OPSIALManual

v1.0

©2016XiaofengTan.AllRightsReserved

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1.Introduction.............................................................................................................................................31.1SpectralCalculator&Fitter(SCF)..........................................................................................31.2AutomatedAnalyzer(AA)..........................................................................................................3

2.WorkingPrinciplesandWorkflowsofOPSIAL.........................................................................42.1RTModel...........................................................................................................................................42.1WorkflowofSCF.............................................................................................................................52.2WorkflowofAA..............................................................................................................................5

3.Tutorial...................................................................................................................................................10References..................................................................................................................................................13

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1.Introduction OPSIAL(OpticalPlasmaSpectralCalculatIonAndParametersRetrievaL)is

softwarepackageforcalculatingemissionspectraofplasmasandforautomaticallydeterminingchemicalspeciesandimportantplasmaparameters(i.e.,chemicalspecies,mixingratios,plasmaLTEtemperature,andelectrondensity)ofaplasmafromitsemissionspectra.Itiscomprisedoftwomajorcomponents:1)SpectralCalculator&Fitter,2)AutomatedAnalyzer.

1.1SpectralCalculator&Fitter(SCF)TheSCFusesanultra-fastline-by-line(LBL)radiationtransport(RT)algorithm

developedbyDr.Tan(Tan,X.“Anultrafastline-by-linealgorithmforcalculatingspectralTransmittanceandradiance”,J.Quant.Spectrosc.Radiat.Transfer,129,p101–108,2013)forcalculatingemissionspectraofaplasmabasedonlineofsight(LOS)informationoftheplasmaspecifiedbytheuserthroughthegraphicalinterfaceofOPSIAL.HighlightedfeaturesofSCFinclude:

• Anultra-fastLBLalgorithmforperformingaccuratefirst-principlescalculationsofemissionspectraofplasmas.

• Coveringthe150nm–1000nmspectralrange.• IncludingallionicandneutralatomicspeciesintheNISTandCFAatomic

databases.• SupportingmultipleLOSsegments.• SupportingspectralemissioncalculationsforbothLTEandNLTEconditions.• Automaticallyfittingtotheinputplasmaemissionspectrumbyoptimizing

chemicalspeciesmixingratios,temperatures(LTEandNLTE),andpressuresoftheplasma.

1.2AutomatedAnalyzer(AA)TheAAusespatentedtechnology(Tan,X.“Methodforautomatically

determiningchemicalspecies,mixingratios,temperatures,andelectrondensityinplasmasfromobservedemissionspectra”,patentpending#62354170,2016)forautomaticallydeterminingchemicalspecies,mixingratios,plasmaLTEtemperatures,andelectrondensityinaplasmafromitsemissionspectra.Highlightedfeaturesinclude:

• Fullyautomatedanalysisworkflowthatdoesnotrequirehumaninterventions.

• Automaticallyidentifyingchemicalspecies(coveringallatomicspeciesintheNISTandCFAdatabases)inaplasmafromitsemissionspectra.

• Producingquantitativemetricsforthespeciesidentification,includingsensitivityandspecificity.

• Automaticallydeterminingthemixingratiosoftheidentifiedspecies,plasmaLTEtemperature,andelectrondensity.

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• Automaticallyestimatingwavelengthcorrectionfortheinputemissionspectrum.

• Basedonfirst-principlesmethodsandabuilt-inperformancelibraryanddoesnotrequireuser’strainingofthechemicalidentifier.

• Supportinginputspectrawitheithercalibratedspectralradianceorwitharbitraryspectralradianceunits.

2.WorkingPrinciplesandWorkflowsofOPSIALTheworkingprinciplesandworkflowsoftheOPSIALcodearebrieflydescribedinthismanual.FordetailedinformationonthemethodsusedinOPSIAL,pleaserefertothereferencesinthe‘References’sectionofthismanual.

2.1RTModelTan’s(2003)ultra-fastLBLRTmodelisusedtoquicklycalculateemission

spectraoftheplasma.ThisRTmethodisbasedonfastconvolutionofspectrallineprofileusingtheFastFourierTransform(FFT)method.ThetheoreticalframeworkforapplyingthismethodtotheRTcalculationinOPSIALisbrieflydescribedasfollows.

Solutionstotheequationofradiativetransfer(GoodyandYung1989)for

calculatingspectraltransmittanceandradianceinplasmasrequirecalculationofopticaldepthasafunctionofthepaththoughtheLOS.Innumericalapproaches,thiscalculationisdecomposedintocalculationsoftheopticaldepththroughanumberofhomogenoussegmentsalongtheLOS.WithineachoftheseLOSsegments,temperature,pressure,andspeciesmolefractionsareassumedtobeuniform.InaLBLmodel,thewavelength-dependentopticaldepthforagasmixtureinahomogeneoussegmentisgivenby:

𝜏 𝜈;𝑇,𝑃,𝑈!,𝑈!,⋯ ,𝑈!! = 𝑈! 𝑆!,!𝑉 𝜎!,! , 𝛾!,!; 𝜈 − 𝜈!,!

!!!

!!! , (1)

where𝜏 𝜈;𝑇,𝑃,𝑈!,𝑈!,⋯ ,𝑈!! istheopticaldepththatdependsonthewavenumber𝜈,temperaturesTandtotalpressureP,andthecolumndensities𝑈!,𝑈!,⋯ ,𝑈!! ofthe𝑁!speciesinthesegment;𝑆!,! isthelinestrengthforthei-thlineofspecies𝛼thathas𝑁! linesintotal;𝑉 𝜎!,! , 𝛾!,!; 𝜈 − 𝜈!,! isthelineprofileforthei-thlineofspecies𝛼whosecentralwavenumberis𝜈!,!;𝜎!,! and𝛾!,! aretheDopplerwidthandthecollisionbroadenedhalfwidth(HWHM)forthei-thlineofspecies𝛼,respectively.Forsimplicity,itmaybeassumedinOPSIALthatDopplerandcollisionbroadeningaretheonlylinebroadeningmechanismsintheplasmaandasaresultthelineprofileintheemissionspectrumisVoigt.Thecollisionbroadeningofspectrallinesareattributedtothecollisionsofthecarrierspecieswithgasspeciesandelectronsintheplasma.Thebroadeningwithgasspeciesmaybeapproximatedas:

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𝛾!,! = 0.08 !!"!!

!.!𝑃, (2)

where𝑇!isthegaskinetictemperatureoftheplasmainKandPisthepressureinatm.Ineq.(2),itisassumedthatallspeciesintheplasmaaresubjecttoasamebroadeningwiththesurroundinggasintheplasma.CollisionbroadeningwithelectronsmaybeobtainedfromvariousexperimentaldatasourcesorfromtheoreticalvaluessuchasthoseintheStark-Bdatabase(http://stark-b.obspm.fr).

Insteadofcalculatingtheopticaldepthusingeq.(1)directly,whichrequiresalot

ofcomputationalpowerwhen𝑁!sarelarge,asolutiontoeq.(1)intheFouriertransformspaceissought.Eq.(1)canbeeasilyrewritteninFouriertransformspaceusingtheconvolutiontheorem:

𝜏 𝑘;𝑇,𝑃,𝑈!,𝑈!,⋯ ,𝑈!! = 𝑈! 𝑆!,!𝑒𝑥𝑝 −𝜎!,!!𝑘! − 𝛾!,! 𝑘 − 𝑖𝑘𝜈!,!

!!!

!!! , (3)

where𝑘istheFouriertransformvariableofwavenumber𝜈.IftheLOSinformation(i.e.,𝑇,𝑃,𝑈!,𝑈!,⋯ ,𝑈!!)andthespectrallineinformation(i.e.,𝑆!,! foralllinesofallspecies)areknown,onecansumoverallthetermsintherightsideofeq.(3)togettheFouriertransformcoefficientsoftheopticaldepthandthenperformsaninverseFouriertransformtogettherealopticaldepth.

2.1WorkflowofSCFTheworkflowofSCFisverystraightforward.ItinvolvesspecifyingLOSparameters(i.e.,species,mixingratios,temperatures,pressures)oftheplasmaforspectralcalculationsintheCalculatormodeorspecifyinganinputspectrumandLOSparameterstobeoptimizedandtheirboundsintheFittermode.Theworkflowsofthetwomodesareself-explanatoryintheOPSIALgraphicfront-end.

2.2WorkflowofAAFig.1depictstheworkflowoftheAAinOPSIAL.Theinputemissionspectrum

(300)iscomprisedofwavelengthandspectralradiancepairsinwhichatleasttwoemissionpeaksarepresent.ThereisnoupperlimittothenumberofemissionpeaksthatcanbehandledbyOPSIAL.Theinputdatacanbeinunitsofcalibratedspectralradianceorinarbitraryunits.Currently,emissionpeaksinthespectralrangeof150nmto1000nmareusedbyOPSIALforanalysis.

ASpectralFeatureExtraction(SFE,302)methodisusedtoextracttheemission

peakinformationfromtheinputspectrum.Itperformsde-noising,emissionpeakidentification,andcontinuumbaselineremovalfromtheinputemissionspectrum.AnimportantaspectoftheSFEisthatitfitstheemissionpeaksintheemissionspectrumtoanappropriatepeakfunctionandaccuratelydeterminethepositions,heights,andwidthsofallemissionpeaksintheinputspectrumthatformthespectralfeatures(304)forfurtheruse.OPSIALusesGaussiantofitallpeaksinthe

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emissionspectrumforsimplicity.AReferenceSpectralLibrary(RSL,308)isusedinOPSIALandiscomprisedofa

collectionofkeyandvaluepairsforallatomicspeciesintheNISTandHarvardCFAatomicdatabases.OPSIALAAassumestheLTEconditionandasingleLOSsegment.ThekeyfieldofanentryintheRSLiscomprisedofLTEtemperaturesrangingfrom800Kto30000Kwithastepsizeof1000Kandemissioninstrumentslit(Gaussianassumed)widthsrangingfrom0.008cm-1to2.6cm-1inageometricsequencewithacommonratioof2.ThevaluefieldofanentryintheRSLiscomprisedofpeakdescriptionsextractedfromemissionspectracalculatedwiththeRTcodeusingthecorrespondingkeyfieldoftheentryasinputtogetherwithadditionalLOSconditionssuchasLOSlength(e.g.,1cm)andLOSpressure(e.g.,1atm).

Theextractedspectralfeatures(304)oftheinputspectrumarecomparedwith

thevaluefieldsoftheentriesintheRSL.Twopeaksareconsideredapotentialmatchifthedifferenceofthepositionsiswithinawavelengththresholdspecifiedintheadditionalmatchparameters(310)bytheuser.ThelinearcorrelationcoefficientofthepositionsofthepairedpeaksischeckedagainstathresholdspecifiedinthematchparametersandtheentryintheRSLisignoredifthecoefficientdoesnotmeetthethreshold.ForanRSLentrythatpassestheabovecheck,twofeaturevectorsareformedbyOPSIALusingtheintegratedintensitiesofthepeaksintheRSLentryandintheinputspectrum,respectively.Amatchscoreiscalculatedusingthefollowingequation:

𝑆 = 1− !!!!!!

∙ !!(!)!!

(!)!!!!

!!(!)!!

!!! !!(!)!!

!!!

, (4)

where𝑋!

(!)and𝑋!(!)aretheintegratedintensitiesofthepeaksintheinputspectrum

andintheRSLentryinthewavelengthrangeoftheinputspectrum,respectively;N1andN2arethenumberofpeaksintheinputspectrumandintheRSLentry,respectively;andNisthenumberofuniquepeakspresentinboththeinputspectrumandtheentryoftheRSL.Itcanbeseenthateq.(4)isthecosinesimilaritybetweenthetwofeaturevectorstimestheratioofthenumberofcommonpeaksoverthetotalnumberofpeaks.TheminimumnumberofcommonpeaksandthemaximumnumberofthestrongestpeaksintheRSLentrytouseincalculatingmatchscoresarealsospecifiedintheadditionalmathparameters(310).

OPSIALfeaturesaPerformanceLibrary(PL,318)thatisconstructedandtrained

usingresultof~6000randomcomputerexperiments,eachofwhichcontains1to5randomlygeneratedspecieswithrandomlygeneratedmixingratiosandplasmaLTEtemperatures.ThesameLOSconditionsasusedinconstructingtheRSLareusedinthecomputerexperiments.TheresultsoftherandomcomputerexperimentsareusedtogenerateperformancemetricsforthespeciesidentifierofOPSIAL,suchastheTruePositiveRate(TPR)andtheFalsePositiveRate(FPR)asfunctionsofthematchscore.TPRsandFPRsarefittedtoempiricalexpressionsasfollows:

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𝑇𝑃𝑅 = 1− 𝑆 ∙ 𝑒!!/!!"# , (5)and𝐹𝑃𝑅 = 1− 𝑆 ∙ 𝑒!!/!!"# , (6)

whereSisthematchscore;𝜏!"# and𝜏!"# areconstantstobefitted.Foreachspecies,acutoffmatchscore𝑆!"#$%%isdeterminedaccordingtothefollowingequation:𝑇𝑃𝑅 + 𝐹𝑃𝑅 = 1− 𝑆 𝑒!!!"#$%%/!!"# + 𝑒!!!"#$%%/!!"# = 𝑅 , (7)whereRisathresholdspecifiedbytheuser.InOPSIAL,thematchscoreisconvertedintomatchindexduringspeciesidentification.Thematchindexisdefinedas:𝐼 = 𝑆/𝑆!"#$%% . (8)

OPSIALfeaturesamethodforperformingwavelengthcalibration,LTEtemperaturesestimation,andspeciesidentificationoftheinputspectrum.Theworkflowofthemethodisasfollows.Firstly,peakyspectralfeaturesareextractedbytheSFE.TherelativeintensitiesofthesefeaturesarethencomparedtothoseoftheentriesoftheRSLtocalculatematchscores.Secondly,overallmatchscore(OMS)valuesarecalculatedtofacilitateestimationofplasmaLTEtemperaturesandwavelengthshiftintheinputspectrum.TheOMSisdefinedas:

𝑂𝑀𝑆 𝑇;Δ𝑤 = 𝑆 𝛼;𝑇;Δ𝑤 /𝑁!

!!! , (9)

where𝑂𝑀𝑆 𝑇;Δ𝑤 isafunctionoftheplasmaLTEtemperaturesTandthewavelengthshiftΔ𝑤;𝑆 𝛼;𝑇;Δ𝑤 isthematchscoreofspecies𝛼;andthesummationisoverforallspecies.TheOMS’arecalculatedforalltheLTEtemperaturesintheRSLandforallΔ𝑤sinaspecifiedwavelengthrange.ThewavelengthshiftoftheinputspectrumisestimatedwiththeΔ𝑤associatedwiththelargestOMS.PlasmaLTEtemperaturesisestimatedusingthematch-scoreweightedaverageofallthetemperaturesintheOMS’attheestimatedwavelengthshiftΔ𝑤!:𝑇! = 𝑒 !"# !;!!! ∙!"# !! !"# !;!!!! , (10)where𝑇!istheestimatedplasmaLTEtemperature;Δ𝑤!istheestimatedwavelengthshiftby.Thirdly,aspeciesisidentifiedifitsmatchindexcalculatedfromeqs.(7)and(8)isgreaterthan1.0.Onceaspeciesisidentified,theTPRandFPRfortheidentificationarethencalculatedfromeq.(5),(6),and(8).Finally,foranidentifiedspecies,aspecies-specificwavelengthcalibrationisdeterminedbyfittingtheextractedemissionpeakpositionsofthematchedpeakstothepositionsintheRSLforthatspecificspecies.Afinalwavelengthcalibrationisdeterminedusingthe

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match-indexweightedaverageofallthespecies-specificwavelengthcalibrations.Theidentifiedspecies,estimatedtemperatureLTE𝑇! ,andguessedinitialmixing

ratios(320),togetherwithadditionalLOSinformation(e.g.,LOSlengthandpressure)(324)specifiedbytheuser,aresenttoaSahaequationsolvercodeandtheRTcode(324)tocalculateanemissionspectrum(326).Thechi-squaredofthedifferenceofthecalculatedspectrumandtheinputspectrumareminimizingbyvaryingthemixingratiosandtheLTEtemperatureusingagradient-descentbasedoptimizer.ThefinalmixingratiosandLTEtemperaturearedeterminedwhentheoptimizationconverges.TheelectrondensityoftheplasmaisdeterminedbysolvingtheSahaequationattheseconditions.

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Figure1.FlowchartoftheAutomatedAnalyzer.

Spectralfeatureextraction

Calculatematchscores

Emissionspectrumofplasma

Spectralfeatures

Matchparameters

Referencespectrallibrary

Matchscores

IdentifySpeciesandestimatetemperatures Performance

library

Species,temperature,andmixingratios

SolveSahaequationandcalculateemissionspectrumwithRTcode

Calculatedemissionspectrum

Plasmaparameteroptimization

AdditionalLOSinformation

Emissionspectrumofplasma

Converged?

Plasmaparameters

300

Yes

No

302

304

322

310

318

324

320

308

312

330

332

326

306

314

328

Performanceparameters

316

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ItisimportanttonotethattheconstructionofthePLofOPSIALisavery

time-consumingprocessandthatresultsofmorerandomlycomputersimulationsarestillbeingconstantlyaddedtothePLtoimprovetheaccuracyofthespeciesidentifierofOPSIAL.Asaconsequence,itisimportantfortheusertokeepupdatingthePLcomeswithareleaseofOPSIAL.

3.TutorialInthistutorial,wearegoingtoanalyzethefirstLIBSspectrumofMarstakenby

theChemCaminstrumentboardingtheNASAroverCuriosity*.Thespectrumcanbeseenonlineathttp://www.msl-chemcam.com/blog/chemcams-first-spectrum/.

Step1.StartOPSIALandselecttheAutomatedAnalyzertabsothatwecanhaveOPSIALautomaticallydeterminespecies,mixingratios,temperature,andelectrondensity.LoadfileMars_First_Spectrum_part.datinsidepathexamples/ChemCamoftheOPSIALinstallationdirectory.Thisspectrumcoversthe240–340nmspectralrange.SelectArbitraryUnitsintheSpectrumRadianceUnitstohaveOPSIALusetherelativeintensitiesofthespectrumtoperformanalysis.

Step2.MakesurethefollowingparametersintheAutomatedAnalyzeraresettothefollowingvalues:

• IdentifySpecies&EstimateLTETemperature.CheckthisradioboxtohaveOPSIALidentifyspeciesandestimateplasmaLTEtemperature.

• SpectrumSlitWidth:0.2nm.Thisistheslitwidthofthespectrumasseenfromthewidthofthepeaksinthespectrum.

• TPR+FPR:1.2.Thisisthethresholdusedineq.(7)forcalculatingcutoffmatchscoresforspecies.

• LOSLengthincm:1.0.ThisisanestimatedLOSlengthoftheplasmacreatedbytheChemCaminstrument.

• LOSPressureinatm:0.06.ThisistheaverageairpressureonthesurfaceofMars.

• NumberofOptimizationIterations:30.ThisisnumberofiterationsforfittingtotheinputspectrumtodeterminethemixingratiosandtheLTEplasmatemperature.

• Min.NumberofPeakstoMatch:4.Thisistheminimumnumberofpeakstomatchbetweentheinputspectrumandaspectruminthereferencelibraryinorderforthereferencespectrumtobeconsideredasapotentialmatchtotheinputspectrum.

*WeareverygratefultoDr.R.C.WiensandDr.A.ShanerfortheassistanceonretrievingthespectrumfromtheChemCamonlinedatabases.

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OtherparametersontheAutomatedAnalyzershouldnormallytakethedefaultsvaluessincethosearethevalueswithwhichtheOPSIALspeciesidentifieristrained.AscreenshotafterthisstepisshowninFig.2.

Figure2.SettingsofOPSIALinStep2.

Step3.ExecutetheAction|StartCalculation/Analysismenucommandorclickthebuttonwithtwogearsonthetoolbar.OPSIALstartstoidentifyspeciesintheplasmaandestimatestheLTEplasmatemperature.Theresultlookslikethefollowing:****************************************************************OpticalPlasmaSpectralIdentification&AnaLysis(OPSIAL)TheAutonomousSpecies&TemperatureModule(LTEOnly)(c)2016XiaofengTan,Ph.D.,AllRightsReserved.****************************************************************>>>StartAnalysisat2016-07-07.14:12:03<<<Successfullyread2048linesofdatafrom/Users/xtan/opsial/examples/ChemCam/Mars_First_Spectrum_part1.dat!Identifyingspeciesandestimatingtemperature...Finishedestimatingtemperature!========================================================================Fe 3.36 93% 1% 1.00004e+00*w-9.33909e-03

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Mg 2.06 95% 5% 9.99984e-01*w+4.18955e-03Si 1.61 99% 8% 1.00026e+00*w-7.16134e-02Ti 1.43 99% 10% 9.99897e-01*w+3.00783e-02Est.T:2.49086e+04KEst.WavelengthScaling:9.99965e-01*w+1.03931e-02========================================================================ItisworthmentioningthatthePLusedbyOPSIALisstillbeingactivelydeveloped(i.e.,moreandmoretrainingdataarebeinggeneratedtotrainthespeciesidentifierandtogenerateupdatedPL).Asaresult,theversionofOPSIALtheuserusesmayproducedifferentspeciesasshownaboveduetothedifferencesbetweenthePLs.

Step4.NowintheAutomatedAnalyzer,checktheradioboxDetermineSpecies,MixingRatios,LTETemperature,andElectronDensityandthenexecutetheAction|StartCalculation/Analysismenucommandorclickthecorrespondingbuttononthetoolbar.ThistimeOPSIALperformsanoptimizationtodeterminethemixingratiosandLTEtemperatureafterthespeciesidentificationandtemperatureestimation.Theresultlookslikethefollowing:

--Segment#1(w/#1nexttothedetector)Information--T=24744.3K,P=0.06ATM,Length=0.01m.MolefractionforFe:9.54716e-06MolefractionforMg:4.61802e-07MolefractionforSi:2.84595e-06MolefractionforTi:2.57678e-06Sumofmolefractions:1.54317e-05Electrondensity=2.74259e+17cm^-3.NotethatthemixingratiosdeterminedwithArbitraryUnitsselectedfortheSpectrumRadianceUnitsintheAutomatedAnalyzerarerelativemixingratiosbutnotabsolutemixingratios.ThecalculatedspectrumwiththeoptimizedmixingratiosandtheplasmaLTEtemperatureisplottedtogetherwiththeinputspectrumareshowninFig.3.

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Figure3.CalculatedandinputspectrainStep4.

References

Tan,X.“Anultrafastline-by-linealgorithmforcalculatingspectralTransmittanceandradiance”,J.Quant.Spectrosc.Radiat.Transfer,129,p101–108,2013.

Tan,X.“Methodforautomaticallydeterminingchemicalspecies,mixingratios,

temperatures,andelectrondensityinplasmasfromobservedemissionspectra”,patentpending(application#62354170),2016.

Goody,R.M.;Yung,Y.L.Atmosphericradiation:theoreticalbasis,2nded.NewYork:Oxford;1989.