pulsed-laser excitation of acoustic modes in open high-q photoacoustic resonators for trace gas...

Pulsed-laser excitation of acoustic modes in openhigh- Q photoacoustic resonators for trace gasmonitoring: results for C 2H4

Christian Brand, Andreas Winkler, Peter Hess, Andras Miklos, Zoltan Bozoki,and Janos Sneider

The pulsed excitation of acoustic resonances was studied with a continuously monitoring photoacousticdetector system. Acoustic waves were generated in C2H4@N2 gas mixtures by light absorption of thepulses from a transversely excited atmospheric CO2 laser. The photoacoustic part consisted of high-Qcylindrical resonators 1Q factor 820 for the first radial mode in N22 and two adjoining variable acousticfilter systems. The time-resolved signal was Fourier transformed to a frequency spectrum of highresolution. For the first radial mode a Lorentzian profile was fitted to the measured data. The outsidenoise suppression and the signal-to-noise ratio were investigated in a normal laboratory environment inthe flow-through mode. The acoustic and electric filter system combined with the averaging of thephotoacoustic signal in the time domain suppressed the outside noise by a factor of 4500 173 dB2. Thedetection limit for trace gas analysis of ethylene in pure N2 was 2.0 parts in 109 by volume 1ppbV2 1minimalabsorption coefficient amin 5 6.1 3 1028 cm21, pulse energy 20 mJ, 1-bar N22, and in environmental air, inwhich the absorption of other gas components produces a high background signal, we can detect C2H4 to,180 ppbV. In addition, an alternative experimental technique, in which the maximum signal of thesecond azimuthal mode was monitored, was tested. To synchronize the sampling rate at the resonancefrequency, a resonance tracking system was applied. The detection limit for ethylene measurementswas amin 5 9.1 3 1028 cm21 for this system.Key words: Trace gas analysis, pulsed photoacoustic spectroscopy, acoustic resonance, air pollutant

monitoring, ethylene, transversely excited atmosphere CO2 laser, noise reduction.

1. Introduction

The potential of photoacoustics 1PA’s2 to detect ultra-low gas concentrations was first recognized by Kreu-zer.1 He performed trace gas analysis experimentsin the frequency domain by using a modulated cwlaser and a small nonresonant PAcell equipped with amicrophone. A few years later Dewey et al.2 pointedout that acoustic amplification factors that exceed100 can be obtained by using a sample cell designed asan acoustic resonator. If the modulation frequency

C. Brand, A. Winkler, and P. Hess are with the Institute ofPhysical Chemistry, University of Heidelberg, Im NeuenheimerFeld 253, D-69120, Germany; A. Miklos is with the Institute ofIsotopes, Hungarian Academy of Sciences, P.O. Box 77, H-1525Budapest, Hungary; and Z. Bozoki and J. Sneider are with theDepartment of Quantum Electronics, JATE University, H-6720Dom ter 9, Szeged, Hungary.Received 5 October 1994; revised manuscript received 4 January

1995.0003-6935@95@183257-10$06.00@0.

r 1995 Optical Society of America.

coincides with one of the resonance frequencies of thechamber, a standing acoustic wave is excited and thesystem works as an acoustic amplifier. In the follow-ing years many groups showed that such a PA detec-tion scheme can be used to monitor molecules ofinterest in a buffer gas 1e.g., N22 at the parts in 106 byvolume 1ppmV2 to the parts in 109 by volume 1ppbV2level. A review of this work is given, for example, inRefs. 3 and 4. PA detection not only provides a highsensitivity but also provides the selectivity needed toanalyze multicomponent mixtures by the use of tun-able IR lasers,3,4 as demonstrated by Bernegger andSigrist, who employed a line-tunable CO laser,5 andby Meyer and Sigrist, who employed a CO2 laser.6For trace gas analysis with a resonant cell, the

maximum signal at only one of the resonance frequen-cies is needed. If the quality factor Q of the resona-tor has a value of several hundred, the full-width athalf-maximum of the acoustic resonance profile isonly a few hertz. In this case the synchronization ofthe modulation frequency to the actual resonancefrequency of the PA cell becomes a serious problem

20 June 1995 @ Vol. 34, No. 18 @ APPLIED OPTICS 3257

because of the shift of the resonance frequency withcomposition, temperature, or pressure. Common ap-plications of modulated laser PA’s therefore use low-Qresonators in order to be independent of these fluctua-tions. Although the problem can be solved by theapplication of an additional control loop for the lightmodulator,7 the system becomes more complicated.A computer-controlled measurement of the wholeresonance profile has been developed8; however, sucha point-by-point construction of the resonance curvein the frequency domain is too slow for in situpollution monitoring.PA trace gas analysis can be performed, not only in

the frequency domain, with periodic modulation ofthe light source and lock-in detection of the micro-phone signal, but also in the time domain. In thelatter case pulsed lasers are used for excitation, andthe time evolution of the microphone signal is de-tected with a boxcar integrator or a transient recorder.Such a pulsed method not only extends the number oflaser wavelengths with accidental coincidence, butalso allows the application of tunable solid-state lightsources by the use of nonlinear optical phenomenasuch as optical parametric oscillators 1OPO’s2 or tun-able dye lasers.The first pulsed experiments in the visible and UV

spectral regions with low-Q cells were performed byClaspy et al.9 and by Leugers andAtkinson.10 With ahigh-Q cylinder used as a sample cell, it has beenshown that Fourier transformation 1FT2 of the time-resolved signal yields the mode spectrum of theexcited acoustic resonances with a single laser pulse.11Because the entire profile of the mode selected fortrace gas detection is measured in this way, theanalysis is not sensitive to a slow drift of the reso-nance frequency caused by changing operation condi-tions. Therefore it is possible to improve the signal-to-noise 1S@N2 ratio by the use of resonators with thehighestQ factors available.Our aim is to investigate the fundamental behavior

of pulsed excitation of resonances in closed and openhigh-Q resonators. Two different setups are intro-duced. In the first, a Lorentzian resonance profile isfitted to the first radial mode 11002 of the cylinder inthe high-resolution FT spectrum to determine thesignal strength. In the second setup, the samplingrate is adjusted to the frequency of the second azi-muthal mode 10202 of a cylinder by a resonancetracking circuit, and the signal strength at the reso-nance frequency of the low-resolution FT signal ismeasured.Coherent acoustic background signals often deter-

mine the sensitivity of PA trace gas analysis, whichmeans that the periodic heating of the windows and ofthe chamber walls by reflected or scattered lightdefines the ultimate detection limit. To overcomethese problems, resonant cells without windows havebeen investigated, allowing continuous monitoring ofambient air. Relatively high-Q factors of ,500 inwindowless modulated operation have been achievedwhen the beam was allowed to enter and leave the

3258 APPLIED OPTICS @ Vol. 34, No. 18 @ 20 June 1995

cylindrical cell at pressure nodes.12 An alternativedesign is to fit acoustic filters to the openings of thecylindrical resonator, as described in Refs. 13 and 14.In this paper it is shown that a high-Q factor of 820can be obtained in an open cylinder fitted withoptimized acoustic filters.

2. Experimental

A. Optical System and Gas Handling

A pulsed line-tunable CO2 transversely excited atmo-spheric 1TEA2 laser 1Lumonics Model 102-22 was oper-ated at 0.5–1 Hz, using a gas mixture lean in N2 togive a relatively short main pulse with a length of lessthan 200 ns. By adjusting the amount of N2 flowingthrough the optical cavity, we controlled the lengthand the magnitude of the N2 tail to ,0.5–1.5 µs.Thus it was possible to check whether relatively longlaser pulses affect the generation of sound waves thatis due to possible phase shifts. The output beampassed through an 1.5-cm-diameter aperture andthen through a convex ZnSe lens of 2.4-m focal length.Optical energies were measured with a joulemeter1Gentec Model ED-5002. The average total energy ofthe output pulse was ,600 mJ. An additional dia-phragm adjoining the acoustic cell was used to stopdown the beam to a diameter of less then 3 mm todiminish spurious PAsignals produced bywall absorp-tion. Thus the actual total pulse energy passingthrough the acoustic cell was 20 mJ, which corre-sponds to an average power of 0.1 mW.The trace gas ethylene 1Messer Griesheim, purity

99.95%2was mixed with N2 1Messer Griesheim, purity99.996%2 in a range from 10 ppmV to 400 ppmV. Thegas-handling system consisted of four flow controllers1Tylan Model FC-2602 with control units 1Tylan ModelRO 70102 to mix the two gases in the flow-throughmode. Ethylene andN2 were premixed with two flowcontrollers into a glass bulb with a 6-L volume, then,in turn, this gas mixture was mixed with a N2 flow of300 SCCM 1SCCM denotes cubic centimeter perminute of STP2. With this method C2H4@N2mixturesin the range from 20 ppmV to a few percent could beobtained, although only the range from 20 ppmV to,800 ppmV was practicable because of the relativelyhigh optical absorption of ethylene. Capacitancema-nometers 1MKS Model 2202 were used to control theabsolute pressure in the resonator and the excesspressure in the glass bulb. During the measurementperiod of,3min, the pressure and the temperature inthe cell were stable with absolute values of ,1000mbar and 25–30 °C, respectively.

B. High-Q Resonance System

The PA detector system is shown in Fig. 1. It is afurther improved modular version of a PA detectordesign published earlier.13,14 It was used as an openPA cell as well as a closed cell with NaCl windowsmounted at each end of the acoustic filter system.The cylindrical resonator machined from stainlesssteel was 5.15 cm in radius and 10.3 cm long. To

enhance the quality factor of the cylinder, the innersurface was polished. The Q factor of the first radialmode of this resonator was measured to be <820 inN2, whereas the theoretical value for pure N2 is<1150, according to boundary layer theory.15 Thedistance of the laser beam to the cell axis could bechanged. Thus it was possible to pass the laser beamthrough the cell at nodal points of various acousticmodes. The microphone was positioned halfwayalong the cylinder surface. Five acoustic filter ele-ments, three l@4 pipes and two buffer volumes, weremounted at each end of the cell. Their dimensionscould be changed to suppress various spectral compo-nents of the outside noise.13,16 In order to suppressoutside noise in the range of the first radial mode ofthe resonator, the three solid l@4 filters had an innerradius of 3.0 mm and a length of 16.6 mm, and thetwo acoustically optimized filter volumes in betweenhad an inner radius of 24.7 mm and a length of13.3 mm. The gas inlet and outlet were positioned atthe end of the filter system. Thus the strong gas flowof more than 300 SCCM did not increase the noiselevel.The PA signal was measured by an electret micro-

phone 1Sennheiser KE 4-211-22. It was calibrated toa sensitive condenser microphone 1Bruel & KjaerModel 41652 in the Acoustic Laboratory at the Fraun-hofer Gesellschaft in Vaihingen, Stuttgart, Germany.The sensitivity of the microphone was 40 [email protected] noise reduction was ensured when the micro-phone was coupled to a selective low-noise preampli-fier 1System Gaspar Model PA-LAB-22, which could beset on amplification factors from 50 up to 40,000.The field-free frequency response of the entire micro-phone–amplifier circuit was found to be linear in therange from 2.5 to 5 kHz, while frequencies below andabove this bandpass were efficiently suppressed.The PA and optical signals were fed into a digital

oscilloscope 1LeCroy Model 9400A2, where they weredigitized and averaged synchronously by the triggersignal of the joule-meter. Typically we averaged 100laser pulses in order to reduce incoherent noise. Theaveraged data were transferred to a PC for FT andLorentzian resonance profile fitting. With this setupwe recorded a time signal of length 0.5 s with asampling rate of 16.67 kHz to achieve a FT spectrum

Fig. 1. Schematic of the experimental setup of the high-Q system:M, microphone; A@F, amplifier and bandpass filter; D, light detec-tor.

resolution of 2 Hz with a total of 8192 points for theLorentzian curve fitting.To reduce the acoustic background produced by

absorbing species in the resonator 1H2O, CH4, CO2,dust, etc.2, the cell with attached windows, as well asthe entire gas-handling system, was evacuated downto 1 3 1023 mbar for at least 10 h, heated, and flushedwith N2 before every measurement series. For thispurpose the connections of the different cell moduleswere Viton sealed. Care was taken to avoid disturb-ingHelmholtz resonances caused by unwanted connec-tor volumes.

C. Resonance Tracking System

We tested another setup inwhich synchronized analog-to-digital 1A@D2 conversion of the PAsignalwas applied.This system allows a much higher time resolution fortrace gas monitoring than the high-Q system does.The design of the resonant PA chamber and theadjoining acoustic filters was essentially identical tothat of an open PA cell developed earlier.7,13The inner cylindrical resonator machined from

stainless steel with an outer layer made from alumi-num was 4.9 cm in radius and 5.6 cm long. Thus thevolume of this cell was approximately half the volumeof the high-Q resonator.The schematic of the experimental setup is shown

in Fig. 2. The PA signal of the second azimuthalmode 10202 near 3400 Hz was excited and detected.As the resonance frequency of the cell can be shiftedbecause of changes of temperature or gas composition,a resonance tracking circuit 1System Gaspar, PAR-12was applied.7 The operation of the resonance track-ing circuit is based on the fact that the ratio ofeigenfrequencies of two arbitrary modes of an acousti-cal cavity is constant. A phased-locked loop keepsthe frequency of an oscillator 1reference frequency2permanently on a higher resonance than the reso-nance used for PA detection; then, in turn, thisreference frequency is divided by the constant ratio of

Fig. 2. Schematic of the experimental setup with the resonancetracking system: 1–4: microphones; A@F, amplifier and bandpassfilter; RTS, resonance tracking system; A@D, 16-bit A@D card; D,light detector.


the two eigenfrequencies. Thus the result is theactual PA resonance frequency.The key element of the resonance tracking system

is an acoustic oscillator based on a small sound sourceand a microphone 13 and 4, respectively, in Fig. 22 andan electronic feedback circuit. This oscillator perma-nently runs at the frequency of the second radialmode 12002 1,7.8 kHz in air2 selected deliberately asthe reference frequency. For themeasurement of thePA signal a matched pair of bandlimited, high-sensitivity electret microphones 1Knowles EA 3029,normal sensitivity 50 mV@Pa, measured sensitivitywith a modified driving circuit 150 mV@Pa; positions1 and 2 in Fig. 22 was used. The microphone signalswere amplified and filtered by the same low-noisemicrophone amplifier 1System Gaspar, PA-Lab-22 asused in the other setup, except that the bandpassfilters were adjusted to the 10202mode of the resonator.The difference signal of the two microphone channelsfrom microphones 1 and 2 was fed to the input of a16-bit A@D card 1Intelligent Instrumentation, PC-20041C2, mounted in a PC.Although both PA systems use A@D conversion

followed by FT calculation, the method of sampling isdifferent for the resonance tracking system. As theresonance tracking circuit produces an external sam-pling signal for the A@D card, the A@D conversion canbe synchronized to the cell resonance in such a waythat exactly 16 samples 1data points2 are taken forevery period of the signal at cell resonance. As aconsequence of the synchronized sampling, the peakof the second azimuthal resonance in the spectrum ofthe recorded PA signal always coincides with the nthFT line 1where n 5 number of FT’s@162. Thereforeonly the magnitude of this line has to be monitored.That is, no curve-fitting procedure is needed for thedetermination of signal strength at resonance; thusthe measuring time can be reduced. A high spectralresolution is not necessary and a further reduction ofthe measurement time is possible by a decrease in thenumber of data points. In the case of 256 points, themeasurement time is less than 0.1 s.It should be mentioned that synchronized samples

can be used only if the resonance tracking circuit isproperly locked during the A@D conversion. High


electromagnetic disturbances produced by the laserdischarge may temporarily unlock the system.As the second PA cell was developed for continuous

monitoring of pollutants in air, it was not leaktightenough to be evacuated. Therefore a permanent flowof pure N2 was applied, and, in addition, the systemwas heated to reduce the background signal. Themain features of the two PA detection systems aresummarized in Table 1.

3. Theory

The absorption of the laser light and the relaxation ofthe excited vibrational degrees of freedom of the gasare very fast compared with a period of the soundwave. The laser pulse duration is of the order of 1026

s, including the tail of the pulse shape. For excita-tion of the sound wave, vibrational states are excitedby IR laser radiation. For the relatively high pres-sure 11 bar2 used in these experiments, the relaxationtime tVT for vibrational–translational energy ex-change is in the range 1026–1029 s. The frequency ofthe sound waves is in the kilohertz range, correspond-ing to a time scale of milliseconds. Thus the pulsedexcitation can be treated as a sudden process.If we neglect the influence of the thermal and the

viscous interaction of the gas, the wave equation ofthe acoustic pressure changes p is15,16

≠t2p1r, t2 2 c2=2p1r, t25 1g 2 12≠tH1r, t2, 112

where c is the 1complex2 speed of sound in the gas andH1r, t2 represents the rate of heating produced by theabsorption of the laser light. The absorption coeffi-cient a is included by

H1r, t2 5 aI1r, t2, 122

where I1r, t2 is the intensity of the light.The solution of the inhomogeneous wave equation

112 is described by the eigenfunction series,

p1r, t2 5 ojAj1t2pj1r2exp1ivjt2, 132

where pj1r2 are the eigensolutions and Aj1t2 describesthe time-dependent amplitudes of the differentmodes.

Table 1. Characteristics of the Two PA Systems

Characteristic High-Q System Resonance Tracking System

Cylinder dimensions R 5 5.15 cm, L 5 10.3 cm R 5 4.9 cm, L 5 5.6 cmMode used 11002 First radial 10202 Second azimuthalQuality factor ,820 ,160Resonance frequency 1in N22 fR , 4170 Hz fR , 3400 HzFilter location Cell axis Node of first radial modeMicrophone Sennheiser KE 4-211-2 Knowles EA 3029, 2 pcSensitivity 40 mV@Pa 1at ,4100 Hz2 150 mV@Pa 1at ,3400 Hz2Sampling frequency 16.67 kHz 16 3 fR 154 kHz2Record length 8192 Points 256 points 14096 pointsa2PA signal level measured Resonance curve fitting Maximum of the 10202mode

aWhen nonsynchronized sampling was used. In this case the PA signal level was determined by Lorentzian curve fitting.

For a cylinder with radius R0 and length L0 incylindrical coordinates 3r 5 1r, w, z24, the eigensolutionis

pj1r25 Jm1krr2cos1kzz23sin1mw2

cos1mw24 . 142

Jm are the Bessel functions of orderm, kr 5 xmn@R0, kz5 nz@L0, and xmn is the nth zero of the first derivative.The subscript j on the left-hand side is a notation ofthe trial 1n, m, nz2. The frequency of the jth eigen-mode is given as

vj 5 c1kr2 1 kz221@2. 152

The effects of thermal and viscous interaction canbe treated by a complex description of vj:

vj ; fj 1 igj 5 kjc. 162

The real part fj represents the resonance frequency ofthe mode, and the imaginary part gj describes thedamping of the sound wave. 2 3 gj is the full-widthat half-maximum of the resonance. The quality fac-tor of the resonance is defined by Qj 5 fj@2gj. Atheory of the losses at the wall and in the bulk forcylindrical cavities is extensively discussed by Tru-sler.15The combination of Eq. 112with Eq. 132 yields

oj1≠t

2Aj 1 2ivj≠tAj2pj exp1ivjt2 5 1g 2 12≠tH1r, t2.

172

Projection on the mode j by e · · · pj*dV gives arelation for the amplitude Aj1t2 of this mode:

≠t2Aj 1 2ivj≠tAj 5

g 2 1

Vjexp12ivjt2

3 eVCell

≠tH1r, t2pj*dV. 182

The normalization of the eigenfunctions is introducedby Vj ; eVCell pj*pjdV. Integration e

2`

t · · · dt of Eq. 182provides a general formula for the resonance ampli-tude Aj1t2:

≠tAj 1 2ivjAj

5g 2 1

Vje

2`

t eVCell

exp12ivjt2≠tH1r, t2pj*dVdt. 192

For a short laser pulse 1Dt 9 1 ms2,

H1r, t2 5 H1r2exp12t@t2 1102

is used. The exponential term with the time scale t

represents the relaxation phenomena leading to ther-

mal equilibrium. With this ansatz

≠tAj 1 2ivjAj 5 2g 2 1

VjeVCell

H1r2pj*dV

3 e2`

t exp12t@t2

t3 exp12ivjt2dt 1112

is obtained. The time integral is calculated for thelimit t = 0. This is fulfilled for 1@vj: t. This leadsto the exponential description of the Dirac d function:

limt=0 e

2a

1a exp12t@t2

tf 1t2dt 5 e

2a

1a

d1t2 f 1t2dt 5 f 102,

a . 0. 1122

This means that the details of the deactivation of theoptically excited degrees of freedom are not importantfor the generation of the PA signal. We checked thisby computer simulation, in which the long tail 1< mi-croseconds2 was included and different pulse shapeswere tested. Equation 1112 thus simplifies to

≠tAj 1 2ivjAj 5 Sj, 1132

Sj ; 2g 2 1

VjeVCell

H1r2pj*dV. 1142

Sj is constant for a certain geometry. It describes theoverlap between H and the standing acoustic wave ofthe mode pj. It contains information on how effec-tively the sound wave can be excited. The generalsolution of Eq. 1132 is

Aj1t2 5 A0 j exp122ivjt2 1Sj

2ivj

. 1152

The first term describes an exponentially increasingsignal and thus must be discarded. Therefore thefinal result for p1rM, t2 at the microphone position r 5

rM is

p1rM, t2 5 ojpj1rM2exp1ivjt2

Sj

2ivj

. 1162

The signal measured in the time domain can beconverted into a spectrum by FT p1rM, v2 5

Œ2@p e0`p1r

M, t2exp12ivt2dt:

p1rM, v2 51

Œ2pojpj1rM2

Sj

vj1v 2 vj2, 1172

which describes a sum over real and imaginary partsof Lorentzian profiles of possible eigenfrequencies ofthe resonator.


4. Results

A. High-Q Resonance System

The entire series of experiments was performed attotal pressures of 1 bar. Measurements were madeat two laser wavelengths, the 10P14 and the 10P10lines in the 10.6-µm band, with wave numbers of949.48 and 952.89 cm21, respectively, lying in thecentral Q branch of the n7 band of the ethylenespectrum. According to Brewer et al.17 and Olafssonet al.,18 the absorption coefficients for these two laserlines, which were measured with a cw CO2 laser, areaP14 5 30.4 1cm atm221 and aP10 5 2.98 1cm atm221.Thus a ratio of ,10 between the two PA signals for agiven concentration was expected. With an averagetotal energy of 20 mJ, we obtained only a factor of ,3between the 10P14 and the 10P10 lines, whereas atlower pulse energies of ,2–3 mJ a factor of ,10 wasindeed measured. This shows that on the 10P14 linewe were close to the saturation range, where Cs .1@tV=T according to Meyer and Sigrist6 and Giroux etal.,19 where C, s, and tV=T represent the photon fluxthrough the cell, the absorption cross section for thespecific line, and the vibrational–translational 1V =T2relaxation time, respectively.As a first step, the environmental noise was checked

in the laboratory. The five-pole acoustic filters effi-ciently suppressed this noise, which was furtherreduced by the bandwidth-limitedmicrophone–pream-plifier response. The noise inside the resonator wasmeasured with and without CO2 laser pulses passingthrough the resonator, signal averaging, and N2 flow,separately. The spectral distributions of signal andbackground measurements were determined by nor-malized FT.The noise performancewas impressive. The acous-

tic and electric filter combination reduced the wide-band noise by a factor of 500. This level was furtherreduced by a factor of 8 when 100 pulses wereaveraged. Although the wideband noise increasedconsiderably when the CO2 laser was operating, thespectrum showed no significant noise production inthe frequency range of the first radial resonance.Because the gas inlet and outlet were positioned atthe ends of the acoustic filters, the average gas flowthrough the resonator of ,300 SCCM did not increasethe incoherent noise level at all.To test the efficiency of the acoustic filters and the

influence of windows mounted at both ends of theacoustic filters, additional spectra were measuredwith the open setup in the flow-through mode. If thewindows are mounted at the ends of the acousticfilters, the small window signals reaching the acousticresonator do not interfere within the spectral range ofthe first radial mode.We investigated signal and noise for the high-Q

system by theoretically modeling the cell behavior.A calculated spectrum based on Eqs. 132 and 1142 iscompared with a measured spectrum in Fig. 3. Theagreement between theory and experiment is good.The measured data include the PA signal and thenoise, whereas the calculation is done only for the PA


signal. Thus the effect of vectorial addition of signaland noise is not considered in the theoretical curve.This can be seen for the 10202 mode, which does notappear in the calculated spectrum 1the lower one inFig. 32, and therefore is generated by misalignment,scattered light, and noise.With pure N2 flowing through the closed acoustic

cell, the background level around the first radialresonance was 0.23 µV, corresponding to 5.7 3 1026

Pa acoustic pressure. This background level wasreached only after careful cleaning and repeatedflushing of the entire gas-handling system, includingthe resonator. There was a significant change of thebackground level when laboratory air was introducedinto the resonator. The background was comparablewith that reported by Meyer and Sigrist,6 who mea-sured a PA background signal in synthetic air 180%N2, 20% O22 of 50 nV, corresponding to 6.25 3 1026 Paacoustic pressure for the 10-µm branch of the CO2laser emission.The spectrum of the Fourier-transformed PA signal

with 20 ppmV C2H4 in N2 and the N2-flow backgroundare shown in Fig. 4. Both measurements were per-formed with average laser energies of 20 mJ. Thesignal spectrum shows one strong peak at 4167 Hz,which is the frequency of the first radial mode 11002 ofthe resonator at T 5 298.3 K, whereas other reso-nances of the cell and the Helmholtz resonances of theacoustic filters are efficiently suppressed. ALorentz-ian profile was fitted to the corresponding signal ofthe first radial mode. As one can see in Fig. 5, afrequency resolution of ,2 Hz in fact was needed foran accurate fitting of the narrow resonance profiles.The signal amplitude for the 11002 mode with

20-ppmV ethylene was 2.3 mV, corresponding to0.058-Pa acoustic pressure. Therefore the S@N ra-

Fig. 3. Comparison of the calculated 1lower spectrum2 with themeasured 1upper spectrum2 PA Fourier spectrum of the signal inthe high-Q system for 20 ppmV C2H4 in 1-bar N2. For a bettercomparison, the lower spectrum is shifted down 4 orders ofmagnitude. In both spectra the first radial 11002, the adjoiningsecond longitudinal 10022, and the combination 11022 modes areexcited. The second azimuthal mode 10202 does not appear in thecalculated spectrum.

tio for the 20-ppmV measurement on the 10P14 linerelative to the N2 background was 10,000 180 dB2,whereas with the 10P10 line we reached 3,700 171 dB2.The S@N ratio relative to the laboratory air back-ground on both lines was 100 140 dB2. Thus practi-cal estimations of the sensitivity of the PA system onthe 10P14 and 10P10 lines can be made by the extrapo-lation of the measured calibration curves in Fig. 6 tothe background signal of pure N2. The sensitivitylimits on the 10P14 and 10P10 lines with N2-flowbackground are ,2.0 ppbV and 5.4 ppbV, respec-tively.The 10P14 measurements were performed near the

optical saturation limit, whereas the 10P10 absorptionwas far from saturation. Therefore the calibration

Fig. 4. PA Fourier spectrum for the high-Q system with 20 ppmVC2H4 in N2 1upper spectrum2 and for pure N2 1background, lowerspectrum2. The 10P14 line of the TEA CO2 laser with an averagepulse energy of 20 mJ was used. The frequency resolution is2 Hz.

Fig. 5. Measured Lorentzian profile of the first radial mode 11002for 20 ppmV C2H4 in N2. The 10P14 line was used with anaveraged and normalized pulse energy of 20 mJ. The filled circlesrepresent the measured values, and the curve indicates the fittedLorentzian profile. The resonance frequency is n100 5 4164.9 Hz,and the full-width at half-maximum is Dn100 5 5.08 Hz. Thiscorresponds to aQ value of 820.

lines of these two optical wavelengths show differentslopes, which are represented as parallel shifts on thelog–log plot in Fig. 6. Giroux et al.19 observed thesame phenomenon with a pulsed TEACO2 laser and aphoton flux comparable with our values. Thus theestimated detection limits for these wavelengths dif-fer by only a factor of 3 instead of the factor of 10expected from the ratio of the absorption coefficients.The corresponding minimum absorption coefficientsamin also differ by a factor of 3.3. The detection limitsobtained from the measurements with pure N2 flowcan be taken to estimate the corresponding minimumabsorption coefficients amin. These are 6.1 3 1028

cm21 for the 10P14 line and 1.6 3 1028 cm21 for the10P10 line. The estimated sensitivities and mini-mum absorption coefficients in laboratory air andpure N2 are listed in Table 2.To test the application of the experimental tech-

nique for environmental ethylene monitoring, we alsoperformed measurements in laboratory air. A typi-cal spectrum is compared with a spectrum of 10-ppmVC2H4 in N2 in Fig. 7. The resonance profiles in airare shifted to lower frequencies compared with the

Fig. 6. Calibration curves for the two PA setups. The filledcircles and the filled squares represent the measurements on the10P14 and 10P10 lines, respectively, with the high-Q system. Theopen circles 110P142 and open squares 110P102were recorded with theresonance tracking system. Because of saturation, the calibra-tion curve of the two laser lines have a parallel distance in thislog–log plot corresponding to a ratio of,3 instead of the theoreticalvalue of ,10.

Table 2. Overview of the S @N Ratios, Estimated Detection Limits, andMinimum Absorption Coefficients of the High- Q Setup AhQB and the

Resonance Tracking System ARTB

SetupGas

MixtureLaserLine

DetectionLimita

1ppbV2amin

1cm212

hQ C2H4 and N2 10P14 2.0 6.1 3 1028

hQ C2H4 and N2 10P10 5.4 1.6 3 1021

hQ C2H4 and laboratory air 10P14 180 5.5 3 1026

RT C2H4 and background 10P14 3.0 9.1 3 1028

RT C2H4 and laboratory air 10P14 1200 3.6 3 1025

aExtrapolated from the calibration curves in Fig. 6.


data in N2. This is due to the change of the meanmolarmass by other components such as O2, H2O, andCO2. A comparison of Fig. 7 with Fig. 4 shows thatthe background is almost the same, except that nowsome additional acoustic resonances are excited.From the background level we can estimate that theethylene detection limit in the high-Q setup is ,180ppbV for this method.

B. Resonance Tracking System

For the detection system designed for azimuthalmode excitation with resonance tracking, the acousticnoise and the background signal were also measuredwith a flow of N2 at a rate of 300 SCCM. Because ofthe high microphone sensitivity, quite high signallevels 125 mV2 were detected for 20-ppmV ethylene inN2 at the 10P14 line, but the noise level was alsohigher 121 µV2 than that of the high-Q system. Theoscillator of the resonance tracking circuit is pro-tected by proper electric and acoustic bandpass filtersagainst stationary noises and periodic signals thathave different frequencies. However, high-ampli-tude pulsed sound signals can still unlock the system.Therefore the system could not be used above 60-ppmV ethylene concentration. This problem wasavoided by a reduction in the optical pulse energy.To obtain data comparable with the measurementsperformed with the high-Q setup, we used the samepulse energy of ,20 mJ and the same signal process-ing; that is, nonsynchronized sampling and Lorentz-ian curve fitting were used for the 10P14 line. Thefrequency resolution was 13.3 Hz.Measurements at the 10P10 line were performed by

synchronized sampling without any problems. Typi-cal spectra recorded with the resonance trackingsystem of the PA signal and the environmentalacoustic background signal are shown in Fig. 8. In

Fig. 7. PAFourier spectrum for the high-Q system with 20-ppmVC2H4 in N2 1upper spectrum2 and in air 1background, lowerspectrum2. The 10P14 line of the TEA CO2 laser with an averagepulse energy of 20 mJ was used. The shift of the resonancefrequencies between the two spectra is caused by the change of themean molar mass. The background signal in air that is due toH2O or CO2 absorption corresponds to a C2H4 concentration of 180ppbV.


this case only 256 data points were recorded. Thefrequency resolution of the FT was 3400@16 5 212.6Hz; therefore the details of the acoustic spectrumcannot be recognized. However, the S@N ratio can beestimated to be ,5,000 174 dB2.We measured this value by switching the light on

and off while themixture of 20-ppmVC2H4 in 1-bar N2flowed through the system. The PA background sig-nal was measured by the use of pure N2 flow. As theresonance tracking system cannot be cleaned like thehigh-Q one, adsorbed water and CO2 molecules pro-duce quite a high background level. For the firstmeasurements, the background level was 2.7 mV,which corresponds to the PA signal produced by2.2-ppmV ethylene. Afterwards this level slowly re-duced to 2.0 ppmV because of the cleaning effect of thecontinuous N2 flow.The theoretical sensitivity limit is estimated to be

3.0-ppbV ethylene for the 10P14 line, but the usablerange is limited by the background signal in thelaboratory, which is equivalent to 2.0-ppmV ethylene.These detection limits are compared with the resultsfor the high-Q system in Table 2.

5. Discussion

In both PA setups, pulsed-laser excitation of high-QPA resonators combined with synchronized averagingof the PA responses provided excellent S@N ratios bysuppressing incoherent noise very efficiently. Thenoise figures of the open and the closed setups werealmost identical. The outside noise was reduced by afactor of ,300–600 150–55 dB2. If windows are usedit is necessary to fit them at the ends of the acousticfilters.The sensitivities of the two PA systems investi-

gated, as well as the dynamic ranges measured withdifferent laser lines, are comparable. The differentvalue of the expression Sj 3Eq. 11424, which describesthe overlap between the light beam and the acoustic

Fig. 8. PAFourier spectrum for the resonance tracking system for20-ppmV C2H4 in N2 1filled circles2 and for the electronic back-ground 1filled squares2. The 10P14 line of the TEA CO2 laser withan average pulse energy of 2.7 mJ was used. The frequencyresolution is 200 Hz.

eigenfunctions of the resonator, the different volumeand resonance frequency, and the higher Q value leadto a slightly higher S@N ratio in the high-Q system.The S@N ratio in the high-Q system was a factor of ,7higher than in the resonance tracking setup undercomparable conditions. Thus, for the high-Q setup,the highest S@N ratio for the 10P14 line was reached,corresponding to an estimated detection limit of 0.6-ppbV ethylene in pure N2. Because we were close tothe optical saturation range on this line, the corre-sponding minimum absorption coefficient for the PAcell is better for the 10P10 line. The value of amin 51.6 3 1028 cm21 for this line and the high-Q setup andagrees well with earlier results obtained by Sigrist4and Meyer and Sigrist.6 This detection limit couldbe further improved by the use of microphones withhigher sensitivity, multipath cells, etc. However, itcannot be substantially increased by a higher pulseenergy.The entire profile of the PA resonance signal could

be determined with just one single laser shot. Thusthe experiment was not sensitive to resonance fre-quency changes because of temperature drifts, etc.Therefore very high-Q resonators can be used.Bernegger Sigrist5 and Meyer and Sigrist6 used a

more sophisticated method for the analysis of multi-component samples. They tuned the cw CO2 and COlasers and measured several different lines one afteranother. Thus cross references are possible and thebackground signal, which is the same for these lines,can be subtracted. This extension to several laserlines yields better detection limits and selectivity,although the time for one full measurement increaseswith the number of lines. This would also be thecase with the pulse technique for multicomponenttrace gas measurements with line-tunable lasers.However, if the signals are relatively large and ifaveraged measurements are not needed in order toachieve excellent S@N ratios, only one pulse per laserline is required for obtaining the full information.Then the measurement time would be essentiallylimited by the time needed to change CO2 laser lines.The highest sensitivity for ethylene detection re-

ported so far is that by Harren et al.,20 who reached apractical detection limit of,6 parts in 1012 by volume,which corresponds to an absorption coefficient of theorder of 1.8 3 10210 cm21. The authors used a smallresonant cell excited in its first longitudinal modeinside the cavity of a CO2 waveguide laser operatingat 100 W.

6. Conclusion

We have demonstrated that, in pulsed-laser PA spec-troscopy, by using open high-Q acoustic resonatorsthe sensitivity levels reported in the literature forcontinuously excited PA detectors can be reached.The noise that is due to window absorption, environ-mental sound sources, or gas flow is suppressed to theelectronic noise level. Therefore our open system issuitable for continuous trace gas analysis, as nowindows are needed, which easily degrade or adsorb

species, causing additional noise. This drasticallyimproves gas sampling. Moreover, the setup can beused as a closed system in the flow-through mode forcalibration purposes and for the analysis of toxicgases, resulting in a substantial reduction of theproblems caused by windows. The measurementtime can be reduced significantly by the application ofsynchronized sampling. The resonance tracking sys-tem, combined with pulsed light sources, may be usedfor trace gas monitoring purposes, when fast responseto concentration changes is necessary.

Financial support of this research work by theDeutsche Forschungsgemeinschaft, the Fonds derChemischen Industrie, and the European Union1PHARE-ACCORD program, contract H 9112-04762 isgratefully acknowledged. Moreover, the authors ex-press their gratitude to I. Gaspar for his valuabletechnical support during the measurements with theresonance tracking system and to Stefan Schafer forhis help in correcting the manuscript.

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pulsed-laser excitation of acoustic modes in open high-q photoacoustic resonators for trace gas...

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