loadingFIG.2.Smallspectralregioncorrespondingtosulfuryl?uoride,takenatdifferentpartialpressuresofsulfuryl?uoride.TheverticaldashedlinerepresentsthepositionofasinglepositionalchannelusedinthefollowingexampleoftheBeer’slaw?tdescribedinthetext.surements(inwhichthestrongpeaksareeitherdown-weightedordiscardedaltogether).Figure2illustratestheprocedureusingsulfuryl?ouride,SOpartialpressures2Fof2;this?gurecon-tains14plotswithSO8.27Pato13985.54Pa(0.062torrto2F104.92rangingfromtorr).ThedashedverticallineinFig.2indicatestheselectedwavenumberbinat?1270cm?1usedfortheexampleoftheBeer’slawplotappearinginFig.3.Itisseenthatforthestrongfeaturestothehigherfrequency,linearbehav-iorisobtainedbyfavoringthesmallerburdenswheretheabsorbancevaluesare?1.6.Butfortheweakerfeaturestolowerfrequency,thebestsignal-to-noiseratioisob-tainedfromthehighconcentrationmeasurements.Acor-respondingcurve-of-growthforabsorbanceversuscon-centrationofabsorber,attheselectedpositionalbin(?1270cm?1)maybeseeninFig.3.Thesolidlinerep-resentsthebestlinear?tthroughthepointsusingtheweightingschemediscussedabove.Anunweightedlinear?tisrepresentedbythedashedline.Notethedeviationofthetwolinesathigherabsorbance(concentration)val-ueisindicativeofnonlineareffects.Themethodthustakesadvantageofthefulldynamicrangeoftheinstru-mentandobtainsafarmorelinearspectrumthancanbederivedfromanysinglemeasurement.Inadditiontobet-terlinearity,usingmultipleburdensgreatlyincreasesthesignal/noiseratio(SNR).Forstrongfeatures,theSNRcanexceed106.Inadditiontothe?tted(composite)spectralvector,adeviationvectorisgeneratedduringtheweighted,linearleastsquares?ttingprocess.Thisdeviationvectorissim-plythestatisticaluncertaintyintheweightedlinearleastsquares?t.Anexampleofthedeviationvectorplottedagainstthe?ttedabsorbancevaluesforSOdeviationsoccur2Fat2appearsinFig.4.Notethatthelargerthehigherabsorbancevalues.Anyspectralfeaturesthatdonotscalelinearlywithsampleconcentrationwillexhibitapoor?tandconsequentlylargerdeviationvalues.Thedeviationvectorthusprovidesaninherentandsensitiveprobeforchemicalimpurities.Duringthecourseofameasurement1456
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FIG.3.Curveofgrowthfortheabsorbanceofsulfuryl?uorideattheposition(wavenumber,cm?1)speci?edinFig.2.Thesolidlinerepre-sentstheweightedlinearleastsquares?twhilethedashedlineisthecorrespondingun-weighted?t.series,thetemperatureofthesamplereservoirwillchange.Sinceitisunlikelythatpotentialimpuritiesinthesamplewillhaveidenticalvolatilitiestothoseofthesampleatseveraltemperatures(Henry’sLaw),therela-tiveamountofimpurityvaporwillnotscalethesameasthesamplevaporpressure.Moreover,themolefractionofanyhighervolatilityimpuritytendstodecreasewithtime.Achemicalimpuritysignatureisthuseasilyrec-ognizedinthedeviationvector.Anexampleofetheneimpurityinthe?ttedspectrumofSOtothis?gure,thedeviation2F2appearsinFig.5.Referringvector(middletrace)forSO2F2containsseveralfeaturescorrespondingtoethenethatarenotobviousinthe?ttedspectrumofSO2F2.Areferencespectrumofetheneisincluded(upperFIG.4.Plotofuncertaintyin?ttedabsorptioncoef?cientversus?ttedabsorptioncoef?cient.Notethateachpointcorrespondstoauniquepositional(wavenumber,cm?1)value.Theslopeofthislineisanav-eragestatisticaluncertaintyintheabsorptioncoef?cient.FIG.5.Exampleofusingthedeviationvectortoidentifyimpuritiesinthesample.Lowertrace:?ttedspectrumofSO2Ftrace:reference2;middletrace:devi-ationoruncertaintyvector;upperspectrumofethene.Ethenecontaminationisapproximately0.01%(P/P)oftotalsample.trace)forcomparisonpurposesinFig.5.Notethatthedeviationvectorisplottedaspertheright-handaxis.Forstatistical(typeA)errors,thedeviationvectorde-scribesrandomuncertaintiesassociatedwiththemea-surements.Inordertoestimatethemagnitudeofthesys-tematic(typeB)uncertainties,themaximumuncertaintyofindividualexperimentalparametersmustbeestimated.FractionalvalueestimatesoftheuncertaintiesassociatedwiththeexperimentalparametersarecompiledinTableIII.Solongastheseexperimentalfactorsareuncorrelat-ed,the?ttedcompositeuncertaintyassociatedwiththeinstrumentalparameterscanbecalculatedasfollows:?Bias?k[(?L)2?(?T)2?(?P)2?(?BL)2?(?N)2]1/2(2)wherek?2ischosenatthe95%con?dencelimit(2?).Forthepresentanalysis,weestimate?sumingthatthesystematicuncertaintiesBiasbetween?2.3%.theAs-twolaboratoriesareofthesamemagnitudeanduncorrelatedfromeachother,then[(?Bias2NIST)2?(?BiasPNNL)]1/2?3.2%(3)The3.2%valueprovidesagaugeastowhethermea-surementsbetweenthetwolaboratoriesarewithintheexpected2?deviation.Itisemphasizedagainthattwoentirelydifferentmethodsofsamplegenerationandquantitationwereemployed,yetthedatashouldagreetowithintheseuncertaintyestimates.STABILITYANDLINEARITYOFINTENSITYMEASUREMENTSInadditiontotherandom(typeA)andsystematic(typeB)uncertaintiesdiscussedabove,additionalanalysiswasundertakentoexperimentallycharacterizeboththesta-bilityandthelinearityofthemeasurements.Thestabilitymeasurementquanti?esthedegreeofinstrumentaldriftandinsituchemicaladsorption/desorption,andforthatreasonthestudywasconductedusingapolarmolecule,namelymethanol.Figure6presentsthepercentchangeTABLEIII.Potentialsourcesofsystematicuncertaintiesinspectralmeasurements.EstimatedfractionalParameterSymbolvalueOpticalpathlengthSampletemperature?0.005Samplepressure?L0.002FT-IRbaselinedrift?T0.0010.002MCTnonlinearity?P?BLN0.01(fromzero-time)intheintegratedabsorptionvaluesforaseriesofmeasurementsmadeonthesamemethanol(163.72Pa,1.228torr)plusnitrogensampleinthePNNL20cmcellat298.2K.TheregionselectedforintegrationcorrespondstotheC–Hstretchofmethanol,between2700cm?1and3200cm?1.Eachmeasurement(datapoint)required?4mintoacquire.Thetotaldurationoftheserieswas?30min,signi?cantlylongerthanthetimerequired(?9min)tomeasureatypicalspectrum.Ascanbe?buted1%seenorintolessFig.baselinefor6,allthevariationinintegratedintensityisstabilitypoints.withMuchaofslightthescattertrendseenisattri-fordecreasingintegratedarea.Thisdownwardtrendisper-hapsduetoadsorptionofthemethanolontothecellwallsandwindows.Inordertocoverthelowerfrequencyspectralregion(1200cm?1to600cm?1)athigherresolution,itisnec-essarytouseacooled,photoconductiveMCTdetector.Unfortunately,MCTdetectorsareknownfortheirnon-linearresponse.20,23ToinvestigatethedegreetowhichtheBrukersoftwarecorrectionincombinationwiththedataweightingschememitigatedtheeffectofdetectornonlin-earity,additionalexperimentswereconductedusingde-tectorsknowntohavelinearresponsestophoton?uence.Bothaliquidnitrogencooled,indiumantimonide(InSb)detectorandaroom-temperaturedeuteratedtry-glycinesulfate(DTGS)detectorwereutilizedforthesecompar-FIG.6.Resultscorrespondingtothestabilitytestofapolarsample(methanol)sittinginthesamplecell.ThepercentchangeinintegratedbandareafortheC–Hstretchregionofmethanolisplottedagainsttime,whereintegratedareaatzerotimeischosenforthereferencevalue.APPLIEDSPECTROSCOPY1457
TABLEIV.Comparisonofintegratedbandstrengthmeasurements(etheneandisopropanol)forMCTdetectorwithnonlinearitycorrectionwithInSbandDTGSdetectors.ValuescorrespondtopercentchangefromMCTmeasurements.%Change?(AreaX?AreaMCT)/AreaMCT?100.Dataarepresentedinthemid-wavelengthinfrared(MWIR)andlong-wavelengthinfrared(LWIR)regions.DetectorInSbDTGS,???1.0cm?1MWIRbandarea,C2H4(3300–2900)cm?1?1.97%?2.32%LWIRbandarea,C2H4(1150–800)cm?1NA?0.11MWIRbandarea,IPA(3100–2800)cm?1?0.04%?0.38%LWIRbandarea,IPA(1600–760)cm?1NA?2.21%isonstudies.SincethephotovoltaicInSbhasnoresponsebelow?1850cm?1,itwasonlypossibletocomparein-tensitiesintheC–Hstretchingregion.Inaddition,theD*valuesoftheDTGSpyroelectricdetectoraretwoordersofmagnitudepoorerthanacomparableMCTorInSbdetector,buttheusefulspectralrange(400cm?1to6000cm?1)isnearlyidenticaltoMCTdetectors.DespitethepoorersensitivityoftheDTGSdetectors,theyareknowntohavealinearresponseovermanyordersofmagnitude.FortheseDTGSmeasurements,instrumentresolution(interferometertravel)wasdecreasedto1cm?1,whileallotherparameterswereleftunchanged.The1.0cm?1res-olutionthusallowedthedatatobeacquiredinareason-abletimeandstillyielddecentsignal-to-noiseratios.Eth-eneand2-propanol(IPA)werechosenasthesamplesfordetectorcomparisonsincetheyarebothrelativelyinertandeasytohandle.SamplesofetheneandIPAwerepre-paredandthedatawereanalyzedasdescribedearlier.AllspectroscopiccollectionandFTparameterswereleftasshowninTableII,savethatfortheInSbandDTGSmea-surementsthesoftwarenonlinearitycorrectionwasnotemployed.25Theresultsofthelinearityinvestigationsaresumma-rizedinTableIV.Ascanbeseenfromthetable,theintegratedbandstrengthsareallinexcellentagreement,underthe3%compositeuncertaintyvalue.Thus,thecombinationoftheFTcorrectionalgorithm(fortheMCTdetector)combinedwiththemultipleburdenmeasure-mentfollowedbyaT(?)2weightingschemeyieldsab-sorptioncross-sectionsthatscalelinearlywithopticaldepth.TheresultshavebeenfoundtofollowtheBeer–Lambertlawovermanyordersofmagnitude.Althoughthecomparisonmeasurementsweremadewiththenon-reactivecompoundsetheneandisopropanol(IPA),theexperimentswereundertakenonlytoassesswhethertherewasalinearresponsefromtheinstrument(detector).Thedetectorcorrectionalgorithmincombinationwiththeweightingschemeclearlyhasanacceptablylinearre-sponseatallwavelengths.RESULTSANDDISCUSSIONPerhapsthemostmeaningfultestofabsoluteaccuracyisthroughindependent,cross-laboratorycomparison.Atotalof12differentchemicalsand26correspondingbandswereselectedtocomparetheresultsofNISTtothoseofPNNLandresultsaresummarizedinTableV.Thesampleswereselectedsoastocontainbothpolar(e.g.,methanol,ethyleneoxide)andnon-polarcom-pounds(e.g.,butane,benzene),strong(CCl4)andweakabsorbers(butaneandSO2),aswellasbothhigh(ethene)andlow(n-butanol)vaporpressurespecies.ThelastcolumninTableVcontainsthepercentchange(%?)fortheintegratedbandareasofthePNNLversusTABLEV.Integratedbandstrengthsofselectedmoleculesforintercomparison.%??(PNNL?NIST)/NIST?100.Name(sample#)2-Propanol(1)Benzene(2)Butane(3)n-Butanol(4)Carbontetrachloride(5)Freon-12(6)Ethene(7)Ethyleneoxide(8)Methanol(9)Sulfurdioxide(10)Toluene(11)Trichloroethene(12)Region(cm?1)743–15712511–3085620–7252980–31501198–17812763–3065656–16002507–32663558–3933700–850625–8001220–1310797–11672887–32952820–33781207–1340720–985892–17622513–31501037–12671275–14202411–2545636–8202690729–10503036–3213AreaPNNL0.0435810.0321550.0185970.013210.0057690.0556060.0375140.0548130.0041760.0685850.0231790.0055710.0156770.0073930.01584930.00241650.01347010.0261040.0230010.0041010.0318230.0006480.0123610.0231770.0341180.00172543AreaNIST0.04327450.03242110.01882190.01334720.00577340.05631960.03701350.05450870.00421390.07231020.02401560.00562230.01590120.00746870.01578950.002381960.01314310.02617160.0234350.00415520.03208140.00065740.01244240.02321270.03450950.00169687%??0.71?0.82?1.20?1.03?0.07?1.27?1.35?0.56?0.89?5.15?3.48?0.91?1.41?1.02?0.38?1.45?2.49?0.26?1.85?1.31?0.81?1.46?0.65?0.15?1.13?1.681458Volume58,Number12,2004
FIG.7.ComparisonbetweenNISTandPNNLoftheintegratedbandareasfor12differentsamples.Samplenumberisde?nedinTableV.NISTdata.Aplotof%?versussamplenumbercanbeseeninFig.7.ItrevealsthatthePNNLintegratedbandareasare,onaverage,slightlysmallerthanthecorre-spondingNISTvalues,withanaverage%???0.63%andanrms?1.66.Inanefforttoidentifypossiblecausesforthediscrepancies,%?wasplottedagainstanumberofsampleparametersincludingmolecularmass,gas-phasedipolemoment,integratedbandarea,bandposi-tion,andvaporpressure.Theonlyobvioustrendisthatastronglyabsorbingspeciessuchascarbontetrachloridehasthelargest%?values.Thisisnotsurprisingsincethesesamplesarethemostdif?culttoprepareduetothesmallmixingratio,eitherasagravimetricorasastaticsample.Finally,neitherNISTnorPNNLhavecorrectedforsampleemissionintheircorrespondingspectrallibraries.Sampleemissionisaknownproblemforthespectralregionbelow?1100cm?1andingeneralgivesrisetoanapparentincreaseintheabsorptioncross-section.35Asys-tematicstudyoftheeffectofsampleemissionasafunc-tionofsampletemperatureshasbeendiscussedbyChuetal.36Theyfoundthattheuncorrectedmethanolvaporspectrumat25?C(integratedbetween900cm?1and1150cm?1)was0.4%greaterthanthecorrectedspectrum.Asimilaranalysisforsulfurdioxide(1010cm?1to1275cm?1)yieldedanerrorof0.9%.Athighertemperature(50?C)theerrorsincreasedto1.0%and1.8%formeth-anolandSO2,respectively.SUMMARYUltimatelythedatabaseswillcontainthehigh-resolu-tion(0.1cm?1)quantitativepressure-broadenedinfraredspectraofseveralhundredgas-phasecompounds.Thespectralresolutionissuf?cienttobringoutallsharpfea-tures,whilealsorealizingthatpressurebroadeningwilldictatealinewidth?0.1cm?1inmostcases.Alldatahavebeencalibratedonthewavelengthaxisusingsec-ondarystandards.Wehavedemonstratedthatboththe?owingandstaticmethodscanyieldaccurate,reproduc-ible,andlinearabsorptioncross-sectionsthatareappli-cabletolaboratoryandremotesensingspectroscopy.Pro-videdthatthedatacollectionmethodsarecarefullyplannedandexecuted,boththe?owingandstaticmeth-odshavedemonstratedexcellentagreementforahostofdifferentmolecules.Thetwodatabases,usingentirelydifferentsamplequantitationmethods,havefurtherbeencomparedagainstoneanotherusingspeciesthatrangesigni?cantlyinpo-larity,oscillatorstrength,andvolatility.Severalsourcesofartifactsandnonlinearityhavebeeninvestigated,andthesehaveeitherbeenredressedoraccountedforinthedataanalysis.Thetwolaboratoriesuseddifferentmeth-odsofsamplegenerationtoinvestigatepossiblesystem-aticerrors.Cross-comparisonwith12speciesshowedanrmsdeviationof1.66%forintegratedbandintensities,wellwithinthe3.2%compositeerrorestimate.Datacon-tinuetobecollectedfortheselibraries.ACKNOWLEDGMENTPNNLisoperatedfortheU.S.DepartmentofEnergybytheBattelleMemorialInstituteundercontractDE-AC06-76RLO1830.1.R.J.Bell,IntroductoryFourierTransformSpectroscopy(AcademicPress,NewYork,1972).2.CompendiumofMethodsfortheDeterminationofToxicOrganicCompoundsinAmbientAir,EPA/625/R-96/010b(1999),2nded.3.U.S.EnvironmentalProtectionAgency(EPA)Method-320,Mea-surementofVaporPhaseOrganicandInorganicEmissionsbyEx-tractiveFourierTransformInfraredSpectroscopy(1999).4.R.M.Measures,LaserRemoteChemicalSensing,ChemicalAnal-ysis,94(WileyInterscience,NewYork,1988).5.L.R.Brown,M.R.Gunson,R.A.Toth,F.W.Irion,C.P.Rinsland,andA.Goldman,Appl.Opt.35,2828(1996).6.N.Jacquinet-Husson,etal.,J.Quant.Spectrosc.Radiat.Transfer62,205(1999).7.N.Husson,B.Bonnet,N.A.Scott,andA.Chedin,J.Quant.Spec-trosc.Radiat.Transfer48,509(1992).8.L.S.Rothman,etal.,J.Quant.Spectrosc.Radiat.Transfer60,665(1998).9.MidacCorporation,Standards:GasPhaseInfraredSpectralStan-dards.Acollectionofapproximately150vapor-phaseinfraredspectrasuppliedindigitalformat.MidacCorporation,Irvine,CA.AvailableovertheWorldWideWebathttp://www.midac.com.10.P.Hanst,InfraredSpectraforQuantitativeAnalysisofGases,In-fraredAnalysisInc.Acollectionof296vapor-phaseinfraredspec-trasuppliedindigitalformat.InfraredAnalysisCorporation,Ana-heim,CA.AvailableontheWorldWideWebathttp://www.infrared-analysis.com.11.NIST/EPAGas-PhaseInfraredDatabase.AvailableontheWorldWideWebathttp://www.nist.gov/srd/nist35.htm.12.C.J.Pouchert,Ed.,TheAldrichLibraryofFT-IRSpectraVaporPhase(TheAldrichChemicalComp.Inc.,Milwaukee,WI,1989),vol.3,1sted.13.P.M.Chu,F.R.Guenther,G.C.Rhoderick,andW.J.Lafferty,J.Res.Natl.Inst.Stand.Technol.104,59(1999).14.J.R.BirchandF.J.J.Clarke,Spectrosc.Eur.7,16(1995).15.R.C.M.Learner,A.P.Thorne,andJ.W.Brault,Appl.Opt.35,2947(1996).16.L.Mertz,Infr.Phys.7,17(1967).17.D.B.Chase,Appl.Spectrosc.36,240(1982).18.R.C.M.Learner,A.P.Thorne,I.Wynne-Jones,J.W.Brault,andM.C.Abrams,J.Opt.Soc.Am.A12,2165(1995).19.J.W.Johns,Mikrochim.Acta111,171(1987).20.D.B.Chase,Appl.Spectrosc.38,491(1984).21.M.Birk,D.Hausamann,G.Wagner,andJ.W.Johns,Appl.Opt.35,2971(1996).22.J.Ballard,R.J.Knight,D.A.Newnham,J.VanderAuwera,M.Herman,G.DiLonardo,G.Masciarelli,F.M.Nicolaisen,J.A.Beu-kes,L.K.Christensen,R.McPheat,G.Duxbury,R.Freckleton,andK.P.Shine,J.Quant.Spectrosc.Radiat.Transfer66,109(2000).23.M.C.Abrams,G.C.Toon,andR.A.Schindler,Appl.Opt.33,6307(1994).24.R.L.Richardson,Jr.,H.Yang,andP.R.Grif?ths,Appl.Spectrosc.52,572(1998).APPLIEDSPECTROSCOPY1459