Technique of laser calibration for wavelength- …cetegen/CGDRL/Cetegen_publications/70.pdfTechnique of laser calibration for wavelength-modulation spectroscopy with application to

Technique of laser calibration for wavelength-modulation spectroscopy with application

to proton exchange membrane fuelcell measurements

Ritobrata Sur, Thomas J. Boucher, Michael W. Renfro,* and Baki M. CetegenDepartment of Mechanical Engineering, 191 Auditorium Road, Unit-3139,

University of Connecticut, Storrs, Connecticut 06269, USA

*Corresponding author: [email protected]

Received 30 September 2009; revised 25 November 2009; accepted 25 November 2009;posted 30 November 2009 (Doc. ID 117797); published 21 December 2009

A diode laser sensor was developed for partial pressure and temperature measurements using a singlewater vapor transition. The Lorentzian half-width and line intensity of the transition were calibrated forconditions relevant to proton exchange membrane (PEM) fuel cell operation. Comparison of measuredand simulated harmonics from wavelength-modulation spectroscopy is shown to yield accuracy of �2:5%in water vapor partial pressure and �3 °C in temperature despite the use of a single transition over anarrow range of temperatures. Collisional half-widths in air or hydrogen are measured so that calibra-tions can be applied to both anode and cathode channels of a PEM fuel cell. An in situ calibration of thenonlinear impact of modulation on laser wavelength is presented and used to improve the accuracy ofthe numerical simulation of the signal. © 2009 Optical Society of America

OCIS codes: 300.1030, 280.4788.

1. Introduction

Tunable diode laser based sensors provide an excel-lent tool for in situ measurement of physical pa-rameters, such as partial pressure of species andtemperature, in challenging environments such ascombusting flow fields and fuel cell flow channels.In a typical experiment, a laser is passed throughan absorbing medium and the laser wavelength isscanned over an absorption transition. The transmis-sion of the laser is measured to determine absorptionby the gas medium, which is then related to gas con-centration or temperature when multiple transitionsaremeasured.When the light absorption by the gas islarge, a simple ratio of the laser powerbefore andafterabsorption can be utilized. However, in many casesadditional modulation of the laser is used to either re-ject noise or discriminate from background transmis-

sion variations, thus enhancing the sensitivity of theabsorption measurements. Modulation spectroscopymethods have been used widely in various applica-tions, ranging from atmospheric pressure monitoringof trace gases [1] to simultaneous measurement oftemperature, pressure, and velocity in shock heatedoxygen flows [2] and hydrocarbon combustion [3–5],and also have long been recognized as an importanttool in the study of electronic andmolecular structure[6]. The theory of tunable diode laser absorptionspectroscopy and the objective of this study are firstpresented in the following sections.

A. Absorption Spectroscopy

Light transmission through an absorbing mediumfollows the Beer–Lambert law [7] as

II0

¼ expð−ZL

0

α½νðtÞ�dlÞ; ð1Þ0003-6935/10/010061-10$15.00/0© 2010 Optical Society of America

1 January 2010 / Vol. 49, No. 1 / APPLIED OPTICS 61

where I0 is the beam intensity before transmission, Iis the beam intensity with absorption, αðatm−1 cm−1Þis the absorption coefficient that is dependent on in-stantaneous frequency νðtÞ, partial pressure Ps, andtemperature T. The integration is taken over thetotal optical path length L of the absorbing gasmedium.The absorption coefficient of the absorbing species

can be expressed as [8]

α ¼ Ps × SðT; ν0Þ ×

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi�lnð2Þπ

�r

ΔνD=2× VðX ;YÞ; ð2Þ

where the Voigt line shape function, V, is a convolu-tion between Gaussian and Lorentzian line shapesgoverned by a Gaussian (Doppler) broadening term,X ¼ 2ðν−ν0Þ

ΔνD

ffiffiffiffiffiffiffiffiln 2

p, and a Lorentzian (collisional) broad-

ening term, Y ¼ ΔνLΔνD

ffiffiffiffiffiffiffiffiln 2

p. SðTÞ is the temperature

dependent line intensity,ΔνD is the Doppler FWHM,ΔνL is the Lorentzian FWHM, and ν0 is the line cen-ter frequency. The Voigt line shape function can bewritten as the real part of the complex probabilityfunction [9]

VðZÞ ¼ Re��e−Z2

�1þ 2iffiffiffiπp

ZZ

0

et2dt

��; ð3Þ

where Z ¼ X þ iY.The line intensity is given by [8]

SðTÞ ¼ SðT0ÞQðT0ÞQðTÞ

�1 − exp

�−hc ν0

kT

��1 − exp

�−hc ν0

kT0

��

× exp��

hcE00

k

��1T0

−

1T

��; ð4Þ

where T0 is the reference temperature (296K), Q isthe partition function of the absorbing gas, and E00 isthe energy of the lower state of the transition (listedin the HITRAN 2008 database [10]). The Dopplerbroadening half-width can be easily expressed as afunction of temperature and molecular weight, M,of the absorbing species by assuming a Maxwell–Boltzmann distribution, which can be written as [8]

ΔνD ¼ 7:162 × 107ν0�TM

�0:5

; ð5Þ

where T is in K. The Lorentzian half-width can beexpressed as a function of the self-collision HWHM(γself ), foreign gas collision HWHM (γforeign), partialpressure of the absorbing species (Ps), and total pres-sure of the sample (P) as

ΔνL ¼ 2

�Psγself

�T0

T

�nf þ ðP − PsÞγforeign

�T0

T

�nf�;

ð6Þ

where nf is the exponent of temperature dependence.Combining Eqs. (1)–(6), the absorption of a laser of

any given wavelength can be computed as a functionof temperature, pressure, and chemical compositionfor a path length L. The laser can be slowly tuned sothat the absorption, I=I0, is measured at each fre-quency, ν, to resolve the absorption line shape andthe partial pressure of the gas can be determined. Al-ternatively, modulation of the laser frequency can beused such that themeasured absorption signals are aconvolution of the absorption line shape and the lasermodulation function.

B. Modulation Spectroscopy

Laser current modulation methods are classified asbeing either wavelength-modulation spectroscopy(WMS) or frequency-modulation spectroscopy (FMS).In both cases, a modulation is provided to the lasercurrent controller, which modulates both the laserintensity (intensity modulation, IM) and the wave-length (frequency modulation, FM). Wavelength-modulation techniques are reported to have adetection limit of 10−4 to 10−5 fractional absorption[11,12]. Several new methods of FM spectroscopy,such as two-tone [12–16] techniques, have extendedthe detection sensitivities to 10−7–10−8 [17]. The dis-tinction between the WMS and the FMS techniquesis that the modulation depth frequency for WMS ismuch lower than the half-width of the absorptionprofile, while for FMS it is much greater than the ab-sorption half-width. Themethod ofWMSwas demon-strated for trivalent Nd using an electro-opticallytuned, wavelength-modulated CW dye laser experi-mentally by Tang and Telle [18]. FM spectroscopywas developed by Bjorklund [19] with a single-axial-mode dye laser. The collected signal is filteredat the modulation frequency or at harmonics suchthat the absorption at individual wavelengths isnot resolved, but instead a convolution of the lasermodulation and absorption signal is measured.There has been significant research involving thetheoretical prediction of harmonics of the absorptionprofiles [17,20–28]. Reid and Labrie [20] performed aseries of experiments and demonstrated close agree-ment at low modulation depths with the theoreticalexpressions for harmonics of Lorentzian and Gaus-sian line shapes derived by Wahlquist [21], Arndt[22] andWilson [23]. Cassidy and Reid [11] discussedseveral factors influencing the detection sensitivitiesand identified the important role of residual ampli-tude modulation (RAM). Theoretical expressions forharmonic line shapes including the effects of ampli-tude modulation and varying modulation depthswere obtained by Philippe and Hanson [24]. Suppleeet al. [25] put forward a general theory for frequencyand WMS techniques and also for limiting casesof modulation indices in terms of Bessel series

62 APPLIED OPTICS / Vol. 49, No. 1 / 1 January 2010

expansions. Schilt et al. [26] presented a simple the-oretical model of WMS on a Lorentzian absorptionline for a combined intensity and FM with an allow-able arbitrary phase shift between them, character-istic of DFB diode lasers. Using Fourier analysis,Kluczynski et al. [27,28] developed and implementeda theoretical description of WMS that includes thenonlinear IM, IM-FM phase shift, the nonlinearIM associated with the sinusoidal current modula-tion and wavelength dependent transmission inharsh conditions. Li et al. [17] extended the formula-tion to large modulation depths for measurements inhigh pressure gases. In all these studies, an attempthas been made to semianalytically describe the pro-blem. In the current study, a full-scale numericalsimulation is performed for the convolution ofmodulation and absorption and this simulation isfitted directly to the obtained experimental profilesby a Levenberg–Marquardt nonlinear optimizationroutine.A correction for laser intensity variation by normal-

ization of the WMS signal using harmonics of thesame was first presented by Fernholz et al. [29]. Thismethod was used by Li et al. [17] and Rieker et al. [30]to develop a sensitive high temperature and pressuresensor for temperature and water vapor concentra-tion. The current study also implements a similar nor-malization scheme to correct for laser intensitybaseline variations. This technique ensures thattheabsorption signature obtained is invariant of laseralignment and photodetector gain. The theoreticalapproach to address signal variations due to these ef-fects can be complicated, as discussed in previouswork [17,29,30]. An alternative approach to the dataanalysis is presented in this article. Our approach in-volves fitting a numerically simulated WMS signa-ture versus sample domain to the raw data withoutmaking substantial efforts to numerically correctfor the nonlinearity in the laser amplitude modula-tion and the baseline. This approach is applied tomeasurements of water broadening in air and hydro-gen for application to single line measurements ofwater concentration and temperature in proton ex-change membrane (PEM) fuel cells.

C. Specific Goals

The main objective of the experiments presentedhere is to obtain quantitative distributions of watervapor partial pressure and temperature in a typicalPEM fuel cell at the cathode and anode side gas chan-nels in the presence of air and hydrogen, respectively,for a typical temperature range of 65 °C–85 °C. Basuet al. have previously demonstrated measurementsof water concentration and temperature on the cath-ode side of a PEM fuel cell using direct absorptionspectroscopy [31]. This previous attempt assumedzero absorption at the laser scan extremities, i.e.,the laser ramp peak, which was found to producesubstantial error. Thus the absorption at the ramppeak needs to be considered, which is made possiblethrough the current WMS technique. In the present

study, measurements are made in both the cathodeand anode sides with consideration of the effectof air and hydrogen on collisional broadening usingthe WMS technique with a modified analysis. Thewater vapor spectral transition line at 1469:637nmwas selected using the HITRAN [10] database in theexperiments, keeping in view the high sensitivity ofthis line to both partial pressure and relatively goodsensitivity to temperature. In this method, the diodelaser is excited by a sinusoidal current modulationwith linearly varying DC offset. The generated laserbeam passes through the sample absorbing media(whose constituents are to be measured) where theintensity is attenuated and an absorption signatureis obtained by a photodetector. A LabVIEW-basedsoftware lock-in amplifier is designed to extract thesecond (2f ) and first (1f ) harmonics of the absorptionprofile simultaneously corresponding to the refer-ence frequency (modulation frequency in this case).A ratio of the 2f and 1f signals is taken to eliminatethe resultant profile change due to beam alignmentand beam steering effects. The profile thus obtainedis the raw data that can be analyzed to obtain themeasurement quantities of partial pressure and tem-perature. In the current study, a full numerical simu-lation of the modulation spectroscopy signal isgenerated and fitted to the experimental results. Atechnique to account for the nonlinear modulationof the laser at high frequencies is described. The re-sulting technique can be applied to measurements onboth the anode and cathode sides of a PEM fuel cellwith accuracies of�2:5% in water vapor partial pres-sure and �3 °C in temperature.

2. Experimental Setup

An NEL distributed feedback (DFB) diode laser(NEL NLK1S5G1AA, center wavelength ¼1470nm) was used for the experiments. It wascontrolled by a Thorlabs thermoelectric cooler(TEC2000) and a Thorlabs laser diode controller(LDC500), as shown in Fig. 1. In these experiments,the laser radiation is directed through the absorbingmedium using a fiber-coupled collimator, and thetransmitted beam is subsequently intercepted by aphotodiode. The laser diode current is modulatedby a voltage from the laser control and data acquisi-tion computer. The IM produced as a result of in-jection current modulation in the diode laser isnonlinear as described previously by Kluczynski etal. [27,28] and Li et al. [17]. The IM was consideredas a composite of a linearly increasing part and twoIM harmonics in these studies. The IM features canbe directly measured along with all the nonlineari-ties in an actual diode laser by using data with noabsorption. The background intensity plot of sucha curve is shown in Fig. 2 and can be expressedas I0 ¼ gðtÞ.

In the previous analyses by both Kluczynskiet al. [27,28] and Li et al. [17], the FM was assumedto be a pure sinusoidal modulation around a meanunmodulated frequency as


νðtÞ ¼ ν0 þ a cosðωtþ ψÞ; ð7Þ

where a is the modulation depth and ψ is the IM-FMphase shift [17,26–28]. In the current study, a voltagesignal is sent to the laser current controller that con-sists of a ramp with slope κ and a sinusoidal modula-tion of amplitude vm as

VLDC ¼ κtþ vm sinðωtÞ; ð8Þ

where κ is the slope of the linear DC offset, vm is thevoltage amplitude corresponding to the modulationdepth (m), and ω is the modulation frequency.However, at higher frequencies required for tem-

poral resolution in the fuel cell experiments, thelaser wavelength does not respond linearly and theamplitude of the sinusoidal variation is decreasedsuch that the laser wavelength is found to follow

νðtÞ ¼ Cðκtþ εvm sinðωtþ ψÞÞ; ð9Þ

where C is the calibration function relating the vol-tage to the laser frequency and ε is a factor that in-dicates the degree to which the laser wavelengthcannot follow the modulation command. For slowmodulation, ε approaches unity and for fast modula-tion it approaches zero. The calibration function, C,is determined from steady state calibration of the la-ser wavelength as discussed in the next section, andthe modulation factor, ε, is determined experimen-tally during calibration absorption experiments asshown in Fig. 3 and described subsequently.

During experiments with absorption, Eq. (9) isused along with Eqs. (1)–(6) to compute a simulatedabsorption signal using a Voigt profile generationroutine with the Humlicek algorithm [9]. From this

Fig. 1. (Color online) Schematic for the calibration experiments.

Fig. 2. Modulated ramp for WMS. Measured intensity includesno absorption.

Fig. 3. (Color online) Calibration of diode laser: instantaneouslight frequency—frequency at ramp peak (gigahertz) versus volt-age sent to the laser diode controller.


simulated absorption signal, a software lock-in am-plifier program in LabVIEW, described later is usedto predict 2f =1f WMS curves. This same routine wasused to process the experimental measurements andparameters of the simulation were varied while fit-ting the simulated 2f =1f signal to the experimentalresults.

A. Diode Laser Wavelength Calibration

The wavelength calibration of the diode laser wasperformed by a fiber optic etalon device along witha fiber-coupled spectrum analyzer while supplyinga linearly increasing unmodulated voltage signalto the diode laser current controller [vm ¼ 0 inEq. (9)]. The etalon device consists of a 2 × 2 fiber op-tic coupler in which one arm on one side of the cou-pler is connected to one arm on the other side. Thelaser enters this setup from the free arm at theone side and the output beam with interference pat-terns is obtained from the opposite free end. The freespectral range of this device is 4:27 × 10−4 nm. Thefine wavelength spacing was obtained from thefringe spacing of the interference peaks. The lightfrequency distribution has a nonlinear variationwith the voltage sent to the laser diode controlleras shown in Fig. 3. In choosing modulation depthsfor experiments, vm was selected such that the mod-ulation was around 2.2 times the HWHM of thewater absorption profile as suggested by Reid andLabrie [20] to maximize the signal. With an equalDoppler and collision HWHM (γD ¼ γL ¼ 1GHz), amodulation depth of 3:5GHz is optimum. FromFig. 3,this depth corresponds to vm ≈ 0:17V sent to theLDC. Note that since the actual modulation, ε, is lessthan vm, the applied voltage modulation was in-creased to 0:2V after experimental determinationof ε.B. Software Lock-in Amplifier

A software lock-in amplifier was used for signal pro-cessing instead of a hardware lock-in amplifier asalso successfully implemented by previous research-ers [17,30]. The measured (or simulated) signal fromthe photodiode in this case is multiplied by a sinewave of the same or double the frequency of themodulation applied to the laser. A fifth-order low-pass Bessel filter is used to remove higher harmonicsof the signal. In order to compute the 1f profile (or 2fprofile), the signal is multiplied by a sine functionwith the same frequency (or twice the frequency)and phase-locked with the laser modulation. The1f and 2f versions of the lock-in amplifier were im-plemented on the same signal. The 2f calculationwas normalized by that from the 1f calculation todetermine the 2f =1f signal used in resulting dataprocessing.

C. Experiments in Calibration Cell

A schematic of the experimental arrangement for thecalibration cell is shown in Fig. 1. Gases flowingat controlled flow rates were set at a particular hu-

midity by bubbling through a temperature-controlledhumidifier (Fig. 1, 13). The flow lines leading to thecalibration cell were heated to exceed the saturationtemperature by at least 20 °C to prevent any con-densation. The flow lines were also connected witha tube to feed dry gases to the calibration cell, thusbypassing the humidifier through a series of valves(Fig. 1, 7, 8, 12). The experimental setup wasmounted rigidly on an optical bench to maintain goodoptical alignment. The flow valves were selected sothat they produced as little disturbance as possibleduring switching. The calibration cell (Fig. 1, 1)was a copper tube of length 24:3 cm with an 8° angledantireflective glass wedge (Fig. 1, 16) at the endfor allowing the beam to reach the photodiode (Fig. 1,17) active element. The calibration cell experi-ments are broken into two parts: (1) direct absorp-tion measurements, and (2) wavelength-modulationmeasurements.

1. Direct Absorption Measurements

The gases were first fed into the calibration cellthrough the humidifier at a controlled temperature.The gas stream was assumed to achieve saturationcorresponding to the liquid water temperature afterit leaves the liquid water bath and enters into thepipeline. This assumption was verified by conden-sing the liquid water right after the humidifier exitover an extended period of time and determining theamount of condensate that closely matched with theexpected amount of liquid water for each flow rate.The flow lines connecting the humidified gases werekept well above saturation to prevent condensation.The temperatures were measured along the length ofthe calibration cell with thermocouples and the max-imum temperature difference across the cell wasabout 1 °C. The laser was sent a linear voltage rampwith zero modulation, and a scan of the transmittedbeam intensities [denoted by I in Eq. (1)] was taken.The measurements were then taken for a back-ground ramp by passing dry nitrogen through the ca-libration cell [which corresponds to I0 in Eq. (1)]. Thechanges were performed carefully so as not to disturbthe laser alignment.

2. Wavelength-Modulation Measurements

In these experiments, sinusoidal modulations wereadded to the linear DC ramp voltage signal[Eq. (9)] that was sent to the laser diode current con-troller. The same conditions as those in the direct ab-sorption measurements were repeated for these setsof experiments along with the background rampmeasurements by activating the bypass dry gas line.The ratio I0=I measured during the modulated rampis shown in Fig. 4. The maximum and minimumpoints in the oscillating transmission (the envelopeof the modulation) reflect the shape of the underlyingabsorption feature. These maximum and minimumpoints are shown in Fig. 4 as the curves with sym-bols. With no modulation, a single direct absorption


feature is observed as the laser is scanned across theabsorption feature, and with modulation, two identi-cal absorption profiles form the modulation envelopewith a separation equal to the modulation depth. Thetwo absorption profiles in the modulation envelopeare designated as λu and λl.Simulations were completed of this modulated ab-

sorption signal using the obtained line shape param-eters from direct absorption measurements with awavelength variation corresponding to Eq. (9). Sincethe transition parameters were fixed from direct ab-sorption, only the laser nonlinearity factor, ε, was un-known in the simulations. The envelope features, λu(Fig. 5, pluses) and λl (Fig. 5, circles), were extractedfrom the simulations. The profiles from the WMSmeasurements matched very closely with those pre-dicted using these direct absorption measured pa-

rameters, but the separation between the twoprofiles had to bematched with the actual diode laserby fitting the factor ε to account for the laser transi-ents in Eq. (9).

Figure 5 shows just the extrema from Fig. 4 alongwith absorption profiles simulated using Eq. (9) andEqs. (1)–(6). The modulation factor ε in Eq. (9) wasfitted to give the best agreement, and as seen inFig. 5, this modification was sufficient to describethe laser wavelength; thus, the nonlinearities ofthe laser modulation can be empirically determinedfrom a direct absorption measurement during awavelength-modulation experiment. The IM-FMphase shift was adjusted in this method by keepingthe experimentally measured IM via the parameter εand shifting the FM modulation by a constant phaseshift. Experimental and simulated profiles are com-pared to determine the FM shift once the wavelengthmodulation is obtained for a single value of ε. ThisFM phase shift was assumed to be constant through-out the rest of the measurements at the same mod-ulation frequency as the laser transients were foundto be repeatable. As the software lock-in amplifierused in experimentation employs a LabVIEW-baseddigital fifth-order Bessel low-pass filter, there arealso phase delays associated with the filter. These de-lays were automatically taken into account in the nu-merical simulation as it uses a filter identical to theone used in the experiments to produce an identicaleffect in the simulated profile.

The modulated ramp with absorption featureswas then fed to the software lock-in amplifier, whichoutputs the ratio of the second to the first harmonicof the absorption profile corresponding to the modu-lation frequency. The simulated profiles for 2f =1fprofiles using the direct absorption parameters werein close agreement with the experimentally obtained

Fig. 4. (Color online) I0=I measured with modulated ramp show-ing modulation extreme points.

Fig. 5. (Color online) Comparison of the experimental modula-tion extrema from Fig. 4 with those predicted using the direct ab-sorption technique along with laser modulation from Eq. (9). Theparameter, ε, describing laser modulation nonlinearities was di-rectly fit in the simulations.

Fig. 6. Experimental and simulated 2f =1f absorption profiles un-der varying water partial pressure conditions showing accuracy ofthe numerical simulation. Simulated 2f =1f absorption profiles useparameters fit from calibration experiments such that themodel iscompletely predictive.


profiles as shown in Fig. 6, indicating that the modelfor the laser modulation has been implemented accu-rately. The calibration cell was used to determine theLorentzian half-widths and line intensities of the ab-sorption lines at different water vapor partial pres-sures and temperatures in the presence of air andhydrogen. The calibration data obtained at 1 atmtotal pressure could be used at higher pressures byextending them in the following manner.A simplified form of Eq. (5) can be written as

ΔνL ¼ lPs þmP; ð10Þ

where l and m are functions of temperature and col-lision half-widths. Ps is the water vapor partial pres-sure and P is the total pressure. The straight lines inthe obtained plots for ΔνL and Ps at a particular val-ue of total pressure P can be extrapolated to Ps ¼ 0,which then reveals the intercept valuemP. For othervalues of total pressure P at the same temperatureand water vapor partial pressure, the Lorentzianhalf-width of the absorbing species would then havethe effect of translating this relationship with differ-ent intercept values. Hence, if the calibration wasperformed at 1 atm total pressure, a family of calibra-tion curves corresponding to different total pressurescan be obtained as shown in Fig. 7.

D. Experiments in a Proton Exchange Membrane FuelCell

The developed sensor was used in an operating PEMfuel cell. The experiments in the PEM fuel cell werecarried out in an apparatus similar to the calibrationset up with the calibration cell replaced by a proto-typical PEM fuel cell as shown in Fig. 8(a). The col-limator coupled to the DFB laser was fed directly intothe optically accessible PEM fuel cell. The bipolarplates of this fuel cell had a counterflow serpentinechannel geometry comprised of 15 straight segmentsof which the second and fourteenth channels fromthe air and hydrogen inlets at the cathode and anode

sides were milled out to the end of the bipolar plateso that the diode laser beam can be transmittedalong the channel length as shown in Fig. 8(b). Eachflow channel is 7 cm long with cross-sectional dimen-sions of 1:5mm × 2:0mm. For making measurementssimultaneously in the two anode and two cathodechannels, the fiber-coupled output of the laser wasdivided into four fiber outputs via three 2 × 2 bifur-cated optical fibers connected to four collimatorsfixed at one end of each optically accessible channel.Each laser beam, after crossing the flow chan-nels, emerged out of the antireflective infrared-transparent wedged glass windows fixed at oppositeends of the fuel cell channels and collected by fourdifferent photodiodes (PD 1, 2, 3, 4). The fuel cellwas controlled by a Scribner Associates 890C fuel cellload control box with the aid of a controller computer.The load current was changed, and water vapor par-tial pressure and gas temperature in each channelwere measured at different current settings atsteady state.

The ramp modulation described by the first termin Eqs. (8) and (9) was actually a triangular wavethat was configured to have uneven rising and fallingsides so that more data points were collected duringthe rising edge of the ramp. For the steady statemeasurements, the rising edge contained 75,000sample points, whereas the falling edge had 25,000sample points. Thus, a total number of 100,000 sam-ple points were collected for each spectrum. The fre-quency of the ramp (including the rise and fall), andtherefore the overall collection frequency for eachmeasurement, was 1Hz. The frequency of the modu-lation sine wave (ω) was 240Hz. A faster rampcaused the factor ε to increase due to the dynamicsof the diode laser. To ensure proper modeling, thewavelength-modulation fitting routine describedpreviously was repeated when the overall frequencyof the measurement was changed.

3. Results

The Lorentzian half-widths determined from the ca-libration experiments are shown in Fig. 9 as a func-tion of the partial pressure of water. The lineartrends match with theoretical expectations. It is alsonoted that the values of the Lorentzian half-width formixtures with hydrogen are lower than those withair. This can be explained by the fact that hydrogenmolecules are lighter and the air–water collisionsare much more effective in collisional broadeningthan hydrogen–water collisions. While the self-broadening half-width remains the same for both,the foreign gas collision half-width is smaller forhydrogen than air. Combining Eqs. (6) and (10):

γselfγforeign

¼ 1þ lm

: ð11Þ

From the linear fits to the calibration curves, thefollowing values are obtained:

Fig. 7. (Color online) Prediction of ΔνL for 0.6, 0.8, 1.0, 1.2, and1.4 total pressures.


γselfγair

¼ 4:7 andγselfγH2

¼ 6:1; hence;γH2

γair¼ 0:77:

ð12ÞThe values of γself and γair are obtained as 0.477 and0.095 from the HITRAN 2008 [10] database, which

indicates a γself=γair ratio of 5.02, which is reasonablyclose to the obtained value of 4.7. The half-width ofwater-hydrogen collisions for this particular transi-tion can be written as γH2

¼ 0:078. As obtainedexperimentally, the line intensity has unchangedvalues for both experiments with hydrogen–waterand air–water mixtures as shown in Fig. 10.

4. Application in a Proton Exchange MembraneFuel Cell

In the experiments involving an unknown partialpressure and temperature, the 2f =1f profiles atexperimental conditions of interest were obtained.Subsequently, numerically simulated 2f =1f profilesusing interpolated values from the list of databasecreated for the half-widths and line intensities fromthe calibration experiments were used to fit to thosecurves using the Levenberg–Marquardt curve fit al-gorithm. The partial pressure and temperature val-ues that minimized the error between these two areconsidered to be the corresponding actual valuesfrom the experiments.

Fig. 8. (Color online) (a)Experimental setup formeasurements inaPEMfuel cell and (b)PEMfuel cell gas channels showingoptical access.

Fig. 9. (Color online) Lorentzian half-width versus Ps for (a) air–water and (b) hydrogen–water mixtures.

Fig. 10. (Color online) Variation of line intensity SðTÞ withtemperature.


Sample measurements of water partial pressureand temperatures for four measurement channelsat steady state are shown in Figs. 11 and 12. Forthe case shown in Fig. 11, the anode gas supplywas fed with hydrogen at 80% relative humidityand the cathode was fed with air at 18% relative hu-midity. At zero current density (nonoperating fuelcell), the anode gas stream decreases in water con-tent from inlet to outlet due to transfer of water tothe cathode side via diffusion. Likewise, the cathodeside water content increases from inlet to outlet. Asthe current density of the fuel cell is increased, addi-tional water is produced within the cell. The changein water content on the anode side from inlet to outletdecreases, but the cathode side shows a substantialincrease in outlet water concentration. This is a re-sult of the water production being localized to thecathode side of the cell. The steady state measure-ments of water concentration in Fig. 11 indicate thatthere is a monotonic rise in the partial pressure ofwater corresponding to the electrochemical reactionat the cathode side. The rise is not linear, however, asthere is some backdiffusion of water toward the an-ode. Figure 12 shows the measurements of tempera-ture at the same locations. The polarization curves(voltage versus current density) in Figs. 11 and 12reflect the performance of the fuel cell. The perfor-mance of the fuel cell was not optimal, which wasbelieved to be due to the particular membrane-electrode assembly used and the ratio of active tosupport areas in the bipolar plate.An uncertainty of �2:5% in partial pressure and

�3 °C in temperature is predicted from the calibra-tion experiments. These uncertainties arise dueto the optical noise that could not be completelymodeled and the fluctuations in temperaturesthroughout the calibration experiment setup. Theline intensities also have a little scatter (Fig. 10)and result in further inaccuracies in temperature.Especially at the higher humidity levels, the conden-sation of liquid water in the optical path causes op-tical noise, leading to poor data.

5. Conclusions

A sensor utilizing WMS spectroscopy and ratios ofsignal harmonics (2f =1f ) was developed for applica-tions in PEM fuel cells. A new approach to the dataanalysis procedure was described, involving full-scale numerical simulation of the harmonic profilesand utilization of direct absorption measurementswhile modulating the laser to account for nonlinearlaser dynamics. This approach was shown to providegood agreement between measured and simulatedspectra. The Lorentzian half-widths and line inten-sities for water-air and water-hydrogen transitionsat different water vapor partial pressures and tem-peratures were measured by both direct absorptionandWMS techniques. A procedure is described to ob-tain the corrected Lorentzian half-width for differenttotal pressures from data obtained at 1 atm. Thehalf-widths for hydrogen–water vapor collisions wereobtained. Finally the sensor was tested for measur-ing water vapor partial pressure and temperatureinside an operational PEM fuel cell within an un-certainty of �2:5% in partial pressure and �3 °Cin temperature as predicted from the calibrationexperiments.

Appendix A: List of Abbreviations

Abbreviation Term

WMS Wavelength-modulation spectroscopyIM Intensity modulationFM Frequency modulationRAM Residual amplitude modulationPEM Proton exchange membraneLDC Laser diode controllerTEC Thermoelectric coolerPD PhotodiodeTC Thermocouple

This work was sponsored by Connecticut Innova-tions Incorporated and United Technologies underthe Yankee Ingenuity Program.

Fig. 11. (Color online) Variation of PEM fuel cell water vapor par-tial pressure with current density at four different locations.

Fig. 12. (Color online) Variation of PEMFC temperature withcurrent density at four different locations.


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