Photoacoustic spectroscopy of C_2H_4 with a tunable waveguide CO_2 laser

Photoacoustic spectroscopy of C2 4 with a tunablewaveguide CO2 laser

Ari 6 lafsson, Mads Hammerich, and Jes Henningsen

A photoacoustic gas spectrometer using a wave-guide CO, laser, tunable over 500-MHz windows in 70lines, is described. The spectrometer is used for mapping Doppler-limited spectral signatures of ethyleneand for measuring pressure-broadening rates for collisions with N,, Ar, and He. A total of 41 observedtransitions are assigned to the V7, v,,, and v4 bands of normal ethylene and to the U7 band of the "C"CH4isotopomer.

I. Introduction

Photoacoustics with CO2 lasers has long been used fortrace-gas detection in ambient air and a thoroughreview of work in this field has recently been given bySigrist et al.' Trace gases absorbing in the 10-gimrange can be identified through their differentialabsorption in different lines of the CO2 laser, and atthe same time the relatively high laser power inconjunction with the use of resonant photoacousticcells allow for high sensitivity. The best result re-ported so far is that of Bicanic et al.,2 who reached adetection limit for ethylene of 6 parts in 102,corresponding to an absorption coefficient of theorder of 10- cm-'.

The ultimate sensitivity is reached if monitoring isperformed at ambient pressure, where the acousticproperties of the resonator are favorable, and wherethe large pressure-broadened linewidths frequentlyimply contribution from numerous individual lines tothe absorption coefficient. Under such circumstances,the absorption coefficient is essentially constant in-side the tuning window around each CO2 line, and itcan be probed at the CO2 line center so that thelimited tunability in each line is of no concern.

However, the price paid to optimize the sensitivityis a reduction in selectivity, as all interfering mole-cules that have lines within 5 GHz from the

A. 61afsson is with the Science Institute, University of Iceland,Dunhaga 3, 107 Reykjavik, Iceland. M. Hammerich is with thePhysics Laboratory, H. C. 0rsted Institute, Universitetsparken 5,DK-2100 Copenhagen 0, Denmark. J. Henningsen is with theDanish Institute of Fundamental Metrology, Building 307, Lund-toftevej 100, DK-2800 Lyngby, Denmark.

Received 2 July 1991.0003-6935/92/152657-12$05.00/0.C 1992 Optical Society of America.

probing frequency will contribute to the signal. Asignificant improvement in selectivity is obtained ifthe gas is probed at a reduced pressure, where thelinewidth approaches the Doppler limit of typically

100 MHz. Under these conditions the tunabilitywithin a single line becomes relevant. In 1974 Abrams3demonstrated 1200-MHz tunability in the strongestline 1P20, and recently 500-MHz tunability hasbeen reached in more than 80 lines.4 If we takeadvantage of this extended tunability, a spectralsignature within a single window may lead to theunambiguous identification of the trace molecule.5

The aim of this study is to demonstrate mapping ofthe spectral signatures of the medium-sized moleculeC2H4 in the windows of a 500-MHz tunable wave-guide CO2 laser, and the measurements of pressure-broadening parameters for selected lines. Such map-ping has been done for CH30H by Inguscio et al.6 andTang et al.,7 for CHCN by Kornilov et al.,8 and for 03in a few lines by Menzies.9 Mapping of absorptioncenters in single windows of the CO2 laser has beendone for SF6 by Beterov et al. and Lerberghe et al.,"and for (H2CO), and OCS by Lyszyk et al.'2

The choice of ethylene is motivated by its biologicaland environmental impact. As a plant hormone itregulates plant processes, hinders growth, and speedsup the withering of leaves and the ripening of fruit. 3

Mehlhorn and Wellburn suggested that ethylene alsoplays a role in the forest decline process.4 In anenvironmental context, ethylene is important as aprecursor for smog formation. Meyer and Sigristmeasured ethylene concentrations in the streets ofZuirich and correlated the concentration peaks of 50parts in 19 to the traffic rush hours. 5 When measur-ing the exhausts of motor vehicles directly, theyfound ethylene concentrations of a few hundred partsin 106. Nelson and Quigley6 analyzed the hydrocar-

20 May 1992 / Vol. 31, No. 15 / APPLIED OPTICS 2657

bon composition of exhausts from gasoline-fueledvehicles and found that ethylene and acetylene eachaccount for 20% (volume) of the total nonmethanehydrocarbon emission. Ethylene is thus an idealcandidate for the monitoring of hydrocarbon emis-sion from street traffic.

II. Experiment

The optical setup is shown in Fig. 1. The CO2 laser is apyrex waveguide laser, similar to the one described inRef. 17, tunable over 420-500 MHz in any of the 70strongest lines. The grating is mounted on a motor-ized rotation stage and a motorized translation stage,with the position of both electronically encoded. Thelength of the laser resonator can be varied over a 5-cminterval as required to keep the length optimal as theline selection is changed. 4 ' 8 Tuning within a line isachieved by moving the grating with a piezoelectrictransducer. At line center the average output powervaries from 800 mW for the strongest lines to 200mW for the weakest fully tunable lines.

The sample cell is constructed with Teflon as wallmaterial.'9 The gas port is fitted with a stainless-steelvalve and all joints in the vacuum system are sealedwith grease-free Viton 0 rings. The optical access tothe cell is through ZnSe Brewster windows, which aremounted on glass tube holders with cementless opti-cal contact. The optical path length within the cell is30 cm, allowing us to use the cell for linear absorptionmeasurements for the stronger lines.

The open acoustic resonator is a 12-mm i.d. by160-mm polished stainless-steel tube with a single1.27-cm BrUel & Kjoer condenser microphone of type4165 mounted at the pressure maximum at thecenter. The microphone is modified for increasedback ventilation and is followed by an impedancetransformer mounted on the tube. To avoid arcingunder reduced pressure operation, we bias the micro-phone with 27 V rather than the specified 200 V.Around the operating pressure of 10 mbars, the Qvalue of the resonator is 10.

A small nonresonant photoacoustic cell filled withCO2 at a pressure of 5 mbars is used to mark the zerooffset for the laser frequency. At the same time thiscell serves to reveal any departure from single lineand single mode behavior of the laser. Such devia-tions will reveal themselves as additional structures

<1 /BS

Fl CO2waveguidelaser

D2Li~~~CE

Sample cell

Ref. cell

in the signal from the reference cell long before theycan be seen in the power profile.

Figure 2 is a schematic diagram of the vacuumsystem. Pump P1 is a 50-L/min turbomolecularpump that ensures hydrocarbon-free vacuum. P1 isbacked by a two-stage rotary vane pump P2; withclean walls the ultimate pressure is 10-' mbar. Thethree pressure gauges attached to the system are aPenning cold-cathode transducer MI to monitor thedegassing rate of adsorbates, a capacitance manome-ter M2 to monitor the working pressure up to 10mbars, and a piezoresistive pressure transducer M3to monitor the pressure > 10 mbars. The mixingchamber has five gas inlets that are fitted withmotorized dosing valves, so mixing can be performedeither by hand or by computer control. Two inlets arereserved for the N2 buffer and the gas-mixture reser-voir respectively, leaving three ports for sample bot-tles.

III. Data Analysis

In this section we treat the generation of a frequencyaxis for the spectra, the normalization of the photoa-coustic signals, and the least-squares method forfitting Voigt profiles to the data and for extractingphysical parameters.

A. Frequency Calibration

To establish a linear frequency axis, we have devel-oped a technique for self-calibration that is accurateto within 1% of the free spectral range. As a firststep we generate an axis 4j, which is linear in thegrating translation, by fitting the power profile to theperiodic function

P = A + B sin l,

where * is a second- or third-order polynomial in thepiezo voltage. The linearization procedure is assistedby the additional requirement that the photoacousticpeaks from the reference cell be periodic in qi. Next,data from different periods are superimposed by

A0

Fig. 1. Photoacoustic spectrometer with sample cell; referencecell; beam splitter BS; and detectors D1 and D2.

Fig. 2. Vacuum system with turbomolecular pump, P1; rotaryvane backing pump, P2; motorized dosing valves for gas inlet,D1-5; and pressure gauges, M1-M3.

2658 APPLIED OPTICS / Vol. 31, No. 15 / 20 May 1992

- - - sGs7

1

I&

introducing a i axis defined by

= mod

A preliminary frequency axis is obtained by scalingthe period to one free spectral range, reduced by afrequency pulling factor, and by locating zero offset atthe center.

This procedure does not take into account thattuning may be nonlinear" and that the maximum ofthe gain profile will exhibit pressure shifts of < 100kHz/Torr.2 0 The preliminary frequency assigned tothe reference peaks is blue-shifted by an amount thatin severe cases may reach 30 MHz. In contrast, acareful study of CO2 absorption wings showed thatthe tuning edges are located symmetrically withrespect to zero. To accommodate both of theseobservations we subject the frequency axis to afurther second-order transformation, which leavesthe tuning edges unaffected, but shift the frequencyof the reference peaks to zero.

We refer to the data sets as unfolded when they aredisplayed as collected, i.e., as functions of the piezovoltage. After the preprocessing frequency self-calibration and stacking of the free spectral ranges,we refer to the sets as folded data, displayed asfunctions of frequency.

A set of unfolded and folded data is shown in Fig. 3.In this particular case the preliminary frequency

V

0

P.

0

1000

800

600

400

200

0

n02

,

44

_ I

M 0.08

0

0 g 0.04

0.02

n n

offset assigned to the reference peak was 8 MHz. Theaccuracy of this self-calibration procedure is tested bycomparing a large number of measured offset frequen-cies for ethylene with the corresponding offsets asdetermined by saturated absorption spectroscopy andheterodyning." For lines inside the tuning windowthe deviation is typically < 5 MHz, which we discussfurther in Section IV.

B. Normalization of Photoacoustic Signals

For samples with optical thickness a°Lcell < 1%, thenormalization is performed with the almost unper-turbed transmitted power profile P, as measured byD2. However, if the beam suffers appreciable attenua-tion when passing through the cell, the resonator ispumped harder at the front end than at the trailingend and the transmitted power is too low for thenormalization purpose. As a better approximation weuse the power P at the center of the cell, whichaccording to Beers law is given by

PC = (Pi P)" 2 . (1)

The reference power Pr as measured by D1 is propor-tional to the input power to the cell Pi, but theproportionality constant is line dependent and gener-ally unknown. However, if the signal contains enoughstructure so that the sample is optically thin some-

;4V

0

V

1-

+,

U

V

+0

xvezo voltage V AUU -200 -100 0 100 200Piezo voltage (V) Frequency (MHz)

Fig 3. Left: data set displayed as function of piezo voltage, showing the photoacoustic amplitude and phase for the sample cell and the CO,reference cell, and the transmitted and reference power signals (top frame). Right: same data set after the preprocessing frequencyself-calibration and stacking of free spectral ranges.


U.UU

where in the tuning window, then the quantity

P,(v)g() Pr(V)

will have a maximum gm. such that

Pi gm,, Pr.

assuming proportionality between the input and ref-erence powers, we get

(2)

(3)

The normalization procedure is especially critical forthe linewidth measurements, as all errors in thenormalization power level will affect the shape of themeasured line profile.

A spectrum for a sample with an optical thicknessof the order of 1 is shown in Fig. 4. The photoacousticsignal, shown in the lowest part of the figure, hasbeen normalized with the power level halfway insidethe cell. The middle frame contains the linear absorp-tion spectrum (see Subsection III. c., below). Thewidth of the two profiles is the same, showing that thenormalization procedure can cope with an opticalthickness of at least 1.

C. Linear Absorption Measurements

Although photoacoustics is several orders of magni-tude more sensitive than linear absorption with a30-cm absorption path, the latter is needed for cali-brating the photoacoustic response, as well as forcorrect power normalization for the strongest absorb-ing lines.

With the two power signals P, and P,. we have thetools to determine the absorption spectrum to withinan arbitrary additive constant. Using Beers law and

a

00,0

800

600

400

200

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0.02

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-60

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n LX-200 -100 0 100 200

Frequency (MHz)

a

0

P:4a

0

Co

Fig. 4. Photoacoustic (PA) spectrum, bottom, and linear absorp-tion spectrum, center, for a sample with maximum optical thick-ness - 1. Top frame shows the transmitted and reference powersignals used for normalizing the photoacoustic spectrum and forproducing the linear absorption spectrum.

[P,(v)lInI,_ = In G - a(v)L, (4)

where G is the proportionality constant

G = Pi (5)

For samples with isolated narrow lines, so thatsomewhere in the tuning window the optical thick-ness is low enough, we get G g which is adirectly measurable quantity. Even if G is not directlymeasurable the usefulness of the measurement is notreduced, because the least-squares routines (see sub-section D., below) will fit a number of Voigt profilesplus a constant background signal, and thus willevaluate G.

One problem in this method is associated with theetalon nature of the beam splitter that produces P,.The beam splitter consists of a 3-mm-thick ZnSe platethat is mounted close to the Brewster angle; thepower reflection coefficient 11G is therefore slowlychanging as the laser is swept over the tuning win-dow. This phenomenon shows up as a tilted baselinein the measured absorption spectra. The frequencydependence of 1/G is described with an Airy function,and the steepness of the baseline is determined by thegradient of the Airy function at the working point.Changes in the reflection coefficient of < 3% betweenthe tuning edges of the laser are often seen. Thesechanges correspond to an apparent shift in the absorp-tion coefficient of 10-3 cm'1.

D. Fit to Voight Profiles

To extract the physical parameters, we fit the foldeddata to the appropriate number of Voight profiles22

with complex amplitudes and a constant complexbackground. The four parameters fitted for each lineare the frequency offset v, the strength A, theLorentz width AvL, and the signal phase. Thus, if M isthe number of lines used in the analysis, a total ofM x 4 + 2 parameters are fitted, with the last two asthe amplitude and phase of the background signal. ADoppler width AVD has to be specified for each line.

The Voight profiles are evaluated with the complexerror function w (z):

a(v) = A "VI (r In 2)/ Re {w(z)1] (6)

w(z) = exp(-z4){1 - erf(-iz)},

Z = [(V - V) + i / AVJ (InP 2 X

2kT In 2 /2

AVD = VO MC2 )1/

nA = rr^U- -

(7)

(8)

(9)


us,,hi I, III III III III II, I... 11"111 1111111 -111 11 11 11 id

o l y l I~~~rr ....... ...... .

mu

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Z.

�v 7

I .

: .I

v

H ~~~~~~~~~~tion strength:

A = yA.

The response coefficient y is pressure dependentbecause of the influence of pressure on the acousticallosses in the resonator. The acoustical strength re-ceives all of its pressure dependence through theresponse coefficient.

Numerical truncation problems develop in Eq. (7) ifthe modulus of z is too large, so that erf( -iz) ap-proaches 1. The z plane has therefore been dividedinto two parts, so that for IjzI < 3.5 we use Eq. (7) andfor I z Ž 3.5 we use an asymptotic expansion forW(z) :2

WZ) 1 if , 0.5 0.75 1.8751.w 7z -i--2 [1 +- + Z6J

H(E) G)H

Fig. 5. Vibrational deformation of the C molecule for themodes v, v,,, and v. Out-of-plane displacement, plus and minus;in-plane motion, arrows.

The real part of the leading term in this expansiongives the Lorentz form.

If we have data only on the far wings of a line, theinformation about the Lorentz width and the absorp-tion strength degenerate, as the wing form can beexpressed as a function of the product A (AVL )2:

The quantity within the brackets in Eq. (6) satu-rates to 1 at high pressure and zero frequency offset.The multiplier A in front of the bracket is a measureof the absorption strength. It is independent ofpressure, as both the number density n and theLorentz width AL are proportional to the pressure.The normalized photoacoustic signal is proportionalto the absorption coefficient ut, with a complex propor-tionality constant determined by the acoustical envi-ronment, the microphone, and the relaxation rates inthe gas sample. We define an acoustical strength A forthe photoacoustic line profiles, similar to the absorp-

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I I I I I I I I I I I I I I I I

ov)=an 1 A (AUL)2'~TAUL + (V Vfj (V _ V,)2 I V - VO »> AL. (12)

Thus the data contain information only about theLorentz width and the strength in the form of theproduct A (Avd 2 , and we cannot separate the two.

The fitting of the complex amplitudes A41 amountsto solving a set of linear equations, so these parame-ters have been separated from the nonlinear ones inthe procedure. The nonlinear parameters v and AVLare fitted with an iterative Gauss-Newton-typemethod, in which the linear parameters are updated

IP

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9R 9P IOR lopFig. 6. Maximum photoacoustic signals for different CO, laser windows, recorded at 10 mbars for 1% CH 4 in N2. Filled squares, theabsorption maximum corresponds to a line centered inside the- 500 MHz tuning window; circles, the line center cannot be reached. Tailsindicate the contrast in the spectra and reach down to the lowest signal level within each window. R/P, photoacoustic signal amplitudenormalized to laser power.


H

(10)

(1 1)

10

1

0.1

0.01

0.001

----------------------------------

------

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-200 0 200

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1.50 .,

1.00

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0.00 200

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0.00-200

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0 200

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. :f :

: * .~ . ,

0.10

0.08

0.06

0.04

0.02

n np;

0.04

0.03

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n-nn E

0 200 -200

0 200

1OP34

0 200

1OP28

-200 0 200

1OP22

0 200

Offset (MHz)Fig. 7. Photoacoustic window spectra for 1% C2H4 in N2 at 10 mbars; R/P, photoacoustic signal amplitude normalized to laser power.

after each step. For reasonably strong lines, residualimperfections in the self-calibration procedure lead toa maximum deviation of 3% around the turningpoints of the line profile.

IV. Application to C2 H4

A. -Spectral Signatures

Ethylene is a planar, nearly symmetric, prolate topwith a structure as shown in Fig. 5. The displace-

ments of the v4, V7, and v,0 vibration modes areindicated in the figure. The strong C-type V7 bandcovers the range 800-1100 cm-' with the Q branchpeaking at - 949 cm-', close to the 10P14 CO2 line.The weaker v,0 band is centered 826 cm-'. A fewlines in the IR forbidden v4 band gain strength fromclose resonances with V 7 levels.2 4

Montgomery and Hill25 studied the range 947.1-951.9 cm-' around the Q-branch peak in V7 by usinglinear absorption with diode lasers. They found a


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0.10

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0 200 -.

0.40

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-200 0 200

lopo. .. . .. .. . .

0 200

10R4

0 200

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0 200

-200

1.00

0.50

n n L

Offset (MHz)Fig. 7. continued

total of 169 resolved transitions in this range, corre-sponding to an average density of 1 line/850 MHz.There are several strong ethylene lines in the nearvicinity of the 10P14 CO2 laser line.26 When probed at1 atm these lines merge into a broad absorption bandwith an absorption coefficient at the 1P14 linecenter of at = 30 cm-' atm'1, which is approximatelyan order of magnitude higher than that found in anyother CO2 laser line for ethylene.2 7None of these linecenters can be reached with our limited tunability.

Figure 6 shows the window spectra for 1% C2H4 inN2 at a total pressure of 10 mbars compressed to alarge-scale discrete spectrum. The filled squares referto spectra in which the absorption line center lieswithin our + 250-MHz tuning window. The circlesare used for spectra in which the ethylene line centeris outside the range of our laser so that only one wingof the line is seen. These spectra will show a strongpressure dependence because of the p2 scaling law forthe Lorentz wings. The tails indicate how structured


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-200 0 200

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-200 0 200

9P30

-200 0 200

9P16

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0.20

0.15

0.10

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0.50

0.40

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Offset (MHz)Fig. 7. continued

the spectrum is, with the lower tip indicating theminimum signal level in the window. The highestabsorption coefficient in the low-pressure spectra, at =0.95 cm-' (scaled to 100% ethylene), is found in the10R28 window.

The window spectra for 1% ethylene buffered withN, at 10-mbar pressure are shown in Fig. 7. We find aresolved line structure for ethylene in most cases andthe majority of the spectra have been fitted to Voigtprofiles. The extracted physical line parameters arelisted in Tables I and II together with offsets mea-

sured or calculated by other authors and their lineassignments.

The most reliable offset measurements are proba-bly those of Herlemont et al.," who used a wave-guideCO2 laser locked to the Lamb dip of the ethylene line,heterodyned against another laser locked to the CO,line center. For 12 lines located within the tuningwindow of our laser, the rms deviation between ouroffsets and those of Ref. 21 is 5 MHz, with thedominant contribution coming from two lines dif-fering by 9.6 and 11.4 MHz, respectively.


4.,

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S a'

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II

- - -

Table I. Line Parameters in the lOP CO, Laser Band for Absorption in 1% CH 4 Buffered with N, at 1 O-mbar Pressure. Transitions Belong to the BandUnless Otherwise Marked. Conversion from Acoustic to Absorption Strength Requires the Conversion Factor c = 1.7 10-3 cm-1/mV/W

Lorentz Acoustic AssignmentCO, Offset, Width, Strength, Offset,

Laser Av AVL A Transition AvLine (MHz) (MHz) (mV/W)a J' K.' K' - J" K.," K (MHz) Reference

1OP46 99 40 1.70 05 02 03 -06 03 03 107 24-141 42 0.41 25 04 21 -25 05 21 -143 24

1OP44 37 1.91 17 08 9/10-16 09 7/8 50 2409 00 09 -10 01 09 61 24

206 21 0.32 24 03 21 -25 02 23 220 241OP42 193 25 0.05

-106 38 0.031OP40 63 32 0.06

222 24 0.051OP38 -117 28 0.03

300 37 0.17 20 11 10/9-19 10 9/l10 314 241OP30 -105 27 0.13 -110 211OP28 435 45 1.76 02 01 02 -02 02 00 420 301OP26 109 55 1.64 06 01 05 -06 02 05 106.3 211OP24 149 25 0.40 21 06 15 -20 07 13 149.4 21

280 - - 21 06 16 -20 07 14 308 241OP22 32 34 0.06 33.5 21

-231 20 0.021OP20 187 (81) (0.19) 04 00 04 - 04 01 04' 196.6 21,29

-248 (77) (0.09) 29 08 22 - 28 10 18d -258 24lOP18 80 47 0.10 20 01 19 - 20 02 19C 82.0 21,29

-207 - - -220 281OP16 -78 25 0.25 25 06 19 -24 07 17 -80.1 211OP14 268 42 1.02 28 01 27 -28 02 27 285.7 21

-434 36 5.90 21 01 21 -21 00 21 -476 241OP12 28 037 39 00 39 -39 01 39 108.1 21

105 28 0.37 39 01 39 -39 00 39 100.0 21-236 23 0.19 -259.6 21

lOP1O -98 40 1.48 05 00 05 -04 01 03 -97.5 21-243 20 04 16 -19 05 14 -283 24

1OP8 47 33 0.26 32 04 29 - 32 03 29 58.4 211OP6 -121 19 0.13 -100 28

aA is defined through Eq. (10).bTransition belongs to the v,0 band.'Transition belongs to the V7 band of the "C"2CH4 isotopomer of ethylene.dTransition belongs to the V4 band.

A total of 41 observed transitions have been as-signed. The majority of the assignments are obtainedfrom a recent rotation-level compilation of the groundstate and the 4, V7, and v modes by Cauuet et al.2 4

The compilation is a model calculation that is basedon the experimental work of Herlemont et al., 2 1 2 8

extensive Fourier transform IR measurements per-formed at Universit6 Pierre et Marie Curie in Paris,and diode laser spectra from Namur.24 A few assign-ments and offset measurements originate from Her-lemont et al.28 and Vleeschouwer et al.,2 9 who usedlinear absorption methods with waveguide CO2 la-sers. One line assignment at a large offset is obtainedfrom Thi6beaux et al.,'0 who used a spectrometer withtwo broadband thermal sources heterodyned with aCO2 laser.

Two lines in the spectra are assigned to the forbid-den v4 band, one to the weak vl0 band, and two to the13C12CH4 isotopomer, which is present in the sample

in its natural abundance of 2.2%. The isotopic down-shift for the v7 mode is of the order of 3 cm-', which inthe 10P band of the CO2 laser corresponds to a shiftby less than two laser lines.

All of the stronger features in our spectra areidentified except for the medium-strength line in the9R10 window.

The linewidth analysis of the spectra gave a spreadof values for the Lorentz width from 19 to 55 MHz,not counting the anomalously large widths of 77 and81 MHz found in the 10P20 window (probably causedby unresolved features). The uncertainty in the widthdetermination is 3 MHz for isolated lines wellwithin the windows and is somewhat larger for linesoutside the windows. The apparent Lorentz widthcontains an 5-MHz contribution from the laserbandwidth.

In the windows 1P44 and 1P12 we are dealingwith almost degenerate transitions,2 ' 24 which we can-


Table II. Line Parameters In the OR, 9P, and 9R CO, Laser Bands for Absorption In 1% CH 4 Buffered with N, at 1O-mbar Pressure

Lorentz Acoustic AssignmentCO, Offset, Width, Strength, Offset,

Laser Au AOL A Transition AVLine (MHz) (MHz) (mV/W) J' K,,' K' - J" K,, K (MHz) Ref.

10R4 102 26 0.60 21 07 14 - 22 06 16 113 24-45 39 0.10

10R12 -573 40 2.76 10 03 07 - 10 02 09 -550 2410R16 -230 36 0.07

48 7 0.87 12 06 06 -13 05 08 426 24480 37 0.87 12 06 07 - 13 05 09 465 24

10R22 112 44 2.03 04 03 01 -03 02 01 111.4 2110R24 212 30 0.16 200 2810R28 -212 35 5.53 06 03 04 -05 02 04 -228 2410R34 -25 -15 2810R38 -278 24 6.02 09 03 07 -08 02 07 -307 249P36 330 48 0.61 27 04 24 -26 03 24 295 249P34 33 19 0.54 27 03 25 -26 02 25 32 24

302 43 3.85 09 08 01/02-08 07 01/02 299 249P30 109 26 0.71 22 10 12/13-22 09 14/13 116 249P24 -117 41 0.06

143 55 0.069P18 -59 24 0.90 24 07 17 -23 06 17 -63.1 21

209 38 0.12 34 03 31 -33 02 31 205 249P16 -215 25 0.11 21 15 06/07-22 14 08/09 -244 249R10 -21 22 0.81 -20 289R30 130 30 0.31 29 08 22 - 28 08 20' 132 24

'Transition belongs to the V4 band.

not resolve with our Doppler-limited technique. Thequoted values of offset, width, and strength then referto the combined spectral structure rather than toindividual transitions. A related situation is found inthe 10R16 window, where a doublet with a splittinglarger than the Doppler width is placed outside thewindow.24 The wing signature of these lines cannotreveal the doublet nature.

B. Pressure BroadeningTwo well-isolated lines in the 9P30 and 10P26 win-dows were chosen for measuring pressure-broaden-ing coefficients. The lines have been assigned thefollowing quantum numbers.

10P26: J' K,' K,'-J" K,' K," = 06 01 05-06 02 05;

9P30: J'K,,'K,,'-J"K,,"K,,"=221012/13-220914/13.

The results for N2 broadening of the line in the 9P30window are shown in Fig. 8, and a linear fit of theLorentz width versus pressure leads to

MHzAOL = 2.03 P+ 2.9 MHz. (13)

According to Ref. 24, the transition 22 6 18 - 22 5 18is placed at an offset of 680 MHz from the 9P30 linecenter. To minimize the disturbance of this line onthe Lorentz width estimates, we included it in theanalysis at the higher-pressure values.

The broadening coefficient cN, = 2.03 MHz/mbar is15% below the band-averaged value of 2.3 MHz/mbar

of Tejwani and Yeung.3 ' The constant term in Eq. 13is caused by the instrumental bandwidth. It has anuncertainty of several MHz, and from the presentresults we may state that it is below 5 MHz, a valuewhich has been corroborated by numerous linewidthmeasurements for CO2 and SO2.

Broadening of the ethylene line in the 1P26window has been measured by both photoacousticsand linear absorption for N2 broadening, and byphotoacoustics for broadening by He and Ar. Theresults obtained by the two methods for N2 broaden-ing, as shown in Fig. 9, agree well. The statisticaluncertainty is smallest for the photoacoustic data,because of the much better signal-to-noise ratio. All

N

._l

N.1

a0

100

50

A0 20 40

Pressure (mBars)

Fig. 8. N broadened Lorentz width as a function of pressure forthe V, 22 10 12/13-22 9 14/13 ethylene transition in the 9P30window.


9P30 window2% C2H4 in N,v, 22 10 12/13 - 22 9 14/13

..

N

_5s

1OP26 window *1% CH4 in N2 °

150 -v: J K. K,6 1 5 - 6 2 5 0

' 100:5

S 50

00

-1 0 -) 20 40 60Pressure (mBars)

80

Fig. 9. N broadened Lorentz width for the V7 6 1 5-6 2 5 CH 4line in the 10P26 window as measured with photoacoustics andwith linear absorption.

results are summarized in Table III. The noblegas-broadening rates disclose a slight dependence onthe mass of the atomic collision partner, but the valuefor Ar does not reach that of the diatomic N2 mole-cule, even though the Ar mass is higher.

The anomalously high residual linewidth of 20MHz found for the 10P26 data is not understood. Theline could be an unresolved doublet with a splitting ofthe order of 10 MHz, but notably that was notrecognized by Ref. 21.

C. Trace Detection

The line in 10R28 seems to be the best candidate fortrace detection of C2H4 at low pressure. It has thehighest measured absorption coefficient, and its -2 12-MHz offset is ideal for monitoring under conditionswith CO, interference. The l"C"2CH4 isotopomer canbe monitored on the lines observed in the 10P20 of1OP 18 windows. The former line is the stronger of thetwo, but the large linewidth suggests that it maycontain some admixture of a different line, probablybelonging to the normal isotopomer.

For the present spectrometer, which is not opti-mized for sensitivity, an estimate of the signal-to-noise ratio for operation at 10 mbars leads to adetection limit of 1 part per 106 for the normalisotopomer and 0.3 parts per 106 for 13C12CH4 . Animmediate improvement can be obtained by the use ofseveral balanced microphones, and the acoustic re-sponse coefficient can be improved by a modestincrease of the pressure to 20 mbars without sacri-ficing the spectral characteristics. The price paid forretaining the spectral information will be associatedwith the difference between the multiline absorption

Table fll. Broadening Rates for the Ethylene Line in the 10P26 Window

Broadening InstrumentRate Width Collision

(MHz/mbar) (MHz) Partner Method

2.53 ± .05 20 ± 3 N2 Photoacoustics2.41 ± .15 21 ± 6 N, Linear absorption1.76 ± .04 19 ± 3 He Photoacoustics2.21 ± .04 23 ± 3 Ar Photoacoustics

coefficient 30 cm-' observed in 10P14 at atmosphericpressure, and the single-line absorption coefficient

1 cm-' in 10R28 at the highest pressure that willstill allow for a characteristic spectral signature.

V. Conclusion

The photoacoustic spectrometer discussed above hasproved to be useful for the study of collision broaden-ing of molecular absorption lines that are in nearcoincidence with CO, laser lines. Although this re-quirement of near coincidence is a major limitation,there are also numerous advantages associated withour technique. Primarily, the feature of having theCO2 line centers as built-in frequency references,combined with the frequency self-calibration thateliminates the need for a reference laser to keep trackof the offset from the line centers, leads to a highaccuracy for the frequency axis. This accuracy isparticularly critical for molecules in which a highspectral line density dictates that measurements beperformed close to the Doppler limit to reduce overlapproblems.

A second advantage of our technique is associatedwith the high sensitivity of photoacoustic detection,which allows for measurements on weakly absorbinglines without the need for a long optical path length.Photoacoustics is a difficult technique from the quan-titative point of view, because the resulting signal isdetermined not only by the molecular absorptioncoefficient, but also by the molecular kinetic processesinvolved in the conversion of vibrational excitationenergy to heat, and by the acoustic properties of theresonator. Nevertheless, a careful comparison of lineprofiles for strong lines, in which linear absorptionmeasurements can be used in parallel with photoa-coustics, has shown that the two techniques give thesame result for the Lorentz broadening.

This research was supported by the Danish ScienceResearch Council under grants 5.17.4.6.19 and5.17.4.1.23.

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Photoacoustic spectroscopy of C_2H_4 with a tunable waveguide CO_2 laser