref. II-9). In Fig. II-2, the ratio of the anti-Stokes to Stokes bandwidth factors
is shown as a function of temperature for bandwidths of 10, 50 and 100 &. Of note
is the near linearity displayed by the ratios at temperatures above 1250-1500°K.
The number of Stokes photoelectrons, S-j_, generated by the Stokes photomultiplier
can be expressed as
where T] is the Stokes photomultiplier quantum efficiency and mj_s, a factor to
account for tube shot noise fluctuations, mi3 will be Poisson distributed about
unity (Ref. 11-12) and can be written as
n-i5 - 1 -nn^1 (II-3)
where m^3 = 1, m^s = 0.
For an average photon flux from pulse to pulse of n, the average number of
photoelectrons created will be Tin. Here bars over symbols denote ensemble and not
time averages. The actual number of photoelectrons will vary about the average from
shot to shot with a variance given by a = |jn (Ref. 11-12). From the definition of
the distribution variance, i.e. [(PJ_ - p)2!F, it can easily be shown that
II-2
-------
FIG.H-I
BANDWIDTH FACTOR VARIATION WITH TEMPERATURE
FILTER BANDWIDTH (A)
100
STOKES
ANTI-STOKES
500
1000 1500 2000
TEMPERATURE-DEG KELVIN
2500
3000
II-3
-------
FIG. E-2
BANDWIDTH FACTOR RATIO VARIATION WITH TEMPERATURE
1.3
1.2
Q 1.1
I-
1 1.0
O
£ 0.9
u.
£ 0.8
g 0.7
CD
ffi °'6
O
£ 0.4
O
*? 0.3
P
z
< 0.2
0.1
0
FILTER BANDWIDTH (A)
10,
500
1000 1500 2000 2500
TEMPERATURE-DEG KELVIN
3000
Il-k
-------
Density/Species Measurements
By combining Eqs. (ll-l) and (II-2), the number density of the species of
interest may be related to the measured number of Stokes photoelectrons
By measuring the energy, e-j_, on each pulse, the number density can be measured to an
accuracy dependent on the shot noise fluctuations and temperature. By proper band-
width selection fs(Ti) can be made nearly independent of temperature (Fig. II-l) and
the number density can be measured with an accuracy determined by the magnitude of
the shot noise fluctuations. By signal averaging the energy normalized per pulse
photoelectron yield, Sj_*, the average number density can be obtained
§ 1 -]- S
Expressing Nj_ in terms of the mean and a fluctuation
% = N + Nj/ where w"1" = 0 (lI-T)
and using Eq. (II-3)
N^i3 = K •»• NJ_ + mi N + %'mj_ (H-8)
Upon averaging
P 1-1
the result following from the fact that Ni'n^8 = 0. This arises due to the statis-
tical independence of the number densrty fluctuations and shot noise fluctuations
permitting N^'mi3' to be separated to % mp^1" (Ref. 11-13) which vanishes. Hence,
from which the average density is obtained after a suitable calibration.
Temperature Measurements
If the anti-Stokes to Stokes ratio is formed, the instantaneous number density
and pulse energy cancel and a temperature measurement can be made from the ratio
n-5
-------
with some error due to the shot noise term, mi3/10!3' Intuitively one might suspect
these temperature measurement errors to cancel out over a large sample of measurements.
However, this is not always the case. For example, consider the case of a laminar
flame with constant (in time) temperature T at the measurement location. The ratio
corresponding to this temperature will be denoted by Ro, i.e. T(RQ) = T. The measured
ratio on any pulse will vary from Ro due to the shot noise fluctuations
The error in measured temperature from the true temperature can be obtained by
expanding T about RQ
, x d2T(Rp) -2
i - i —£$* Ri
Expressing T&±a, m^s as in Eq. (II-3) and expanding m^a/m^s, R^T can be shown to be
for m^8" « 1. The maximum temperature error is approximately
where m^' has been assumed equal to the variance from Eq. (II-4) and the second
drivative in Eq. (II-13) has been assumed equal to zero (Fig. II -2). The temperature
measurement error at 2000°K for a 10 A bandwidth can be estimated from Fig. II -2;
dT(R0)/dR at 2000°K is approximately 1667 K deg. Assuming 1000 photons ^collected
on both the anti-Stokes and Stokes ; channels and 10 percent quantum efficiencies, the
maximum measurement error would be about 220°K, or - 11 percent. If these erroneous
measurements are averaged, substituting Eq. (ll-l4) into Eq. (II-13), one obtains
illustrating that shot noise fluctuations do not average out in general, but lead
to an error in mean temperature for a non-zero second derivative. At high tempera-
tures, the bandwidth ratios vary nearly linearly with temperature (Fig. H-2) resulting
n-6
-------
R77-92665-6
in a very small or nonexistent second derivative. If the shot noise fluctuations are
small enough so that the instantaneous ratios reside within the range of linearity,
then averaging will yield the true average temperature even though each individual
measurement is in error.
It should also be noted that in general T is not obtained from R. Consider the
situation of temperature measurements in a fluctuating medium with average tempera-
ture T where the instantaneous temperature can be measured quite accurately, i.e_.,
shot and other noise being insignificant. Expanding Rj_ in a power series about T
where Tj_ = T + T.j_ ' , T^ ' being the deviation of temperature at any instant from the
mean. Upon averaging one obtains
R «R(T) +iV (11-18)
Only in those cases where R is a linear function of T over the range of temperature
fluctuations does R~ = R(T) .
Very importantly it should be_ noted that the average temperature is not obtained
from A/S or equivalently A*/S*. A* is obtained from
Expanding fa(Ti) about T
(n_20)
and expressing density and temperature in terras of mean and fluctuating quantities
one can show
This relation also derives from the fact that the shot noise fluctuations are
statistically independent (i.e., uncor related) of fluctuations in medium properties
(N1, T1), so that terms such as m^^T^ are separable (Ref. 11-13) to m^' Tj_' and
vanish. A similar relation pertains to S*; if the Stokes bandwidth factor is inde-
pendent of temperature then Eq. (11-10) pertains and one obtains
II-7
-------
a
A*/S* ,
TfkV L ' » dT 2 dae N 'J (11-22)
Hence the ratio of the separately averaged Raman "band intensities depends not only
on average temperature but also on the magnitude and correlation of the fluctuations
in medium properties. Dug to the exponential dependence of the anti-Stokes intensity
(Fiq. II-l) |£a > 0 and |||^ < 0, the last two terms in Eq. (11-22) tend to cancel
the degree to which depends on the nature of the fluctuations.
Other Sources of Noise
There are diagnostic situations, particularly in relation to practical device
probing, where despite limited "bandwidth, polarization discrimination, high peak
power and/or high focal flux diagnostic approaches (Ref. H-8) there are sources of
noise, either naturally occurring or laser induced, present in the signal. Hence
the number of Stokes photoelectrons for example, is then
„ / s snx
a * ±1 -ns VP1 + EH 7 „ S /TT
S = = Tj C m (11-
where nj[sn are the number of "noise" photons in the Stokes "bandpass. In this situa-
tion, the signal to noise ratio does not improve merely by averaging if the noise is
more than a random occurrence. If another channel is placed in a spectral region
adjacent to the Raman spectrum, the noise can be sampled assuming that it is fairly
smooth spectrally. This is generally the case for laser modulated (Ref. H-8) or
naturally occurring soot incandescence. The noise sampling channel will detect S]%
noise photoelectrons
„.. -s sn sn
SN1 T1 m m
(11-210
where for simplicity the quantum efficiency is considered the same for each tube.
The desired "signal" can be obtained by subtracting the Stokes noise from the Stokes
with the result
s s _s sn
< M ni -. / s sn\
1 + -S^- (mi - ni ) (11-25)
the subtraction being imperfect due to the uncorrelated shot noise on each tube.
Upon sufficient signal averaging, Eq. (11-25) becomes
sn sn'
L Pi
(n-26)
n-8
-------
Again due to the statistical independence of the shot noise and the signal photons,
the (-)m term is separable and the first term simplifies to Tls(Iis). if the fluctua-
tions in pulse energy are small permitting the denominator in the second term to
be expanded, it can be shown that this term vanishes resulting in
As before if fs(T) is designed to be constant with temperature, the average number
density can be obtained. A similar result would be obtained if the signal and noise
channels were separately averaged, then subtracted.
Similarly jSf can be shown to be independent of shot and background noise effects
resulting in Eq. (11-22). ^//gp is not a measure of average temperature alone but
depends on the magnitude and correlation in the fluctuations.
If the ratio '"±± is formed first, the situation is analytically .intractable.
I? id. and ^ are expressed in a form (From Eq. H-25)
s s s sn, s snv
,,„ n (m-j -EH )
n
T + ' r3 (11-28)
where KE deontes the relative error, then '"y can be cast into a form similar to
Eq. (TI-12) permitting an B^' -to be defined. Although the situation is still intrac-
table, it was shown in the discussion following Eq. (II-12) that errors in a ,set of
"instantaneous" "temperature" measurements would not average out and that an erroneous
average temperature would result, Eq. (II-16), for a nonzero second derivative. Here
an erroneous temperature measurement will result with each laser pulse except for
the extremely rare instance when the shot noise on the four channels is the same.
The measured averaged temperature will depart from the time average (averaging
Eq. (11-13)) _ _
T dT(Ro) iT" i 1 d2T(.Rj r '2 - ..... -
}'.T- dR i 2 2 x
depending upon %' (not necessarily zero in the background subtraction situation) and
Ri'2- These terms will be dependent on the signal and noise levels in a particular
situation.
Implications of Signal Averaging
There are a number of conclusions which can be drawn from the foregoing analyses.
In measurement situations where the anti-Stokes and Stokes intensities cannot be
determined to a high level of accuracy, the density and temperature measured at each
instant will, of course, be erroneous. Quite importantly the average of these
II-9
-------
erroneous measurements may not yield the true average, but may depart from the true
average depending on the magnitude of the gasdynamic and shot noise fluctuations.
Average density measurements appear possible in the presence of shot and/or background
noise if the Stokes band.vri.dth factor is designed to be independent of temperature.
In this case, the time averaged density is obtained from the averaged Raman data des-
pite the character of the fluctuations. The situation with temperature measurements
is less fortuitous. True average temperature can be obtained by signal averaging
Raman data in the presence of shot noise only if: (l) the anti-Stokes to Stokes ratio
is first formed, (2) by manipulation of spectral bandwidths and center frequencies,
the anti-Stokes/Stokes ratio is made a linear function of temperature over the "tem-
perature" range of interest. By "temperature" range is meant the temperature inferred
from the measured anti-Stokes to Stokes ratio; this range may well be considerably
larger than the actual physical temperature range. This would be the case for example
when subtracting out large background interferences; and (3) the fluctuations in tem-
perature are within the range of linearity. In this case the second derivative of the
temperature with anti-Stokes to Stokes ratio vanishes prohibiting temperature fluctua-
tion terms from accumulating during averaging. When fluctuations are very large, so
as to extend beyond the range of ratio linearity as may be the case in practical com-
bustor devices (Ref. II-3), accurate average temperature measurements cannot be made.
When anti-Stokes and Stokes data are separately averaged, background can be subtracted
on average and shot noise terms will average to zero. However, temperature inferred
from the ratio of averaged anti-Stokes to averaged Stokes will not be the average
temperature but will depart from the true average depending on the magnitudes and
correlations of the fluctuations.
11-10
-------
APPENDIX II
References
II-l.. F. C. Gouldin: "Role of Turbulent Fluctuations in NO Formations," Comb. Sci.
and Tech., Vol. 9, pp. 17-23 (197M-
II-2. W. P. Jones: "The Effect of Temporal Fluctuations in Temperature on Nitric
Oxide Formation," Comb. Sci. and Tech., Vol. 10, pp. 93-96 (1975).
II-3. R. R. Dils and P. S. Follansbee: "Wide Bandwidth Gas Temperature Measurements
in Combustor and Combustor Exhaust Gases," presented at the 22nd International
Instrumentation Symposium of ISA, San Diego, CA (May 1976).
II-4. C. M. Ho, K. Jakus and K. H. Parker: "Temperature Fluctuations in a Turbulent
Flame," Comb, and Flame, Vol. 27, pp. 113-123 (1976).
II-5. D. F. G. Durao and J. H. Whitelaw: "Instantaneous Velocity and Temperature
Measurements in Oscillating Diffusion Flames," Contemp. Phys., Vol. 17, pp.
21*9-274 (1976).
II-6. M. Lapp and C. M. Penney: Laser Raman Gas Diagnostics, Plenum Press, New
York (197M-
II-7. S. Lederman, M. H. Bloom, J. Bornstein, and P. H. Khosla: "Temperature and
Species Concentration Measurements in a Flow Field," Int. J. Heat Mass Trans.,
Vol. 17, pp. 1V79-1486 (197*0.
II-8. A. C. Eckbreth: "Laser Raman Thermometry Experiments in Simulated Combustor
Environments," AIAA Paper 76-27, lUth Aerospace Sciences Meeting, Washington, DC
(January 1976).
II-9. R. E. Setchell: "Time Averaged Measurements in Turbulent Flames Using Raman
Spectroscopy," AIAA Paper 76-28, Ikth Aerospace Sciences Meeting, Washington, DC
(January 1976).
11-10. s. S. Lazdinis: "Influence of Fluctuations in Electron Beam Diagnostics,"
AIAA J., Vol. Ik, pp. 133-13** (February 1976).
11-11. A. C. Eckbreth: "Laser Raman Gas Thermometry," AIAA Paper 74-3JM, AIAA/SAE
10 Propulsion Conference, San Diego, CA (October 197*0.
11-12. Photomultiplier Manual, RCA Technical Series, PT-61 (1970).
11-13. W. B. Davenport and W. L. Root: Random Signals and Noise, McGraw-Hill, NY
(1958)
11-11
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/7-77-066
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
REVIEW OF LASER RAMAN AND
FLUORESCENCE TECHNIQUES FOR PRACTICAL
COMBUSTION DIAGNOSTICS
5. REPORT DATE
June 1977
6. PERFORMING ORGANIZATION CODE
. AUTHOR(S)
A. C. Eckbreth> P. A. Bonczyk, and J. F. Verdieck
8. PERFORMING ORGANIZATION REPORT NO.
9 PERFORMING ORGANIZATION NAME AND ADDRESS
United Technologies Research Center
East Hartford, Connecticut 06108
10. PROGRAM ELEMENT NO.
E HE 624
11. CONTRACT/GRANT NO.
68-02-2176
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13._TYPE OF RSEQP.T AND PERIOD COVERED
Task 1 Final: 10/76-3/77
14. SPONSORING AGENCY CODE
EPA/600/13
15. SUPPLEMENTARY NOTES IERL_RTP pr0ject officer for this report is William B. Kuykendal,
Mail Drop 62, 919/549-8411 Ext 2557.
16. ABSTRACT
The report gives results of a detailed examination of four techniques for
practical combustion diagnostics: spontaneous and near-resonant Raman scattering,
laser fluorescence, and coherent anti-Stokes Raman scattering (CARS). For diagnosis
of highly luminous, particle-laden flames (ei. g., in hydrocarbon-fueled primary com-
bustion zones), spontaneous and near-resonant Raman scattering appear to possess a
low probability for successful application, even with advanced state-of-the-art laser
sources. However, for clean flame diagnostic or probing of environments with modest
particulate levels (e.g. , some secondary combustion and exhaust/plume regions),
spontaneous Raman scattering is very attractive due to its simplicity, high level of
understanding, and advanced state of development. Laser fluorescence appears capa-
ble of species concentration measurements to 10's of ppm for selected molecules
whose absorptions can be saturated. In this way, fluorescence magnitudes do not
depend on quenching effects. CARS appears to be capable of successful thermometry
and majority constituent measurements in practical flame environments, although
some jeopardies need to be experimentally investigated. Potential detectivities in the
10-100 ppm range may be possible using sophisticated variants of the CARS technique.
17.
KEY WORDS AND DOCUMENT ANALYSIS
a.
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
Air Pollution
Combustion
Flames
Measurement
Raman Spectroscopy
Coherent Scattering
Lasers
Fluorescence
Exhaust Gases
Plumes
Temperature
Measurement
Air Pollution Control
Stationary Sources
Laser Fluorescence
Particulates
13B
2 IB
14B
20H
20E
13. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
173
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
n-12
------- |