Quantitative Intracavity Laser Spectroscopy Measurements with a Ti:sapphire Laser: Absorption Intensities for Water Vapor Lines in the 790–800 nm Region

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

192, 386 –393 (1998)

MS987705

Quantitative Intracavity Laser Spectroscopy Measurements with a Ti:sapphire Laser: Absorption Intensities for Water Vapor Lines in the 790 – 800 nm Region Balazs Kalmar and James J. O’Brien1 Department of Chemistry and Center for Molecular Electronics, University of Missouri-St. Louis, 8001 Natural Bridge Road, St. Louis, Missouri 63121-4499 Received March 25, 1998; in revised form July 29, 1998

The intracavity laser spectroscopy (ILS) technique has been shown to be a very sensitive method for observing absorption spectra. By considering quantitative results (line-strengths and pressure broadening coefficients) obtained using the ILS method with a dye laser, the technique has been shown to provide quantitative information that is in excellent agreement with the values afforded by use of more traditional methods for acquiring absorption spectra. A similar investigation has been conducted for an ILS system based on a Ti:sapphire laser. Presented here are quantitative results for water vapor transitions occurring around 795 nm. Line intensities are determined as a function of water vapor pressure and effective path length (i.e., generation time). The line-strengths are compared with values determined by R. A. Toth [J. Mol. Spectrosc. 166, 176 –183 (1994)] who used a multipass cell and the Fourier transform spectrometer at the Kitt Peak National Observatory. The good agreement between the results demonstrates that quantitatively accurate data can be obtained using the ILS technique with a Ti:sapphire laser. © 1998 Academic Press I. INTRODUCTION

Traditional methods for recording absorption spectra in the visible to near-IR region with multipass cells may not be sensitive enough when intrinsically weak transitions are to be investigated. Intracavity laser spectroscopy (1, 2) and cavity ring-down spectroscopy (pulsed as well as cw versions) (3, 4) are techniques that provide enhanced sensitivity for detecting absorption. To derive quantitative parameters for absorbing species using such methodologies, it is necessary to examine under what circumstances accurate data for absorbers can be obtained with a specific type of laser system. Comparison of results with those obtained using different techniques can indicate if systematic errors influence the derived data. Intracavity laser spectroscopy (ILS) is considered to be one of the most sensitive techniques for performing absorption measurements (5, 6). To employ the ILS method, the absorbing species is contained in a cell with Brewster-angle windows and the cell is located within the resonator cavity of a homogeneously broadened laser such as a dye laser. More recently ILS systems based on vibronic solid state (7) and fiber lasers (8) have been used. The ILS laser operates in a quasi-cw fashion with the time period of spectral evolution (i.e., the generation time) determining the path length. The absorption path length achieved in such cases can be orders of magnitude larger than can be obtained using multipass cell methods. While equivalent path lengths of 1000’s of kilometers are possible (5, 6, 9), maximum values of 100’s of kilometers have been attained in 1

To whom correspondence should be addressed.

practice using the more generally employed standing-wave laser configuration. When quantitative information (line-strengths and widths) about the absorbing species is required, path lengths an order of magnitude less are employed because under such conditions, the spectral width of the intracavity laser remains relatively broad and nonlinear effects that arise as generation times approach the sensitivity limit are avoided (10 –13). In the past few years, ILS studies have been conducted using Ti:sapphire lasers with most of the work being directed toward deriving spectroscopic information. Examples include studies by the Grenoble spectroscopy group of overtone transitions of CHD3 (14, 15), methane (16), CO2 (17), NO2 (18), N2O (19, 20), CHF3 (21), and by Troe and co-workers (22) who reported line assignments and anharmonicity parameters for HOCl overtones. Two of the cited studies were directed also at issues that pertain to obtaining intensity information (17, 19). Baev, Toschek, and co-workers (13) and Katchanov et al. (9, 23) investigated the spectral dynamics exhibited during intracavity absorption by Ti:sapphire lasers and considered the sensitivity attainable in such systems from experimental and theoretical perspectives. Revealed in these studies are several characteristics that may affect derived quantitative results. Generation times must be modified because of relaxation oscillations that occur due to the relatively long upper state lifetime of the laser media. During the cavity buildup and oscillation period, the absorption strength appears to increase in a linear fashion with generation time. There is, however, an offset value associated with the time taken to reach population

386 0022-2852/98 $25.00 Copyright © 1998 by Academic Press All rights of reproduction in any form reserved.

QUANTITATIVE ILS MEASUREMENTS WITH A Ti:SAPPHIRE LASER

387

FIG. 1. Schematic diagram for the intracavity laser spectroscopy instrumentation. The high reflector, fold mirrors, and the output coupler are denoted by M1, M2, M3, and M4, respectively. AOM 5 optic modulator. Resonator cavity length (L) 5 1.4 m, intracavity chamber length (l ) 5 0.6 m.

inversion and this value depends on the pump power and the cavity alignment. Birefringence of the laser crystal results in spectral modulation or channeling as generation times are increased and limits the time over which sensitivity increases linearly with increases in generation time. The channeling effect is very dependent on the exact orientation of the lasercrystal C axis with respect to the polarization direction of the pump beam. Although ILS is primarily directed at deriving spectroscopic information, other applications require the extraction of reliable quantitative data. These include deriving line-strength and broadening parameters for isolated absorption lines and obtaining reference spectra for use in planetary astronomy. The purpose of this paper is to demonstrate that ILS can be used with a Ti:sapphire laser to obtain quantitatively accurate results. We present line-strength information for a series of water vapor lines and compare these values with those of Toth (24). He performed measurements for water vapor lines in the 11 610 –12 881 cm21 region using a more traditionally utilized method. A multipass cell that enabled path lengths of 98 – 433 m was employed and spectra were recorded using the Fourier transform spectrometer at the McMath solar telescope of the Kitt Peak National Observatory. Previously, our group conducted studies that demonstrated the quantitative nature of results derived from ILS with a dye laser (25). II. EXPERIMENTAL DETAILS

The experimental setup is shown schematically in Fig. 1. It is similar to the dye-laser based ILS system [e.g., Refs. (11)

and (25)]. It includes a custom-built, standing-wave, Ti:sapphire laser similar in origin and configuration to that described in Ref. (23). The astigmatically compensated cavity consists of four mirrors M1–M4. The high reflector (M1) and output coupler (M4) are flat mirrors and each fold mirror (M2, M3) has a radius of curvature of 150 mm. The back surfaces of the flat mirrors are wedged at Brewster’s angle. The Ti:sapphire crystal is 15 mm long with optical faces cut at Brewster’s angle. To avoid thermal-induced instabilities, the crystal is cooled by circulating water through the crystal holder. For the absorption cell employed, the occupation ratio is 0.48. The Ti:sapphire laser is pumped by all visible lines of an argon-ion laser (Coherent Innova 200-10/2UV). The pump parameter (h) employed is approximately 1.4. Broadband tuning is accomplished by rotation of an intracavity, uncoated pellicle. The temporal operation of the laser is controlled by two acousto-optic modulators, AOM1 and AOM2. Modulation of AOM1 (IntraAction AOM-703A) causes the pump power to be alternatively above and below the threshold value required for the Ti:sapphire laser. After the laser has operated for a well-defined period of time, referred to as the generation time (t g ), the second modulator (AOM2; IntraAction AFM-603) diverts part of the output beam into a high-resolution spectrograph (McPherson customized model 2062) for a time period (;0.1 ms) much shorter than t g . Dispersed light exiting the monochromator is detected by a 1024 channel diode-array detector whose operation is controlled by a multichannel analyzer (EG&G Model 1461, 1463) interfaced to a PC. Acquisition time for each approximately 5-cm21-wide spectral profile

Copyright © 1998 by Academic Press

388

KALMAR AND O’BRIEN

is about 15 s (for 0.3-s scans and 50 accumulations). Spectral data are stored on the PC for further analysis. Detector dark current data are subtracted from each acquired spectrum and to account for background absorption and the fixed pattern noise of the detector, each water spectrum is divided by one acquired in the absence of the sample at nearly the same time using the same laser settings and without changing the monochromator position. The amount of diffused light in the monochromator also is taken into account. Measurements on saturated absorption lines indicate it to be about 2%. The intracavity compartment is separated into three parts by two half-inch thick, Brewster-angle oriented windows that enclose the chamber containing the absorbing species. The sections outside this chamber are evacuated during the entire period of data collection to avoid atmospheric contributions (particularly due to water vapor) which can be significant in the 790 – 800 nm spectral region. Rotary motion, vacuum feed throughs enable the mirrors, the lens, and the position of the Ti:sapphire crystal to be adjusted. Pressures are measured using a 100-Torr MKS Baratron capacitance manometer with a PDR-C-2C-BCD power supply and indicator unit. The quality of the observed spectra is highly dependent upon the place where the pump beam passes through the Ti:sapphire crystal. Because of the inhomogenity of the crystal, extra caution has to be taken to find a path through the crystal that results in a sufficiently “clean” spectrum in that spectral modulation effects (i.e., long-range fringes) attributed to the birefringence of the Ti:sapphire crystal (13, 23) are minimized. The background correction procedure also compensates for the modulation which is observed to increase significantly at higher generation times.

convoluted with the instrument function while the second entails deconvolving the observed spectrum for the instrument function and summing the absorbance over the absorption line. (a) Fitting the Absorption Lines The spectrum observed is a convolution of the ILS spectrum and the apparatus function ( f ins) and can be expressed as I obs 5 I 0exp@2a ~ n ! L eff# # f ins~ n !, where the absorption coefficient (a(n)) is given by

a ~ n ! 5 k~ n ! f ~ n ! N.

ln

F G

I 0~ n ! 5 k~ n ! f ~ n ! N~l/L!ct g, I obs~ n !

[1]

where I 0 ( n ) is the intensity of the laser in the absence of the absorber, I obs(n) is the intensity of the laser in the presence of the absorber, k( n ) is the intensity of the absorption line, f(n) is the normalized absorption lineshape profile, N is the number density of the intracavity absorber, l/L is the occupation ratio or the fraction of the resonator cavity of length L occupied by the absorber, and c is the speed of light. Equation [1] is the Beer–Lambert relationship for ILS with the effective absorption path length (L eff) given by {(l/L) z c z t g }. Two procedures that were employed to determine the intensities of absorption lines were described previously (25, 26). The first entails fitting the absorption line profile to a Voigt lineshape

[3]

The absorption lineshape f(n) is assumed to be a Voigt profile which is a convolution of a Gaussian function due to the Doppler broadening (HWHM 5 gD) and a Lorentzian function due to collision broadening (HWHM 5 gL) and it takes the form

f~n! 5

F G

1 ln 2 gD p

y K~ x, y! 5 p

E

`

2`

1/ 2

K~ x, y!

with [4]

exp~2t 2! dt, y 2 1 ~ x 2 t! 2

where x5

III. METHOD OF ANALYSIS

When the spectral output of the laser is examined at a specific generation time t g , the time resolved, averaged absorbance at a particular frequency n is given by the equation

[2]

F GÎ n 2 ni gD

ln 2,

y5

F GÎ gL gD

ln 2.

[5]

A computer program described previously (25) and similar to one provided by Chenevier and Stoeckel (10) is used to fit the water vapor lines. The program convolutes the instrument function ( f ins) with a Voigt profile and compares the result with the observed line. It provides gL (the collision broadened half-width) and the amplitude {k( n ) NL eff} of the line, from which the intensity can be obtained. The instrument function is acquired in the same spectral region as where the absorption occurs. It is obtained by recording the ILS spectrum of the Ti:sapphire laser operating cw with one thick and two thin intracavity etalons. This results in single frequency operation in the spectral region being viewed by the multichannel detector. A good quality instrument function is essential in achieving good fits to the absorption lines. (b) Deconvolution and Integration To employ this method, the spectrum is first deconvolved for the instrument function using a Fast Fourier Transform (FFT) technique. The details of the procedure and the computer programs used are provided in Press et al. (27). The resulting

Copyright © 1998 by Academic Press

QUANTITATIVE ILS MEASUREMENTS WITH A Ti:SAPPHIRE LASER

FIG. 2. Intracavity laser spectrum for water vapor in the region of 789.5 nm (pressure 3.135 Torr, generation time 51 ms). The solid line shows the initial, background corrected spectrum and the dotted line indicates the deconvolved spectrum obtained using a fast Fourier transform deconvolution technique (26). An instrument function, observed in this spectral region and used to deconvolve the initial spectrum, is shown in the inset.

spectrum is smoothed slightly using a FFT procedure [also presented in Press et al. (27)] to remove oscillations occurring from the FFT deconvolution process. The abscissa of the spectrum is converted to wavenumber units using the water vapor lines and the positions reported by Toth (24) as reference and a third-order polynomial equation describing the dispersion (i.e., cm21/channel) for the detector system. The dispersion varies by 1.8% in an almost linear fashion across the array. For example, for the water ILS spectral profile recorded in the vicinity of 789.5 nm (see above), the dispersion changes from 0.005549 cm21/channel for the first line to 0.005619 cm21/ channel for the fourth line. Intracavity spectra of a 21 inch thick etalon are used to obtain the equation describing the dispersion. The dispersion changes with monochromator position which necessitates obtaining instrument functions in the same spectral region as where the absorption lines occur. In the case of the five water absorption lines occurring in the vicinity of 801.4 nm that also are the subject of this study, the dispersion changes from 0.005083 cm21/channel for the first line to 0.005132 cm21/channel for the fifth line. The amplitude of the absorption line is determined by summing the absorbance over the line in a direct application of the Beer–Lambert relationship ([i.e., Eq. [1]) for ILS. This method is observed to be less sensitive to the shape of the instrument function than the fitting procedure described in section (a). IV. RESULTS AND DISCUSSION

Several relatively isolated water vapor lines in the 789.5and 801.4-nm spectral regions were studied. Line intensities

389

can be obtained by acquiring data as a function of water vapor pressure at a specific generation time (i.e., path length) or as a function of path length for a particular pressure. The effective path length varied between 2.16 and 10.32 km as t g was adjusted for the latter studies. Figure 2 shows the background corrected ILS spectrum taken in the vicinity of 789.5 nm with the deconvolved spectrum overlaid on it and shown as dots. The inset in Fig. 2 shows the instrument function used in deconvolving the corrected spectrum. Figure 3 shows the background corrected and deconvolved ILS spectrum of water taken in the vicinity of 801.4 nm. For both spectral regions, several sets of the same type of data (i.e., as a function of path length and as a function of pressure) were acquired and both procedures described above were used in the analysis of the data. Figure 4 illustrates a typical fit obtained using the fitting procedure described above. The water vapor lines examined are relatively strong ones for ILS and consequently only a range of low pressures were used even for the relatively short effective path lengths employed in this study. For the conditions employed, the Doppler broadening component is the dominant contribution to the absorption line profiles and, consequently, the data are inappropriate for providing good values for the pressure broadening coefficients (25). Intensities of the water vapor lines can be extracted from data plotted in the manner as indicated in Fig. 5, where amplitude {k( n ) NL eff} values derived from fitting the lines to Voigt profiles [i.e., determined using procedure (a)] are plotted versus generation time. The plots shown in Fig. 5 are for the four water vapor lines occurring in the vicinity of 789.5 nm and

FIG. 3. Intracavity laser spectrum for water vapor in the region of 801.4 nm (pressure 3.04 Torr, generation time 41 ms). The solid line shows the initial, background corrected spectrum and the dotted line indicates the deconvolved spectrum. The inset shows the instrument function used to deconvolve the initial spectrum.

Copyright © 1998 by Academic Press

390

KALMAR AND O’BRIEN

FIG. 6. The amplitudes {k n NL eff} as a function of generation time for five water vapor lines occurring in vicinity of 801.4 nm. Water vapor pressure was 3.02 Torr. The deconvolution and integration procedure was used to determine the amplitudes of the lines.

FIG. 4. Fit for a water absorption line centered at 12 665.1595 cm21 to a Voigt profile. Dots indicate the calculated line. The residuals are plotted in expanded form below the fit. For the spectrum, tg was 51 ms and the pressure was 3.135 Torr.

required a series of measurements made at different generation times but at the same sample pressure. The slopes of the linear fits to the data yield the k( n ) values for the various water

FIG. 5. The amplitudes {k n NL eff} as a function of generation time for four water vapor lines occurring in the 789.5-nm spectral region. Water vapor pressure for the series of measurements was 1.53 Torr. The fitting procedure was used to determine the amplitudes of the lines.

absorption lines. Figure 6 shows amplitude values as a function of generation time for water vapor lines occurring in the region around 801.4 nm but with the data determined by deconvolving and integrating over the absorption lines [i.e., determined using procedure (b)]. The upper limit of the generation times used in this study was 71 ms. The effect of the birefringence of the laser crystal which results in spectral modulation becomes more pronounced beyond that time and even resulted in some modulation of the spectra acquired using shorter generation times. Usually, the background correction procedure worked very well in minimizing the broad range modulation component. Precisely where the Ti:sapphire crystal is pumped determines the extent of the modulation. Our preference would have been to employ a larger range of generation times and a broader range of pressures in this study. It is apparent from the plots shown in Figs. 5 and 6, the lines of best-fit do not intersect the x axis at zero but at approximately 7 ms (i.e., it appears as if the t g values have a 7-ms offset). This phenomenon occurs due to the upper state lifetime of the Ti:sapphire crystal and the prominent relaxation oscillations that are observed every pumping cycle. P. F. Moulton, who first demonstrated laser action from Ti:sapphire, observed an upper state lifetime for a Ti:sapphire laser crystal of 3.15 6 0.05 ms at room temperature (28). This issue has been addressed by other research groups who have utilized Ti:sapphire lasers in ILS studies. Kachanov and co-workers (23) modeled the dynamics for Ti:sapphire laser action and showed from computer simulations that the offset nearly corresponds to the time it takes for the population inversion to reach the threshold

Copyright © 1998 by Academic Press

QUANTITATIVE ILS MEASUREMENTS WITH A Ti:SAPPHIRE LASER

FIG. 7. The amplitudes {k n NL eff} as a function of pressure for four water vapor lines occurring in the 789.5-nm spectral region. For the series of measurements, the generation time was set at 51 ms. The fitting procedure was used to determine the amplitudes of the lines.

value. The value observed depends on the threshold value and the pump power employed. While the t g offset does not affect results derived from data acquired as a function of path length (i.e., generation time), it does need to be accounted for when data are acquired as a function of pressure. For a given pump power and cavity configuration, subtracting the offset value from the generation time set on the delay generator yields the effective generation time. This value is used in the analysis of data obtained as a function of absorber pressure and acquired at the same generation time. The average offset value determined for all the lines in a particular spectral region using a given instrument function and the fitting procedure were used in the calculation. Line intensities are extracted from amplitude {k( n ) NL eff} versus pressure plots obtained for a constant generation time. Results for several different absorption lines are shown in Fig. 7. In this case, the results follow a Beer–Lambert-like relationship— linear behavior is observed and the lines of best-fit pass through the origin. The results shown in Fig. 7 were obtained by fitting the four water absorption lines occurring in the vicinity of 789.5 nm using procedure (a). Results observed for the five water vapor lines occurring in the vicinity of 801.4 nm are shown in Fig. 8, where the deconvolution and integration procedure (b) were employed to determine the amplitudes. Several different instrument functions for the two spectral regions were recorded. Very slight differences are apparent in the distribution of intensity across the profile, and this affects the fitting and deconvolution processes used in the analyses of the data. Intensities were obtained for the nine lines investigated using both analysis procedures and a series of instrument functions. We find that some instrument functions taken at the

391

same spectral location are better than others in the sense that better fits (lower x2 values) to the individual lines are obtained when procedure (a) is employed and in that a smaller amount of smoothing is necessary when the deconvolution and integration procedure (b) is the method of analysis. The results obtained using the best instrument function are presented in Table 1, where the reported values for each procedure are derived from the same series of measurements. The results obtained using different instrument functions give an indication of the overall uncertainty in the results. In each measurement series, pressures or generation times were increased to the point where saturation effects were becoming apparent for some of the lines investigated. Only the linear portions of the fits were considered in compiling the results presented in Table 1 although all the data could be fit using a higher order polynomial. A weighted least-squares fitting procedure was used (25). The uncertainty in the result for each method of analysis is given by the uncertainty in the slope for the linear fit. Modulation effects were more pronounced for the lines occurring in the vicinity of 801.4 nm than for the lines occurring in the vicinity of 789.5 nm and consequently the uncertainty in the results is higher for these lines. Errors due to the fit averaged to 0.5% for the lines in the 789.5-nm region and to 1% for the lines in the 801.4-nm region for results derived from the fitting procedure. Averaging results obtained from different runs yields an average discrepancy of 1.4% for lines occurring in the vicinity of 789.5 nm and nearly 6% for lines occurring in the vicinity of 801.4 nm. There is added uncertainty in results derived from measurements taken as a function of pressure because there is some uncertainty in the generation time to be

FIG. 8. The amplitudes {k n NL eff} as a function of pressure for four water vapor lines occurring in the vicinity of 801.4 nm. For the series of measurements, the generation time was set at 31 ms. The deconvolution and integration procedure was used to determine the amplitudes of the lines.

Copyright © 1998 by Academic Press

392

KALMAR AND O’BRIEN

TABLE 1 Comparison of Intensities (cm22/atm at 300 K) of Wate Vapor Lines Measured in This ILS Study with Those of R. A. Toth (24) Who Used a Multipass Cell and Fourier Transform Spectroscopy

Note. Our results were obtained from measurements made as a function of generation time (i.e., effective path length) and as a function of pressure. Two procedures, a fit to the absorption lines with the instrument function taken into account [procedure (a)] and a deconvolution and integration technique [i.e., procedure (b)]. Results for both measurements modes and procedures are presented in the Table. See the text for error estimates which range from 2 to 11% for our results and 2 to 5% for Toth’s results.

used in the calculation. From the uncertainty in the offset values and the generation times employed in the measurement taken as a function of pressure, this contributes an additional 2% uncertainty to the values obtained for lines occurring in the vicinity of 789.5 nm and 5% for lines occurring in the vicinity of 801.4 nm. When results obtained from the use of two different “good” instrument functions are compared, the average discrepancy in the values is 4%. Table 1 provides a summary of line intensities obtained from measurements made as a function of generation time and as a function of pressure. Results obtained by use of both procedures are presented. The intensities are compared with the results of Toth (24). Toth gave uncertainty estimates ranging from 2 to 5% for these lines. He pointed out the values he obtained are considerably different for many of the lines from the values given in the 1986 version of the HITRAN database (29). Our uncertainty estimates range from 2% for the last four lines to 6% for the first five lines for data derived from amplitude versus generation time studies. The estimated uncertainties derived from amplitude versus pressure measurements are 2 and 5% higher, respectively, because of the un-

certainty associated with the generation time offset value. In nearly all cases, our results are in excellent agreement with those obtained by Toth. All the results given in Table 1 are in experimental agreement. In most cases, the results derived from the two different procedures (a) and (b) are in very good agreement. This provides justification for the use of the much faster deconvolution and integration method for determining line intensities. V. CONCLUSION

Quantitative absorption parameters for a series of water vapor transitions observed using the intracavity laser spectroscopic (ILS) method with a Ti:sapphire laser are presented. The obtained results are in good accord with the ones obtained by another well-established technique. Two different approaches are used to extract the intensity information and good agreement between the results from the two approaches is observed. In addition, two different analysis procedures for determining the amplitudes of the lines were employed, and the resulting intensity values are in good agreement.

Copyright © 1998 by Academic Press

QUANTITATIVE ILS MEASUREMENTS WITH A Ti:SAPPHIRE LASER

Spectral modulation effects, arising from the birefringence of the Ti:sapphire crystal, impose an upper limit on the generation times (i.e., effective path length) that could be used in this study. Extra care had to be taken in performing these measurements to find a path through the Ti:sapphire laser crystal employed that minimized the spectral modulation. Relaxation oscillations observed with the Ti:sapphire laser alter the applicable generation time in that actual time is shorter by an offset value. It is observed, however, that although the extent of absorption can be altered by changing the generation time or the pressure of the absorbing sample, the offset delay stays the same for a given laser threshold value and pump power. Consequently, reliable quantitative data can be extracted from the spectra. Both of these effects add to the uncertainty in the quantitative results and make the acquisition of quantitative data using the ILS technique with a Ti:sapphire more of a challenge when compared with measurements made with a dye laser (25). ACKNOWLEDGMENT This work was supported by Grant NAGW-2479 from the Planetary Atmospheres Program of NASA.

REFERENCES 1. P. E. Toschek and V. M. Baev, in “Laser Spectroscopy and New Ideas” (W. M. Yen and M. D. Levenson, Eds.), Vol. 54 of Springer Series in Optical Sciences, pp. 89 –111, Springer-Verlag, Berlin/New York, 1987. 2. A. Campargue, F. Stoeckel, and M. Chenevier, Spectrochim. Acta. Rev. 13, 69 – 88 (1990). 3. A. O’Keefe and D. A. G. Deacon, Rev. Sci. Instrum. 59, 2544 –2551 (1988). 4. D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, Chem. Phys. Lett. 264, 316 –322 (1997). 5. A. A. Kachanov, V. R. Mironenko, and I. K. Pashkovich, Sov. J. Quantum Electron. 19, 95–98 (1989). 6. V. M. Baev and P. E. Toschek, in “Optical Methods in Atmospheric Chemistry” (H. Schiff and U. Platt, Eds.) Proc. SPIE 1715, 381–392 (1993).

393

7. D. A. Gilmore, P. Vujkovic Cvijin, and G. H. Atkinson, Opt. Commun. 77, 385–389 (1990). 8. R. Bohm, A. Stephani, V. M. Baev, and P. E. Toschek, Opt. Lett. 18, 1955–1957 (1993). 9. A. Kachanov, A. Charvat, and F. Stoeckel, J. Opt. Soc. Am. B 12, 970 –979 (1995). 10. M. A. Melieres, M. Chenevier, and F. Stoeckel, J. Quant. Spectrosc. Radiat. Transfer 33, 337–345 (1985). 11. K. Singh and J. J. O’Brien, Chem. Phys. Lett. 229, 29 –34 (1994). 12. B. B. Radak, J. I. Lunine, D. M. Hunten, and G. H. Atkinson, J. Quant. Spectrosc. Radiat. Transfer 53, 519 –526 (1995). 13. J. Sierks, J. Eschner, V. M. Baev, and P. E. Toschek, Opt. Commun. 102, 265–270 (1993). 14. A. Charvat, A. A. Kachanov, A. Campargue, D. Permogorov, and F. Stoeckel, Chem. Phys. Lett. 214, 495–501 (1993). 15. D. Permogorov, A. Campargue, M. Chenevier, and H. B. Kraiem, J. Mol. Spectrosc. 170, 10 –26 (1995). 16. A. Campargue, D. Permogorov, and R. Jost, J. Chem. Phys. 102, 5910 – 5916 (1995). 17. A. Campargue, A. Charvat, and D. Permogorov, Chem. Phys. Lett. 223, 567–572 (1994). 18. R. Georges, A. Delon, F. Bylicki, R. Jost, A. Campargue, A. Charvat, M. Chenevier, and F. Stoeckel, Chem. Phys. 190, 207–229 (1995). 19. A. Campargue and D. Permogorov, Chem. Phys. Lett. 241, 339 –344 (1995). 20. A. Campargue, D. Permogorov, M. Bach, M. A. Temsamani, J. V. Auwera, M. Herman, and M. Fujii, J. Chem. Phys. 103, 5931–5938 (1995). 21. D. Romanini and A. Campargue, Chem. Phys. Lett. 254, 52–58 (1996). 22. B. Abel, H. H. Hamann, A. A. Kachanov, and J. Troe, J. Chem. Phys. 104, 3189 –3197 (1996). 23. A. Kachanov, A. Charvat, and F. Stoeckel, J. Opt. Soc. Am. B 11, 2412–2421 (1994). 24. R. A. Toth, J. Mol. Spectrosc. 166, 176 –183 (1994). 25. K. Singh and J. J. O’Brien, J. Mol. Spectrosc. 167, 99 –108 (1994). 26. K. Singh and J. J. O’Brien, J. Quant. Spectrosc. Radiat. Transfer 54, 607– 619 (1995). 27. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, “Numerical Recipes: The Art of Scientific Computing,” Cambridge University Press, Cambridge, 1988. 28. P. F. Moulton, J. Opt. Soc. Am. B 3, 125–133 (1986). 29. L. S. Rothman, R. R. Gamache, A. Goldman, L. R. Brown, R. A. Toth, H. Pickett, R. Poynter, J.-M. Flaud, C. Camy-Peyret, A. Barbe, N. Husson, C. P. Rinsland, and M. A. H. Smith, Appl. Opt. 26, 4058 – 4097 (1987).

Copyright © 1998 by Academic Press