二維相關光譜

Two-dimensionalcorrelationanalysisFromWikipedia,thefreeencyclopediaTwodimensionalcorrelationanalysisisamathematicaltechniquethatisusedtostudychangesinmeasuredsignals.Asmostlyspectroscopicsignalsarediscussed,sometimealsotwodimensionalcorrelationspectroscopyisusedandreferstothesametechnique.

In2Dcorrelationanalysis,asampleissubjectedtoanexternalperturbationwhileallotherparametersofthesystemarekeptatthesamevalue.Thisperturbationcanbeasystematicandcontrolledchangeintemperature,pressure,pH,chemicalcompositionofthesystem,oreventimeafteracatalystwasaddedtoachemicalmixture.Asaresultofthecontrolledchange(theperturbatiOnhesystemwillundergovariationswhicharemeasuredbyachemicalorphysicaldetectionmethod.Themeasuredsignalsorspectrawillshownsystematicvariationsthatareprocessedwith2Dcorrelationanalysisforinterpretation.

Whenoneconsidersspectrathatconsistoffewbands,itisquiteobvioustodeterminewhichbandsaresubjecttoachangingintensity.Suchachangingintensitycanbecausedforexamplebychemicalreactions.However,theinterpretationofthemeasuredsignalbecomesmoretrickywhenspectraarecomplexandbandsareheavilyoverlapping.Twodimensionalcorrelationanalysisallowsonetodetermineatwhichpositionsinsuchameasuredsignalthereisasystematicchangeinapeak,eithercontinuousrisingordropinintensity.2Dcorrelationanalysisresultsintwocomplementarysignals,whichreferredtoasthe2Dsynchronousand2Dasynchronousspectrum.Thesesignalsallowamongstothers[i][2][3]todeterminetheeventsthatareoccurringatthesametime(inphase)andthoseeventsthatareoccurringatdifferenttimes(outofphase)

todeterminethesequenceofspectralchanges

toidentifyvariousinter-andintramolecularinteractions

bandassignmentsofreactinggroupstodetectcorrelationsbetweenspectraofdifferenttechniques,forexamplenearinfraredspectroscopy(NIR)andRamanspectroscopyHistory[edit]2Dcorrelationanalysisoriginatedfrom2DNMRspectroscopy.IsaoNodadevelopedperturbationbased2Dspectroscopyinthe1980s.[4]Thistechniquerequiredsinusoidalperturbationstothechemicalsystemunderinvestigation.Thisspecifictypeoftheappliedperturbationseverelylimiteditspossibleapplications.Followingresearchdonebyseveralgroupsofscientists,perturbationbased2Dspectroscopycouldbedevelopedtoamoreextendedandgeneralizedbroaderbase.Sincethedevelopmentofgeneralized2Dcorrelationanalysisin1993basedonFouriertransformationofthedata,2Dcorrelationanalysisgainedwidespreaduse.Alternative

techniquesthatweresimplertocalculate,forexamplethedisrelationspectrum,werealsodevelopedsimultaneously.Becauseofitscomputationalefficiencyandsimplicity,theHilberttransformisnowadaysusedforthecalculationofthe2Dspectra.Todate,2Dcorrelationanalysisisnotonlyusedfortheinterpretationofmanytypesofspectroscopicdata(includingXRF,UV/VISspectroscopy,fluorescence,infrared,andRamanspectra),althoughitsapplicationisnotlimitedtospectroscopy.

Propertiesof2Dcorrelationanalysis〔edit]

Demodatasetconsistingofsignalsatspecificintervals(1outof3signalsonatotalof15signalsisshownforclarity),peaksat10and20arerisinginintensitywhereasthepeaksat30and40haveadecreasingintensity2Dcorrelationanalysisisfrequentlyusedforitsmainadvantage:increasingthespectralresolutionbyspreadingoverlappingpeaksovertwodimensionsandasaresultsimplificationoftheinterpretationofone-dimensionalspectrathatareotherwisevisuallyindistinguishablefromeachother,[4]Furtheradvantagesareitseaseofapplicationandthepossibilitytomakethedistinctionbetweenbandshiftsandbandoverlap.[3]Eachtypeofspectralevent,bandshifting,overlappingbandsofwhichtheintensitychangesintheoppositedirection,bandbroadening,baselinechange,etc.hasaparticular2Dpattern.Seealsothefigurewiththeoriginaldatasetontherightandthecorresponding2Dspectruminthefigurebelow.

Schematicpresenceofa2Dcorrelationspectrumwithpeakpositionsrepresentedbydots.RegionAisthemaindiagonalcontainingautopeaks,off-diagonalregionsBcontaincross-peaks.

2Dsynchronousandasynchronousspectraarebasically3D-datasetsandaregenerallyrepresentedbycontourplots.X-andy-axesareidenticaltothex-axisoftheoriginaldataset,whereasthedifferentcontoursrepresentthemagnitudeofcorrelationbetweenthespectralintensities.The2Dsynchronousspectrumissymmetricrelativetothemaindiagonal.Themaindiagonalthuscontainspositivepeaks.Asthepeaksat(x,j)inde2Dsynchronousspectrumareameasureforthecorrelationbetweentheintensitychangesatxandjintheoriginaldata,thesemaindiagonalpeaksarealsocalledautopeaksandthemaindiagonalsignalisreferredtoasautocorrelationsignal.Theoff-diagonalcross-peakscanbeeitherpositiveornegative.Ontheotherhandtheasynchronousspectrumisasymmetricandneverhaspeaksonthemaindiagonal.

Generallycontourplotsof2Dspectraareorientedwithrisingaxesfromlefttorightandtoptodown.Otherorientationsarepossible,butinterpretationhastobeadaptedaccordingly[5]Calculationof2Dspectra〔edit]SupposetheoriginaldatasetDcontainsthenspectrainrows.Thesignalsoftheoriginaldatasetaregenerallypreprocessed.Theoriginalspectraarecomparedtoareferencespectrum.Bysubtractingareferencespectrum,oftentheaveragespectrumofthedataset,socalleddynamicspectraarecalculatedwhichformthecorrespondingdynamicdatasetE.Thepresenceandinterpretationmaybedependentonthechoiceofreferencespectrum.Theequationsbelowarevalidforequallyspacedmeasurementsoftheperturbation.

Calculationofthesynchronousspectrum[edit]A2Dsynchronousspectrumexpressesthesimilaritybetweenspectralofthedataintheoriginaldataset.Ingeneralized2Dcorrelationspectroscopythisismathematicallyexpressedascovariance(orcorrelation).

where:

①isthe2Dsynchronousspectrumv1and?2aretwospectralchannelsjisthevectorcomposedofthesignalintensitiesinEincolumnvnthenumberofsignalsintheoriginaldatasetCalculationoftheasynchronousspectrum[edit]OrthogonalspectratothedynamicdatasetEareobtainedwiththeHilbert-transform:where:

中isthe2Dasynchronousspectrumv1env1aretwospectralchannelsjisthevectorcomposedofthesignalintensitiesinEincolumnvnthenumberofsignalsintheoriginaldatasetNtheNoda-HilberttransformmatrixThevaluesofN,Naredeterminedasfollows:

0ifj=kwhere:

jtherownumberkthecolumnnumber

Interpretation但由日Interpretationoftwo-dimensionalcorrelationspectracanbeconsideredtoconsistofseveralstages,[4]Detectionofpeaksofwhichtheintensitychangesintheoriginaldataset[edit]

Autocorrelationsignalonthemaindiagonalofthesynchronous2Dspectrumofthefigurebelow(arbitraryaxisunits)Asrealmeasurementsignalscontainacertainlevelofnoise,thederived2Dspectraareinfluencedanddegradedwithsubstantialhigheramountsofnoise.Hence,interpretationbeginswithstudyingtheautocorrelationspectrumonthemaindiagonalofthe2Dsynchronousspectrum.Inthe2Dsynchronousmaindiagonalsignalontheright4peaksarevisibleat10,20,30,and40(seealsothe4correspondingpositiveautopeaksinthe2Dsynchronousspectrumontheright).Thisindicatesthatintheoriginaldataset4peaksofchangingintensityarepresent.Theintensityofpeaksontheautocorrelationspectrumaredirectlyproportionaltotherelativeimportanceoftheintensitychangeintheoriginalspectra.Hence,ifanintensebandispresentatpositionx,itisverylikelythatatrueintensitychangeisoccurringandthepeakisnotduetonoise.

Additionaltechniqueshelptofilterthepeaksthatcanbeseeninthe2DsynchronousandasynchronousDeterminingthedirectionofintensitychange[edit]

Asynchronous

TOC\o"1-5"\h\z

4&。?

4&——ifthereisapositivecross-peakat(x,j)inthesynchronous2Dspectrum,theintensityofthesignalsatxandjchangesinthesamedirection

ifthereisanegativecross-peakat(x,j)inthesynchronous2Dspectrum,theintensityofthesignalsatxandjchangesintheoppositedirection

11>-40M2010

PeaKooslUon

Exampleofatwo-dimensionalcorrelationspectrum.Opencirclesinthissimplifiedviewrepresentpositivepeaks,whilediscsrepresentnegativepeaksItisnotalwayspossibletounequivocallydeterminethedirectionofintensitychange,suchasisforexamplethecaseforhighlyoverlappingsignalsnexttoeachotherandofwhichtheintensitychangesintheoppositedirection.Thisiswheretheoffdiagonalpeaksinthesynchronous2Dspectrumareusedfor:

Ascanbeseeninthe2Dsynchronousspectrumontheright,theintensitychangesofthepeaksat10and30arerelatedandtheintensityofthepeakat10and30changesintheoppositedirection(negativecross-peakat(10,30)).Thesameistrueforthepeaksat20and40.

Determiningthesequenceofevents[edit]Mostimportantly,withthesequentialorderrules,alsoreferredtoasNoda'srules,thesequenceoftheintensitychangescanbedetermined.[4]Bycarefullyinterpretingthesignsofthe2Dsynchronousandasynchronouscrosspeakswiththefollowingrules,thesequenceofspectraleventsduringtheexperimentcanbedetermined:

iftheintensitiesofthebandsatxandjinthedatasetarechanginginthesamedirection,thesynchronous2Dcrosspeakat(x,j)ispositiveiftheintensitiesofthebandsatxandjinthedatasetarechangingintheoppositedirection,thesynchr