Ar+ laser-excited fluorescence of C2 and CN produced in a flame

COMBUSTION AND FLAME 49: 197-206 (1983)

197

A r + L a s e r - E x c i t e d F l u o r e s c e n c e o f C 2 a n d C N P r o d u c e d in a F l a m e JOHN A. V A N D E R H O F F , R I C H A R D A. BEYER, ANTHONY J. KOTLAR, and W I L L I A M R. ANDERSON U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD 21005

Fluorescence from C2 and CN has been produced in a CHJN20/N 2 flame situated within the lasing cavity of an Ar+ laser using several prism-selected laser lines. These transitions have been identified, and fluorescence intensity profiles th/ough the reaction zone of the flame have been obtained. Using the Raman-Stokes Q-branch signal from N2, a temperature profile has also been obtained. These fluorescence profiles have been converted to accurate relative concentration profiles. A rough estimate of absolute concentrations has also been obtained.

INTRODUCTION Spontaneous Raman spectroscopy has been used to probe temperature and species profiles in steady-state premixed flames [1]. During the Course of these experiments, intense laser fluorescences resulting from excitation with various prism-selected lines of an Ar + laser were observed. This paper addresses the identification of the radical species producing the fluorescence, the spatial profiles of these species through the flame reaction zone, and the assessment of the potential uses of this fluorescence for characterization of flames properties. As will be discussed later, the identified fluorescing transitions are C z (dang -~ aazru) and CN (BEY.+ ~ XzZ+). Both involve short-lived radicals existing primarily in the reaction zone: Cz is produced in rich hydrocarbon flames and CN occurs in hot flames containing nitrogen. In the past it has been speculated that C2 plays a direct role in soot formation; however, it is presently thought that soot forms from various types of hydrocarbon nucleation centers. Production of CN in a hydrocarbon-air or N 2 0 flame indicates the breakage of a strong N - N bond [/)(N-NO) = 113.7 Kcal/mole and D ( N - N ) = Copyright © 1983 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017

226 Kcal/mole], which at normal flame temperatures is not likely to arise from thermal dissociation but rather a radical reaction mechanism. Both C 2 and CN have been studied in flames using absorption and emission spectroscopy [2-4]. More recently fluorescence spectroscopy of C 2 and CN has been performed in flames [4-5]. Excitation of C2 has been accomplished with discrete lines of an Ar + laser [6-7], but to our knowledge no one has previously reported exciting CN in this manner. EXPERIMENTAL A schematic diagram of the experiment is shown on Fig. 1. A nominal 4-W Ar + laser is used as the excitation source. Its cavity is extended with two highly reflective mirrors of focal length 1 and 0.3 m providing a laser power enhancement of ~20 and an intracavity beam waist of approximately 100 gm diameter. The scattered light is imaged onto the 100 #m horizontal slit of a 0.25 m spectrometer with two double convex quartz lenses. The detected light comes from a volume approximated by a cylinder of 100 #m diameter and 3 mm in length. A silicon-intensified target vidicon tube (OMA I) is used to detect the dispersed light. Using a 1180-groove/mm grating,

0010-2180/83/011974-10503.00

198

JOHN A. VANDERHOFF ET AL. KNIFE EDGES

N2

t

Fig. 1. Experimental arrangement for Raman and fluorescence measurements.

approximately 400 A of radiation can be observed at one time with this system. This radiation is stored in 500 memory channels, and the resolution FWHM is about 4 A. The spectra are recorded with and without the laser light, then subtracted to obtain the signal from the laserexcited fluorescence and/or Raman scattering. Accumulation times for the fluorescence data reported here are usually less than 10 s. The relative laser power is measured by sampling the small amount of light transmitted through one of the high reflectivity mirrors with a thermopile. Rich premixed flames of methane and nitrous oxide burning at atmospheric pressure have been experimentally studied with an open channel curved knife edge burner [8], shown on Fig. 2. The burner is made from two aluminum plates with various gaskets providing the desired channel width. For these experiments the channel dimensions are 50 mm by 3 mm. The radius of curvature of the knife edges is 50.8 mm. Two small independent channels run along each edge of the main channel, and a flow of N 2 through these channels prevents the flame from wrapping around the ends of the main channel. Gas flow to the burner is regulated with rotameters. The spectroscopic results for C z and CN were obtained at different times without an emphasis being placed on the exact flame conditons. Here the approximate conditions are an equivalence ratio ~ = 1.6 with 40% dilution with N 2. For the case where the temperature and fluorescence prof'des were obtained, the flow conditons were measured with a wet test meter after the experimental run. In this case, ~ = 1.36 with 45% dilution with N 2.

MIXED GAS In

Fig. 2. Open channel curved knife edge burner which allows complete optical access to the reaction zone of a flame.

From previous work with this burner, it has been observed that within experimental error (<50K), the maximum flame temperatures measured by Raman scattering are the same as those obtained from an equilibrium flame temperature calculation assuming adiabatic conditions. Thus negligible heat loss to the burner head is assumed. The burner was operated in a horizontal position so that the flame could be viewed end on by the detection optics; that is, the main channel opening of the burner is directly viewed by the spectrometer entrance slits and the long dimension of the channel is aligned with the long dimension of the slit. Attaching this burner to a small milling table provides movement in two directions. This movement is monitored by a precision dial gauge which reads directly to 0.01 mm. RESULTS C~ Hendra et al. [6] and Jones and Mackie [7] have excited Ca with the 5145-A line of an Ar ÷ laser. They state that the excitation results from two R(IO) lines of the (0, 0) vibrational band of the Swan system overlapping the 5145-~, line. Additionally, Hendra et al. have observed C2 fluores-

199

LEF OF C 2 AND CN IN A FLAME TABLE 1 Observed Excitations of the C2 Swan System Using an Ar+ Laser Laser line (A)

Excited bandheads (A)

5145

5165 (0,0)

5017

5129 (1, 1) 5098 (2, 2)

4727

4737 (1, 0)

4658

4715 (2, 1)

cence excitation from 5017-A radiation. We have investigated laser-exCited fluorescence of C2 using various prism selected Ar ÷ lines and the results are shown in Table 1. The lines 4965, 4880, 4765, and 4579-A did not produce any readily detectible C z fluorescence and are thus not listed in the table. Spectral detection ranged from 6200 to 4500-A. The stronger fluorescence lines were readily observable, real time, on the ridicon output display. These signal amplitudes were about three times larger than the substantial flame emission background. The intensities given in Table 1 were normalized to a band head (the most intense fluorescence feature). These numbers are meant to be qualitative only since possible overlap o f transitions and nonlinearities in the vidicon tube response over this spectral and am-

Fluorescence (A)

Intensity

6191 (0, 2) 5635 (0, 1) 5165 (0, 0) 5145 Rayleigh 6122 (1, 3) 6059 (2, 4) 5635 (0, 1) 5587 (1, 2) 5535 (2, 3) 5165 (0, 0) 5129 (1, 1) 5098 (2, 2) 5017 Rayleigh 4737 (1, 0) 4715 (2, 1) 6122 (1, 3) 5585 (1, 2) 5165 (0, 0) 5129 (1, 1) 4737 (1, 0) 4727 Rayleigh 5635 (0, 1) 5585 (1,]2) 5540 (2"3) 5165 (0, 0) 5129 (1, 1) 5098 (2, 2) 4715 (2, 1) 4658 Rayleigh

0.03 0.20 1.0 16 0.1 0.1 0.05 0.6 0.4 0.3 1.0 0.6 30 0.7 0.6 0.07 0.4 0.1 1.0 1.0 8 0.01 0.03 0.2 0.07 0.06 0.2 1.0 17

plitude range were not investigated. To ascertain that the C z transitions Were not saturated, we varied the power of the 5145-A laser line (strongest line) pumping the (0, 0) band and observed that the variation in the fluorescence signal coming from the (0, 1) band was indeed linear. The same test was applied to CN, and similar results were obtained. CN The CN (1, 3) band violet transition occurs at 4578-A and is degraded to the violet. Initially, it was thought there may be sufficient overlap to pump this transition with a 4579-A line; this turned out not to be the case. However, when using the 4545-.~, line, laser-excited fluorescence

200

JOHN A. VANDERHOFF ET AL. C N B2 ~+'-'- X l ~ * e(2,z) P(o,o)

,..ll I Ill

,,~l't~')

~

_

e(l,O}

;,(~ol '

~- ~lYx.

l A

FLAME

EMISSION

WAVELENGTH (A)

Fig. 3. Flame emission and laser excited fluorescence spectra of CN occurring in the reaction zone of a CH4/N20/N 2 flame.

of CN was obtained. No other Ar + line produced detectable CN fluorescence. Figure 3 shows both the flame emission and fluorescence spectra. Clearly, the emission spectra results from the well known violet system (BZ]~+ -+ X 2 ~ +) of CN. The fluorescence spectra demonstrate that the upper vibrational state which the laser pumps is u' = 1. Since AO = --2 is the only nearby vibrational band sequence, the 4545-A laser line is pumping a rotational line in the R-branch region of the (1, 3) band. To identify positively the rotational transition involved, higher-resolution spectra were necessary. This was accomplished by switching to a l-m

P- BRANCH 22

I

388o

387o

0

monochromator-photomultiplier system which has a resolution of 0.15 A. Removing the flame emission from the fluorescence was provided by chopping the laser beam and subtracting the signals resulting from laser on and laser off conditions. A typical high-resolution scan is shown on Fig. 4, where it is readily observed by counting from the band origin that an R(20) line is being pumped. Thus the 4545-,8, laser line is pumping the (1, 3) R(20) transition of the violet system of CN. There is not sufficient resolution yet to determine whether the F 1 or F z component is being pumped. (As discussed in the appendix, the F z component is probably being pumped.) Thus the most intense

S

R - BRANCH 10 15

I I'"'1'"'1'"'1""

3860 WAVELENGTH

20

I

~sso

384o

i.~)

Fig. 4. High-resolution laser-excited fluorescence spectrum of CN in the reaction zone of a CH4/N20/N 2 flame. The 4545-A laser line pumps an R(20) line in the(l,3) band (probably the R2 component). The resolved fluorescence in the (1, 1) band, shown here, exhibits strong R(20) and P(22) lines, as expected for this pumping transition.

LEF OF C2 AND CN IN A FLAME

201

transitions observed are the R(20) and P(22) rotational lines.

TEMPERATURE Flame temperature measurements were made by observing the Raman scattering in the wavelength region appropriate for Stokes rotational-vibrational Q-branch spectra for N 2. These observed spectra were fit with a multiparameter least squares Raman computer program which has been developed to make use of the complete Q-branch spectrum for N 2 in extracting a temperature from the data [9]. A typical N 2 Stokes Q.branch spectrum together, with the computer-generated fit is shown in Fig. 5. This Raman spectrum is one representative data set obtained in determining the temperature proFde of the CH4/N20/N 2 flame. Here the temperature is 2477 :t 21K. The standard deviation in all the flame temperature measurements reported here is about 1%. Typical measurement times were on the order of 1 min, which restrlted in about 106 counts in the re_ 1- peak of the Stokes Q-branch.

FLUORESCENCE INTENSITY PROFILES Fluorescence profiles of Ca and CN together with the temperature through the reaction zone of a CH4/N20 flame of equivalence ratio ~ = 1.36 and diluted with 45% N 2 are displayed on Fig. 6. For the C2 fluorescence measurements, the (0,0) band of the Swan system was pumped with 5145A. radiation and the fluorescence intensity measured by integrating over the (0, 1) band. These data were corrected for small variations in the laser power. For CN, the (1, 3) transition of the violet system was pumped with 4545-A radiation and the fluorescence intensity measured by integrating over the (1, 1) band. Here again the only corrections applied to these data were for small variations in laser power. It is clearly seen from Fig. 6 that the measurements have sampled through the reaction zone into the burned gas region. The temperature was observed to increase from room temperature to 2510K, where it plateaus and then decreases slowly with increasing distance. A computation of the adiabatic flame temperature from the NASA-Lewis [10] thermochemical equilibrium

1.0-

0.8

-

B

0.6--

Z

N 0.4-<

o Z

0.2-

ca

0.e ~ 5460

I 5480

5500 WAVELENGTH (~)

5520

Fig. 5. R a m a n - S t o k e s Q-branch rotational-vibrationalspectrum for N 2 in a C H 4 / N 2 0 / N 2 flame. T h e squares represent t h e data and t h e solid line t h e least squares c o m p u t e r fit. T h e laser excitation line is 4 8 8 0 A.

202

JOHN A. VANDERHOFF ET AL. 10 00(~

-- 3 0 0 0

Q

0 0

~

A A

D

o~

,ooo

A QQ

t ~ l i eee i

0

0

2000 Q

&

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Z Z

.z,

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-

1000

I

& A A 10 ~ 0

i ill

A iliill

II I I I l l l l l t l i l l l i l l I 2 " RELATIVE BURNER POSITIONimm)

3

Fig. 6. Fluorescenc.e intensity profiles for C 2 (s) and CN (o), together with the temperature profile (a), through the reaction zone of a CH4/N20/N 2 flame. The arrow on the temperature ordinate represents the adiabatic flame temperature.

code gives a temperature of 2490K (indicated with an arrow on Fig. 6), which is in excellent agreement with the measured maximum temperature. The maximum in the C z fluorescence intensity appears about 0.1 mm lower (earlier) in the reaction zone than CN and decays faster. The extent of the primary reaction zone is on the order of 1 mm. When comparing these fluorescence intensity measurements with emission studies, several improvements can be readily discerned: 1. the spatial resolution for the fluorescence results can be made more precise since it de. pends on the sampling volume of the collection lens as well as the focusing of the laser beam, 2. flame emissions from other compounds can be subtracted from the spectra as they are usually not laser dependent, and 3. in most cases fluorescence probes the ground electronic state of molecules whereas emission does not; therefore fluorescence is not subject to possible nonequilibrium in electronic levels.

CONCENTRATION PROFILES

By making several assumptions, the fluorescence intensity profiles of Fig. 6 can be adjusted to reflect relative concentration profiles. One assumption is that the quench rate Q is constant for all-the points sampled in the flame. Cottereau and Stepowski [11] have measured the quench rate for OH through the reaction zone of a propane-oxygen flame and find it to be constant. Bechtel and Teets [12] observed similar quench rate behavior for OH in a methane-air flame. This result is not surprising for the latter stages of the reaction zone, where the temperature and major species concentrations are relatively constanL It is necessary to assume rotational and vibrational equilibrium so that a Boltzmann population distribution can be used to compute the total relative concentration as a function of temperature. Additionally, the lower level for the Swan system of C z is a triplet electronic state lying 610 cm - x above the singlet ground state; thus only the

203

LEF OF C 2 AND CN IN A FLAME

0 O

lo"

O f3

0

[3

0

¢a

era

u w Z

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o_

00000

z lO~:

•

1012 i 0

it

11

iii

Itll I I I I I I[II l l l i l i l l l 1 2 3 RELATIVE"BURNER POSITION (ram)

Fig. 7. Concentration profiles for C 2 (e) and CN (n) through the reaction zone of a CH4/N20/N 2 flame.

relative concentration in this state can be obtained unless electronic equilibrium is assumed as well. With these assumptions the fluorescence intensity data can be adjusted to represent relative concentration profiles. Before replotting the profiles, further assumptions and estimates were made to put the concentrations on an absolute scale. 1 The best estimates of the peak values of these concentrations are C2 ~ 2 × 10 i s cm - a and CN "" 3 X l014 cm - a . Details of the computation and necessary assumptions are in the appendix. Figure 7 represents the profiles of C2 and CN 1 In certain situations, absorption measurements can be used to normalize fluorescence intensities to concentration. The main reasons why absorption measurements were not attempted here are that (i) the experiment must be reconfigured for extra cavity probing of the flame in order to do normal absorption measurements, (ii) the estimated densities of the state specific absorbing species is so small that the possibility of detecting an absorption signal for any reasonable path length is remote, and (iii) even ff absorption signals could be measured, the overlap of the laser line with the molecular transition is not accurately known, so that errors in extracting the concentration from absorption measurements would be large, that is, similar to the errors associated with the calculation provided in the appendix.

where the fluorescence intensity has been converted to concentration. The relative shapes of the profiles in Fig. 7 are almost identical to those of Fig. 6. This is not surprising since the temperature has almost peaked before any appreciable radical concentrations are observed and the subsequent fall of temperature is slow. SUMMARY Laser-excited fluorescence of both C2 and CN have been obtained using an Ar + laser operating with the flame intracavity. To our knowledge this is the first time fluorescence of CN has been reported using Ar + laser excitation. This experimentalarrangement has proved to be an excellant diagnostic technique for several reasons. 1. The complete fluorescence spectrum can be observed in real time, allowing easy detection a n d i d e n t i f i c a t i o n o f t h e species p r e s e n t .

2. The fluorescence signals are significantly enchanced because of the increased laser flux obtained with intracavity pumping. 3. These fluorescence signals are substantially larger than the luminous background, allowing

JOHN A. VANDERHOFF ET AL.

204 fluorescence spectra to be recorded in short times (tens of seconds). 4. The experiment can be used for both the detection of trace species with fluorescence and the determination of temperature from Raman signals. 5. The use of the raised knife edge burner permits profiling from the initial reactants, through the reaction zone, to final products.

APPENDIX The two largest sources of uncertainty in deriving absolute concentrations from fluorescence data are the quench rate Q of the excited molecules and. the overlap of the laser line with the transition being pumped. Radical species in atmospheric pressure flames have Q, in general, of the order 1 × 109 s-X. 9 Using this value, we can estimate the concentration of these radicals. By making the assumption that the transitions and laser excitation lines are Doppler broadened, a a solution for the transmission of the laser can be obtained. The derivation of absorption is analogous to that given by Anderson et al. [16] except that a Doppler profile replaces the Voigt profile used for the transition, only a single line is considered, and the result holds only for absorptions < 10%. The result for transmission of the excitation line is

[ hvoL ~ e/eo = I Xexp

[" Aa -]112 L, (A +,o

I

(va - v o )

,

(1)

the transition line center frequency, L is the length of the sample in the direction of the laser beam, c is the speed of light, B 12 is the Einstein absorption coefficient for the pumping transition, Ng is the density in the ground level being pumped, v1 is the laser line center frequency, and A and t~ are related to the line shapes by A = 4 In 2/Ave 2,

2 The high quench rates obtained for C2 [5] and CN [4] from the analysis of saturated fluorescence experiments is because of the simple twoqevel model used for data reduction. See, for example, Refs. [ 13-15 ]. a In reality, the laser line probably contains several cavity mode frequencies within the Doppler width of the Ar+ transition.

(2)

where Av o and AvI are the transition and laser linewidths (FWHM), respectively. In general, atmospheric pressure flames have quench rates much larger than spontaneous emission rates from the excited state. Experimentally it has been shown that the transitions are not saturated. Thus stimulated and spontaneous emission can be ignored. Consequently, the fluorescence emission per unit time F from the probed volume of length L is given by

F=Po[1--(P[Po)] A , '~ hvo

,

(3)

Q

where Au', v" is the Einstein emission coefficient for the observed vibrational band. The integrated signal under the vibrational band, as seen by the detector, is then given by S = F~e/4n,

(4)

where ~2 is the solid angle subtended by the collection optics and e is the transmission efficiency of the detector system. Eqs. (1)-(4) yield a relation between fluorescence signal S and ground rotational state density Ng. The total density N T is found using the equation

NT = N.~,/g., where P and Po are the transmitted and incident power, respectively, h is Planck's constant, vo is

a = 4 In 2/Avl2,

exp

(--Ej/kT),

where tI, is the partition function for the molecule at the measured flame temperature and gj and E j are the degeneracy and energy of the ground state, respectively. The factor ~ e was experimentally determined for the detection system from Raman-Stokes vibrational Q-branch measurements using Na in room temperature air. The number of Stokes

205

LEF OF C2 AND CN IN A FLAME photons detected E s is given by [ 17]

Es -- E~ol(~,dv,)NL~e,

(5)

where E 1 is the number of laser photons, o I is the Raman scattering cross section at the laser frequency, and ~'s is the Stokes frequency. The calibration was performed using both the 4545-A and 5145-A laser lines (the same lines that were used for the fluorescence measurements) so that an absolute measurement of the laser flux was unnecessary. Raman-Stokes shifts for N z are well known [17], and the scattering cross sections [18] for the wavelengths used were scaled by the factor (~4ssoA/vl) 4. Thus the quantity 12eEl can be calculated. The Stokes-Raman signals do not appear at the same wavelengths as the fluorescence signals for which the calibration is required; hence an adjustment using the spectral response "graph for the OMA detector was used. These adjustments changed the efficiency results by less than 20%. The calculations to change the fluorescence intensity to absolute concentration were performed at the peak of the radical concentration profiles, where the temperature is 2500K. This temperature was used in the calculations of Doppler linewidths for the transitions and in the partition functions. The laser line was assumed to be Doppler broadened at 300K. Einstein coefficients for the transitions were determined from radiative lifetimes, Franck-Condon factors, and rotational line strengths. The lifetime of CN BZ~ + is known from the most recent measurements to be about 70 nsec [19]. There is still considerable doubt about the lifetime of darrg C z. The value of Tatarczyk et al. [20], 120 nsec, was u s e d . Most recent measurements are within about 25% of this value [20]. Laser line centers were obtained from the compilation of Harrison [21]. Franck-Condon factors were obtained from Ref. [22] for CN and Ref. [23] for Ca. The linestrength for CN was obtained from a calculation by Lucht et al. [24], while that for C z was assumed to be 1/2, which is nearly correct for a art-art R-branch transition of high N". For CN, the transition line centers were found by using the known transitions for the (1, 1)

band [25] and energy levels for v" = 3 calculated using an improved set of Dunham coefficients [26]. The estimates for the difference between the laser frequency and transition frequency, vI - Vo, were 0.41 cm - 1 for the R 1 transition and. 0.13 cm - 1 for the R z transition. Thus, if the estimated line positions are correct, only the R 2 transition is excited. Using this value of 0.13 cm - 1 , a best estimate of the peak concentration of CN is calculated to be 3 X 10 TM cm- 8 . A lower limit to the concentation can be calculated by assuming vI - ~o = 0, the highest possible pump rate, which yields 4 X 10 xa cm - a . For Ca, two sets of data are available for the transition line centers. According to both sets, the 5145-A line is between the Rz(10 ) and Ra(10 ) transitions. The data of Johnson [27], reinterpreted in terms of modern quantum theory by Budo [28], yield Iv1 - vo I = 0.43 and 0.48 cm - 1 for the Rz(10 ) and Ra(10 ) transitions, respectively. Both of these values result in low pump rates which lead to densities so high (a large fraction of the total flame density) that they must be discounted. The data of Leinen, as reported by Shea [29], yield Iv1 - vo I = 0.23 and 0.70 cm - x . The 0.23-cm - 1 value leads to a reasonable density of 2 X 10 xa cm - a and thus is chosen as a best estimate. The lower limit for the C a density is computed as 1 X 10 xo cm- a . There is considerable evidence in the literature [30] that chemical reactions of C 2 occur faster than singlet ~ triplet energy transfer. Also, chemical reactions for the two states occur at different rates. Thus the xC z and a c 2 may not be in equilibrium. The calculation of ~, and of the ground state density, is" therefore confined to the triplet ground state probed by the laser. However, the 1C z and aC z are so close in zero point energy that if they were in equilibrium, their densities would be very similar and the total C z density would only increase by a factor of about 2-3 over that in the triplet state. Because of the various assumptions and estimates used in selecting values for quench rates, line positions, and lifetimes, error limits on the absolute concentrations were not established; however, these concentrations are thought to be good to about a factor of 10 for CN and 20

206

JOHN A. VANDERHOFF ET AL.

for C2. The relative concentrations as a function of burner position do not depend on these quantities and thus are much more accurate. We thank Mr. M. DelCiMe f o r his assistance in the design and construction o f the burner and electronics.

REFERENCES 1. Vanderhoff, J. A., Beyer, R. A., and Kotlar, A. J., First Specialists Meeting (Int.} o f the Combustion Institute, Bordeaux, France, 1981, Vol. 2, p. 551. 2. Jessen, P. F., and Gaydon, A. G., 12th Symposium (Int.) on Combustion, The Combustion Institute, Pittsburgh, 1969, p. 481. 3. Gaydon, A. G., The Spectroscopy of F&mes, Chapman and Hall, London, 2nd Ed., 1974. 4. Bonczyk, P. A., and Shirley, J. A., Combust. Flame 34: 253-264 (1979). Eckbreth, A. C., in Laser Probes for Combustion Chemistry, Spatially Precise Laser Diagnostics (D. Crosley, Ed.) ACS Symposium Series 134, 1980, p. 271. Verdieck, J. F. and Bonczyk, P. A., 18th Symposium (Int.) on Combustion, The Combustion Institute, Pittsburgh, 1981, p. 1559. 5. Baranovski, A. P., and McDonald, J. R., Appl. Opt. 16:1897-1901 (1977); J. Chem. Phys. 66:3300

(19771. 6. Hendra, P. J., Veal C. J., Moss, R., and MacFariane, J. J., in Laser Raman Gas Diagnostics, Raman Scattering and Fluorescence Studies o f Flames (M. Lapp and C. M. Penney, Eds.), Plenum Press, New York and London, 1974, p. 153. 7. Jones, D. G., and Maekie, J. C., Combust. Flame 27: 143-146 (1976). 8. Beyer, R. A., and DeWilde, M. A.,Rev. Sc£ Insti. 53: 103 (1982). 9. Vanderhoff, J. A., Beyer, R. A., and Kotlar, A. J., Ballistic Research Laboratory Report, ARBRL-TR02388 (January 1982). 10. Svehla, R. A., and McBride, B. J, NASA TN D-7056 (1973). 11. Cottereau, J. J., and Stepowski, K., in Laser Probes for Combustion Chemistry, Laser Induced Fluorescence Spectroscopy Applied to the Hydroxyl Radical in Flames (D. Crosley, Ed.), ACS Symposium Series 134, 1980, p. 131.

12. Bechtel, J. H., and Teets, R. E., Appl. Opt. 18: 4138--4144 (1979). 13. Crosley, D. R.,Opt. Engineering 20:511-521 (1981). 14. Lucht, R. P., and Laurendeau, N. M.,Appl. Opt. 18: 856 (1979). 15. Kotlar, A. J., Gelb, A., and Crosley, D. R., in Laser Probes for Combustion Chemistry, A Multilevel Model o f Response to Laser-Fluorescence Excitation in the Hydroxal Radical (D. Crosley, Ed.), ACS, Symposittm Series 134, 1980, p. 137. 16. Anderson, W. R., Decker, L. J., and Kotlar, A. J., submitted for publication in Combust. Flame. 17. Goulard, R., in Laser Raman Gas Diagnostics, Laser Raman Scattering Applications (M. Lapp and C. M. Penney, Eds.), Plenum Press, New York and London, 1974, p. 3. 18. Eckbreth, A. C., Bonczyk, P. A., and Verdieck, J. F., Appl. Spectros. Rev. 13:52-5.3 (1977). 19. Poliakoff, E. D., Southworth, S. J., White, M. G., Thornton, G., Rosenberg, R. A., and Shirley, D. A., J. Chem. Phys. 73:1786 (1980), and references therein. 20. Tatarczyk, T., Fink, E. H., and Becker, K. H., Chem. Phys. Lett. 40:126 (1976). 21. Harrison, G. R., Ed.,Massachusetts Institute o f Technology Wavelength Tables, Massachusetts Institute of Technology Press, Cambridge, MA, 1969. 22. Nicholls, R. W., J. Res. Nat. Bur. Stand. 68A:75 (1964). 23. McCallum,J. C., as tabulated in Danylewich, L. L., and Nichols, R. W., Proc. Roy. Soc. Lond. A339: 197 (1974). 24. Lucht, R. P., Peterson, R. C., and Laurendeau, N. M., Purdue Univ. Report No. PURDU-CL-78-06 (October 1978). 25. Engleman, R., Jr., J. Mol. Spectros. 49:106-116 (1974). 26. Kotlar, A. J., Field, R. W., Steinfeld, J. I., and Coxon, J. A.,J. Mol. Spectros. 80:86-108 (1980). 27. Johnson, R. C., Phil. Trans. Roy. Soc. 226:157 (1927). 28. Budo, A., Z. Physik 98:437 (1936). 29. Shea, J. D.,Phys. Rev. 30:825 (1927). 30. (a) Donnelly, V. M., and Pasternack, L., Chem. Phys. 39:427 (1979); (b) Pasternack, L., and McDonald, J. R., Chem. Phys. 43:173 (1979); (e) Reisler, H., Mangix, M. S., and Wittig, C., J. Chem. Phys. 73: 2280 (1980), and references therein. Received 1 February 1982; revised 19 April 1982