Microphone triggering circuit for elimination ofmechanically induced frequency-jitter in diodelaser spectrometers: implications forquantitative analysis

Robert L. Sams and Alan Fried

An electronic timing circuit using a microphone triggering device has been developed for elimination ofmechanically induced frequency-jitter in diode laser spectrometers employing closed-cycle refrigerators.Mechanical compressor piston shocks are detected by the microphone and actuate an electronic circuit whichultimately interrupts data acquisition until the mechanical vibrations are completely quenched. In this way,laser sweeps contaminated by compressor frequency-jitter are not co-averaged. Employing this circuit,measured linewidths were in better agreement with that calculated. The importance of eliminating thismechanically induced frequency-jitter when carrying out quantitative diode laser measurements is furtherdiscussed.

I Introduction

In recent years, there has been a dramatic increase inthe number of applications of tunable diode lasers(TDLs). Many of these applications make use of thenarrow spectral linewidth inherent in TDLs for eitherdetermining concentrations of, or spectroscopic pa-rameters for, many important trace atmospheric gases.In most cases, such studies have employed TDLsmounted in a closed-cycle refrigerator system. How-ever, it is well known1 -4 that mechanical shocks fromthe refrigerator compressor induce frequency-jitter onthe resulting high resolution spectrum. Attempts tominimize such mechanical disturbances employingvarious vibration isolation systems2 5-7 have not alwaysbeen totally successful. Melandrone et al. 3 graphical-ly show that this jitter primarily occurs at the maxi-mum and minimum excursion points of the small com-pressor piston which is typically mounted directly onthe diode laser cold head. Such mechanically inducedfrequency-jitter, which also occurs to a much smallerextent in the middle of the compressor cycle, often

Robert Sams is with U.S. National Bureau of Standards, Centerfor Analytical Chemistry, Gaithersburg, Maryland 20899, and A.Fried is with National Center for Atmospheric Research, Atmo-spheric Chemistry Division, Boulder, Colorado 80307.

Received 23 March 1987.

severely distorts TDL absorption spectra. As a result,experimental absorption linewidths can be dramati-cally larger than those calculated.

Despite the fact that this effect has been well docu-mented, the associated systematic error that can resultin quantitative TDL measurements carried out in thedirect absorption mode, to our knowledge, has notbeen addressed in the literature. In direct absorptionTDL measurements, frequently all the additonal ex-perimental linewidth is solely attributed to the inher-ent excess linewidth of the laser. This, as is wellknown, results in a decreased absorbance at line cen-ter. Correction factors in this case, which are subse-quently derived to account for the observed increasedlinewidth assuming a given laser frequency profile, areapplied to the line center absorption data.89 Thisprocedure yields accurate results whenever the inher-ent excess linewidth is the predominant cause of theinstrumental broadening, and the functional form ofthe laser frequency profile is accurately known. How-ever, as discussed here, when mechanically inducedfrequency-jitter is prevalent, significant systematic er-rors can result using this procedure. A solution ispresented here which eliminates this potential system-atic error by not taking data when frequency-jitteroccurs. Alternative approaches to address this prob-lem have recently been reported by Valentin et al.10

and Reich et al.11 In both techniques, the TDL emis-sion frequency is servo-locked to an external interfer-ometer employing a feedback loop. As reported, theresponse time of these systems is such that mechani-

3552 APPLIED OPTICS / Vol. 26, No. 17 / 1 September 1987

II. Experimental

VDFMP- .amp.e i.e

OAP: Off Axis ParabolaBS: Beam Splitter

VDFMP: Vertically Displaced Flat Mirror PairsP: Baratron Pressure Sensor

Fig. 1. Schematic of experimental apparatus. In each verticallydisplaced flat mirror pair (one at the entrance and one at the exit ofthe monochromator) one mirror is above the plane of the figure. Asdiscussed in the text, a removable flat mirror on a kinematic mountwas used instead of the beam splitter to direct the laser through the

interferometer.

cally induced frequency-jitter is suppressed. Al-though both approaches have advantages, it is notclear whether instrumental broadening due to this jit-ter is totally eliminated. As we have determined in thepresent study, such mechanically induced frequency-jitter can be as high as 40 kHz, necessitating a feedbackloop bandwidth in excess of 200 kHz to eliminate com-pletely this effect. Slower response times will averagethe frequency-jitter, but the instrumental broadeningnevertheless will still be present. Regardless of theapproach adopted, we show in this paper the signifi-cance of eliminating, or the very least ascertaining theextent of, mechanically induced frequency-jitter forhigh accuracy in quantitative TDL measurements.

We have developed an electronic timing circuit usinga microphone triggering device to synchronize dataacquisition with the motion of the compressor piston.In this way, data are only acquired during jitter-freetime durations when mechanical shocks are not detect-ed. Melandrone et al.3 first described this approachemploying a He-Ne Laser to track the motion of thecompressor piston through a transparent viewing win-dow in an older model cold head commercially avail-able from Spectra-Physics, Laser Analytics Division.In the newer model Spectra-Physics cold heads,5 how-ever, this transparent window is no longer present, andan alternate triggering device employing a microphonewas, therefore, adopted. Not only can this device beused with any cold head, but also it is more compactthat the optical trigger. Furthermore, this unit actu-ally detects the mechanical shocks and not merely theposition of the compressor piston. As a result, datacontaminated by the smaller shocks in the middle ofthe piston stroke, and possibly in other positions aswell, can also readily be discarded.

A. Apparatus

A schematic diagram of the experimental apparatusis shown in Fig. 1. For a more comprehensive discus-sion of the experimental details, data acquisition, andreduction approaches, the reader is referred to Ref. 12-14. As shown in Fig. 1, the output of a TDL, mountedin a closed-cycle cold head assembly 5, was collimatedwith a series of off-axis parabolic mirrors and directedthrough a 70-cm opaque-limit cell (used to establishthe 100% absorption level) and through two differentarms of a double-beam setup. The main beam passedthrough a pellicle beam splitter and through a 50-cmPyrex sample absorption cell. Approximately 10% ofthe beam (the reference beam) was reflected off thebeam splitter and through a 50-cm confocal interfer-ometer from Burleigh Instruments15 for relative wa-venumber calibration. The sample and referencebeams were both imaged on the entrance slit of amonochromator employing a pair of vertically dis-placed flat mirrors. After passage through the mono-chromator, which was employed for gross mode rejec-tion, each beam was focused onto the surface ofseparate mercury-cadmium-telluride photoconduc-tive detectors.

Since the transmission through the interferometerwas typically <1%, the output intensity was often toolow to be of use. In most measurements, therefore, thebeam splitter was replaced with a mirror mounted on akinematic mount for precise repositioning. Interfer-ometer scans were, therefore, recorded immediatelybefore and after absorption scans by simply placingthe reference arm mirror in the beam path withouthaving to perform major realignment. This proceduredid not degrade the accuracy of our measurements.As we show in Ref. 14, the TDL scan rate stability fromrun to run was better than 9 X 10-5 cm- 1 over a 22-mintime interval, a time period larger than that betweenabsorption and interferometer scans. The small freespectral range of the confocal interferometer (0.00501cm-1 ) yields a high-resolution wavenumber grid neces-sary for accurate interpolation and fit of the diode laseroutput frequency as a function of tuning current. Thefree spectral range of this interferometer was deter-mined employing accurate OCS line positions as wellas from measurements of the interferometer mirrorseparation. As further discussed in Ref. 12, the twodeterminations were in agreement to within 0.1%.

Absorption and interferometer scans were acquiredemploying the technique of sweep integration firstdescribed by Jennings.16 The diode laser current wassawtooth modulated at 200 Hz, and data from eachsweep were digitized and stored in 1024 channels of aPrinceton Applied Research (PAR) model 4203 signalaverager. Data in each channel were then coaddedwith subsequent data taken by repetitively scanningover the same spectral region. Typically 30,000sweeps were coadded in -150 s, and the resulting aver-aged spectrum was then directed into our laboratory

1 September 1987 / Vol. 26, No. 17 / APPLIED OPTICS 3553

c^^1^ r

CompressorMechanical

Vibrations

PinComponent Power GNDLM 339 3 1274 LS168 16 874 LS221 16 874 LS10 14 7

Fig. 2. Schematic of a microphone trigger circuit for synchronization of data acquisition with the motion of the compressor displacer.

8086-based microcomputer for storage and subsequentdata analysis.

In the present study, we examined the effects ofmechanically induced frequency-jitter caused by aclosed-cycle diode laser compressor on quantitativeabsorption measurements of NO2. Measurementswere carried out in the direct absorption mode usingthe 94,6+ absorption line at 1605.500 cm-'. At thereduced sampling pressure of this study, 0.6 Torr, thisline was well resolved from other NO2 lines, thus sim-plifying the line-fitting analysis. An NO2 calibrationsystem, employing three 10-cm long Teflon perme-ation tubes, provided an accurately known source ofNO2 for this study. The output of this system, an 832parts-per-million (ppm) mixture of NO2 in air, wascontinuously drawn through the sample cell at a re-duced pressure of 0.608 Torr. This pressure, as mea-sured by a calibrated MKS Baratron capacitance ma-nometer mounted in the center of the cell, wascontrolled by a pair of valves at the cell inlet and outlet.After 30 min of flowing to completely equilibrate thecell walls, absorption data were acquired. The NO2concentration from this calibration source was deter-mined in the usual manner from measurements of theNO2 permeation rate and the flow rate of the airstreampassing over the permeation chamber. Each perme-ation tube was weighed periodically to obtain the com-bined NO2 permeation rate. The airflow was con-trolled by means of an accurately calibrated mass flow

controller. As discussed in Ref. 12, the calibrationsystem output of 832 ppm was determined with anoverall 2 uncertainty of 1.4%. Additional experi-ments were carried out using an 854 15 ppm com-pressed gas NO2 mixture as the calibration source.This concentration was determined by a calibratedchemiluminescence detector. 1 2

These accurately known NO2 calibration sourcesprovided us with a means for quantitatively evaluatingthe effects of mechanically induced frequency-jitter.This was accomplished by comparing the known NO2concentrations flowing through the sample cell withthat determined by direct absorption using both thepeak absorbance at line center and the integrated-fitabsorbance over the entire line profile, as will be dis-cussed.

B. Microphone Trigger Circuit

The trigger circuit is schematically shown in Fig. 2.Mechanical shocks throughout each compressor cyclewere detected by a miniature electret microphone,Knowles Electronics Corp. model 1759.17 This devicewas mounted directly on the TDL cold-head and waselectrically connected to a high-pass filter. The mi-crophone and filter pair were capable of detecting me-chanical shocks in the 10-Hz-50-kHz range. The re-sulting output signals were amplified, directedthrough a pair of operational amplifiers (LM339), and

3554 APPLIED OPTICS / Vol. 26, No. 17 / 1 September 1987

ultimately triggered a one-shot circuit with a variabledelay (74LS221). This caused the output state of theone-shot to switch from its normal quiescent high stateto the low state for 40 ms, a duration corresponding tothe time required for the mechanical vibrations to becompletely quenched. This low signal was then di-rected to pin 2 of the output NAND gate (74LS10)shown in Fig.2. With the start of each new 5-ms sweepramp, the TDL Sync. output pulse applied a high statesignal to pin 1 of the output NAND gate. However, allthree inputs of this gate must simultaneously be highfor a valid TTL trigger signal to be sent to the signalaverager. During this 40-ms time period, therefore,the NAND gate output remained in a high state regard-less of the voltage applied to pins 1 and 13.

Following the 40-ms mechanical vibrationalquenching period, the one-shot output again appliedits former high state to pin 2 of the output NAND gate.In addition, this high state also actuated both up-down counters (LS168). With each new sweep ramp, avalid clock pulse was received and the counters decre-mented from a preset value down to zero. As long aszero was not attained, signifying that the compressorpiston had not reached the end of its stroke, the outputof the (MSD) counter maintained pin 13 of the outputNAND gate in a high state. With each new sweep ramp,pins 1 and 2 were also high, thus generating a validnegative-going TTL output trigger pulse which wasdirected into the signal averager.

As long as the counters did not decrement to zeroand no additional mechanical shocks were detected,valid trigger signals continued to trigger the signalaverager. Data were thus acquired with each newsweep ramp. However, on reaching zero, indicatingthat the compressor piston was close to one of itsmaximum excursion points, the (MSD) counter outputswitched and applied a low state to pin 13 of the outputNAND gate. In addition to interrupting the generationof a valid output trigger, this also reset both counters.The entire cycle was then repeated. The small me-chanical shocks in the middle of the piston stroke,however, were usually detected well before thecounters completely decremented to zero. Thiscaused the one-shot to turn off the signal averagertrigger pulse for 40 ms in the middle of the pistonstroke. After 40 ms, data acquisition was again re-sumed until either the next mechanical shock was de-tected or the counters decremented to zero near theend of the piston stroke. The LM339 operationalamplifier connected to the input of the one-shot setsthe one-shot trigger threshold level so that smallermechanical shocks can be ignored if desired.

C. Data Analysis

Recorded with each diode laser sample absorptionand interferometer scan were scans of the 100% ab-sorption and transmission base lines. The latter wasobtained by replacing the calibration flow in the sam-ple cell with ultrapure zero air at the same total pres-sure. The incident intensity Io at each point over anentire scan was calculated by digitally subtracting cor-

responding points of both base line scans. Varioussaturated absorption features were linearly fit to ob-tain the 100% absorption base line over an entire scan.The intensity I over each entire sample gas absorptionscan was next digitally ratioed point by point to theincident intensity thus calculated to give the sampletransmission (I/Io) spectrum. Absorbances A at eachpoint were then calculated from

A = -ln(I/I 0 ). (1)

The NO2 concentration flowing through the absorp-tion cell was determined from both the peak absor-bance [A(vo)] at line center (o) as well as from theintegrated-fit absorbance over the entire line profile.A Voigt line profile was employed in both cases usingthe Humlicek algorithm'8 together with the followingline parameters at 296 K for the 94,6+ line: (1) anintegrated absorption coefficient of 1.138 cm-2 atm-',recently tabulated by Toth19; (2) a calculated Doppler-broadened halfwidth-at-half-maximum (HWHM) of0.00146 cm-1; and (3) an averaged air-broadening coef-ficient of 0.073 cm-1 atm-1 , as tabulated by Toth andthe 1980 AFGL Trace Gas Compilation. 2 0 Recentmeasurements of the absorption and air-broadeningcoefficients for this line carried out in our laboratoryare in agreement with the above values to within 2%.

In the first approach, the line center absorbance[A(vo)] calculated from Eq. (1) was used together withthe line center absorption coefficient [a(vo), cm-1

atm-1], calculated from the Voigt profile, and the totalsample pressure (P, atm) and path length (L, cm), inthe well-established Beer-Lambert absorption expres-sion to derive the NO2 sample gas concentration:

[ 2 A(vo)NO]a(v0)PL (2)

In the second approach, the integrated absorbanceover the entire line profile [SA(v)dv] was calculatedusing the Voigt profile in a nonlinear least-squaresfitting routine. The Lorentz width in these calcula-tions was fixed, and the Doppler width was fit. At thereduced sampling pressure of 0.608 Torr, the resultingline shape is predominately Gaussian. Any error inthe air-broadening coefficient would thus have a mini-mal effect on the retrieved Doppler halfwidth. A 10%error in the broadening coefficient, for example, wouldonly affect the retrieved Doppler halfwidth by 0.4%.The resulting NO2 concentration flowing through thesample cell was derived using the calculated integratedabsorbance along with the integrated absorption coef-ficient in Eq. (2) in place of the values at line center.The wavenumber axis necessary for this calculationwas obtained by fitting the interferometer fringes to afourth degree polynomial.

Ill. Results and Discussion

Employing the microphone triggering circuit, thelaser sweeps contaminated by compressor frequency-jitter, corresponding to -20-40% of the total numberof sweeps, are not co-averaged. In Fig.3(a), we displayan oscilloscope photograph of the high-frequency me-

1 September 1987 / Vol. 26, No. 17 / APPLIED OPTICS 3555

Piston Cycle

(a) Microphone-DetectedMechanical Shocks

TTL Output(b) Trigger Pulses

Fig. 3. Oscilloscope photograph of (a) compressor mechanicalshocks detected by the microphone during one piston cycle and (b)negative TTL output trigger pulses generated by the trigger circuitduring shock-free time periods. The leading and trailing edges of

these signals are not apparent on this photograph.

chanical shocks detected by the microphone duringone 300-ms piston cycle. In the lower trace [Fig.3(b)],the negative-going NAND gate output trigger signals,which only occur during the shock-free time periods,are displayed. The leading and trailing edges of thesesignals, however, are not readily apparent on this pho-tograph. As shown, the large mechanical shocks atboth the beginning and end as well as the smaller shockin the center of the piston stroke turn off the outputtrigger signal. The threshold was set so that dataacquisition still occcurred during the smaller shocks.

Improvements in both the laser output frequencyprofile and linewidth employing the microphone trig-gering circuit can be directly observed in the confocalinterferometer fringe scans of Fig. 4. Thirty thousandsweeps of the laser through two fringes were averagedwith both the circuit turned on and off. With thecircuit activated, the fringes are clearly more uniform,a requisite for a meaningful determination of the laserfrequency profile for correcting line center absorptiondata. In addition, the laser halfwidth is 9-10% nar-rower with the circuit activated, which translates toless instrumental distortion in our absorption spectra.

In Fig. 5, Doppler-limited absorption scans of the94,6+ line both with and without the circuit activatedare superimposed. Although not as dramatic as Fig. 4,which was recorded 5 months earlier with a differentset of operating conditions, elimination of the mechan-ically induced frequency-jitter did result in a 3.8%decreased linewidth. A fit-to-calculated Dopplerhalfwidth ratio R of 1.070 and 1.111 was obtained withthe circuit activated and inactivated, respectively.Despite repeated attempts, the instrumental-broad-ening could not be completely removed, suggestingthat excess laser linewidth was the predominate causein this particular case.

It is well known that even in the absence of mechani-cal refrigerator shocks tunable diode lasers often ex-hibit excess linewidth that can be highly variable andmany times broader than the inherent linewidth.Hinkley and Freed,21 for example, demonstrate thatthe inherent linewidth can be as narrow as 54-kHz(FWHM) for TDLs mounted in liquid helium Dewars.By contrast, Jennings4 and Reid et al.2 measured

Microphone Circuit On -------

Microphone Circuit Off

Fig. 4. A 50-cm confocal interferometer scans with and without themicrophone triggering circuit activated.

1.0 -

o'/U)5 0.9895 Trace AU)

m: - Trace B-A /

0.979

-0.0062 -0.0031 0 0.0031 0.0062

RELATIVE WAVENUMBERS (cm 1)

Fig. 5. Direct absorption scans of the 94,6+ line of NO2 with A andwithout B the microphone triggering circuit activated. Pure NO2 ata total pressure of 0.608 Torr was used for these scans. In subse-quent line-fitting analysis, the Lorentz width was fixed at a value of0.000058 cm', and the Doppler halfwidth was fit. Fit-to-calculatedDoppler halfwidth ratios of 1.070 and 1.111 were, respectively, deter-

mined in traces A and B.

linewidths in the 0.6-20-MHz range in the absence ofrefrigerator shocks. In the latter case, the magnitudeof this excess linewidth was found to vary considerablyfrom diode to diode and with the junction temperatureand injection current for any given diode.

In quantitative TDL measurements carried out inthe direct absorption mode employing a closed-cyclerefrigerator system without any form of data acquisi-tion synchronization, it becomes absolutely essentialto ascertain the extent of compressor frequency-jitterbroadening relative to broadening caused by excesslaser linewidth. It is well known that the latter causesa decrease in the peak absorbance at line center whilenot affecting the integrated absorbance over the lineprofile. Correction factors in this case can be deter-mined and applied to the line center peak absorbance

3556 APPLIED OPTICS / Vol. 26, No. 17 / 1 September 1987

_-4----------.00 I.1 cm

| ' 0.00501 cm ~1

100 'Il' i

TraceB-"50 II

Compressor Displace0 -Near MaximumI

.2 of Excursion- 50

.200-

250

-300l I l l l l I l I

Wavenumber (cm' )

Fig. 6. Single sweep absorption traces of NO2 at two differentphases of the diode laser compressor displacer stroke. The sweep is

4 ms in duration and comprised of 800 data points. The resulting

frequency-jitter distortion of trace B gives rise to a nearly identical

peak absorbance as trace A but a much larger integrated absorbance,

as discussed in the text. The 103,7± absorption lines of NO 2 in the

1606.15-cm-' region were used for these measurements.

data by convolving the laser profile, if known, with theabsorption spectrum, as described in detail by Strow 8

and Fridovich et al.9 Alternatively, determinationsbased on a fit of the integrated absorbance over theentire line profile can be used to attain accurate re-sults. However, in the case of frequency-jitter due tomechanical refrigerator shocks we find that the inte-grated absorbance over the line profile is dramaticallyaffected while the peak absorbance at line center isonly minimally changed, if at all. If frequency-jitter isthus the dominate source of the instrumental-broad-ening, the above correction factors associated with ex-cess laser linewidth would introduce a systematic er-ror.

This effect of mechanically induced frequency-jitteris shown in Fig. 6 where two single-sweep absorptiontraces of an NO2 spin-split pair are recorded at twodifferent phases of the compressor displacer stroke.Trace B was taken near the maximum excursion pointof the displacer stroke. Similar to Fig. 2 presented byMelandrone et al.3 , the resulting frequency-jitter isclearly evident. As shown, this jitter dramaticallyaffects the absorption linewidths while hardly affect-ing the peak absorbances, as expected since the rate ofchange of the intensity with frequency is zero at linecenter and maximum near the halfwidth points. Inthis situation, the increased linewidth causes an in-creased integrated intensity, directly opposite to thatcaused by excess laser linewidth. In this particularcase, the absorption linewidth increased by-21%. Al-though these single-scan traces are somewhat extremein that the perturbations shown are not smoothed bysignal averaging, increased linewidths of the order of9% have still been observed in our signal-averagedspectrum (30,000 sweeps) for these same two lines.The signal-averaged peak absorbance at line centerwas nearly constant in this case, in exact concurrence

Table 1. Tunable Diode Laser Direct Absorption Determinationsa UsingTwo Different NO2 Calibration Standards

Line centerb Integrated-fitb Integrated-fitabsorbance absorbance Re normalized by R

Calibration standard: 832 I 12-ppm NO2 permeation system814 913 1.123 813825 915 1.109 825825 914 1.098 832820 871 1.066 817

Av 821 903 1.099 822

Calibration standard: 854 + 15-ppm NO2 compressed gas mixture818 824 1.027 802845 927 1.114 832863 930 1.096 849

Av 842 894 1.079 828

a All concentrations are in ppm.b Estimated 2a uncertainty of 21 ppm.c Fit-to-calculated Doppler halfwidth ratio.

with the observations described above. For the non-distorted spectrum in this comparison A, the diodesweep was synchronized with the compressor displacerstroke motion using the microphone triggering circuit.Further analysis of Fig. 6 reveals that the frequency ofthe mechanical shocks is as high as 40 kHz.

The effects of compressor frequency-jitter are quan-titated in Table I. Here NO2 determinations using the832- and 854-ppm calibration standards are intercom-pared employing both absorption approaches. Theaverage determination based on the line center peakabsorbance for both intercomparisons, 821 + 21 and842 i 21 ppm, was within 1.3 and 1.4% of the respectivecalibration standards. This approach thus yields re-sults that are in statistical agreement with the inputcalibration standards. The integrated-fit determina-tions by contrast averaged 8.6 and 4.6% higher than therespective calibration values. These high NO2 deter-minations were accompanied by average increases of9.9 and 7.9% in the fit-to-calculated Doppler halfwidthratios R. The integrated values when normalized bythe appropriate ratio R resulted in determinationsmore consistent with those based on peak absorbancesat line center as well as the calibration values. Thissuggests that the retrieved Doppler halfwidths andintegrated absorbances are closely correlated, directlyopposite to that expected for excess laser linewidth.Assuming that the excess laser linewidth is solely re-sponsible for the observed increased Doppler half-width in this case, one may erroneously correct the linecenter determinations and thus introduce a positivesystematic bias.

In addition to the systematically high-concentrationdeterminations, frequency-jitter also yields a muchhigher variability than excess laser line width, even fora fixed set of TDL operating conditions as shown inTable I. This may arise in part because each new dataset is taken with a different phase relationship be-tween the data acquisition start and the compressordisplacer stroke. Excess laser linewidth by contrast

1 September 1987 / Vol. 26, No. 17 / APPLIED OPTICS 3557

should result in less run-to-run variability using a fixedset of operating conditions. On the other hand, theextent of instrumental-broadening due to both causesseems to be highly variable with changing TDL condi-tions. For example, the same absorption feature stud-ied in Table I was examined 3 months later without themicrophone triggering circuit employing a much lowerinjection current (0.0906 A compared with 0.2815 Apreviously) and a higher temperature. Nine differentdeterminations based on both absorption approacheswere consistently in agreement to within 1-3%. Theagreement between the fit and calculated Dopplerhalfwidth ratios, furthermore, was within 2%. In con-trast to the previous case, this suggests that neitherinstrumental-broadening mechanism was operative.Repeated absorption determinations using both ap-proaches, therefore, should be very useful in not onlyidentifying circumstances when instrumental-broad-ening is present but also in suggesting the predominatesource.

IV. Conclusions

In TDL measurements carried out in the direct ab-sorption mode, compressor frequency-jitter as well asexcess laser linewidth can both give rise to consider-able systematic errors. To guarantee accurate results,both line center as well as integrated-fit determina-tions, or equivalently, a comparison between the re-trieved and calculated Doppler halfwidths, should becarried out. When both determinations agree, oneobtains very definitive proof that neither error sourceis operative. This situation is clearly the most desir-able. When disagreement does occur, the causeshould be determined before any corrections are ap-plied. For a fixed set of experimental conditions, com-pressor frequency-jitter distortion tends to be highlyvariable from run to run, and thus repetitive determi-nations should be of value in pointing to its presence.If one erroneously corrects peak absorbance determi-nations at line center to account for excess laserlinewidth, or alternatively, erroneously corrects inte-grated-fit determinations to account for compressorfrequency-jitter systematic errors will undoubtedly re-sult. If possible, the above dilemma should be com-pletely avoided by eliminating the source of the com-pressor frequency-jitter by, for example, synchronizingthe data acquisition with the displacer stroke motion,as discussed herein. Employing a liquid cryogen Dewarin place of the closed-cycle refrigerator or utilizinghigh-frequency servo-lock systems are other viable al-ternatives. Any remaining discrepancy in the fit-to-calculated linewidth ratios can then be totally ascribedto an excess laser linewidth.

The authors wish to thank Fillmer C. Ruegg and RonShideler of the National Bureau of Standards for helpin designing and constructing the electronic triggeringcircuit.

The National Center for Atmospheric Research issponsored by the National Science Foundation.

References

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5. Spectra-Physics, Laser Analytics Division, Bedford, MA., tripodsuspension ultrastable laser mount.

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14. R. Sams and A. Fried, "Spin Splittings in the V3 Band of NO2 ,"submitted to J. Mol. Spectrosc.

15. To describe adequately materials and experimental procedures,it was occasionally necessary to identify commercial products bymanufacturer's name. In no instance does this imply endorse-ment by the National Bureau of Standards or the NationalCenter for Atmospheric Research.

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Beam Diode Laser Spectrometer with Sweep Integration,"Appl. Opt. 19, 2695 (1980).

17. Knowles Electronics, Inc., Franklin Park, ILL 60131.18. J. Humlicek, "An Efficient Method for Evaluation of the Com-

plex Probability Function: The Voigt Function and its Deriva-tives," J. Quant. Spectrosc. Radiat. Transfer 21, 309 (1979).

19. R. A. Toth, unpublished results for NO2 in the 3 Band, JetPropulsion Laboratory (1985).

20. L. S. Rothman, "AFGL Trace Gas Compilation Edition of Au-gust 1980," AFGL Hanscom AFB, Bedford MA (1980).

21. E. D. Hinkley and C. Freed, "Direct Observation of the Lorent-zian Line Shape as Limited by Quantum Phase Noise in a LaserAbove Threshold," Phys. Rev. Lett. 23, 277 (1969).

3558 APPLIED OPTICS / Vol. 26, No. 17 / 1 September 1987