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第36卷�第10期中�国�激�光Vol.36,No.102009年10月CHINESEJOURNALOFLASERSOctober,2009��SupportedbyaresearchgrantfromtheNationalNaturalScienceFoundationofChina(30870675).��文章编号:0258�7025(2009)10�2510�07Coordinate�TracingModelofLightForwardScatteredbyTurbidMediaLiuWu(吴�柳)1�ZheLi(李�哲)1�JiashengWang(汪家升)1�XiangqunXu(徐向群)21DepartmentofPhysics,BeijingJiaotongUniversity,Beijing100044,China2SchoolofScience,ZhejiangSci�TechUniversity,Hangzhou,Zhejiang310018,ChinaReceivedApril3,2009;revisedApril13,2009Correspondingauthor:xuxiangqun@zstu.edu.cnAbstract�Opticaltechniquesbasedonmeasuringscatteringpropertiesofbio�tissueshaveapotentialtodetermineinternalphysiologicalstate.Fortissueimaging,theleast�scatteredphotonsarrivingatadetectormayhaveasignificanteffectonthedevelopmentofimagingalgorithms.Tracingleast�scatteredphotonsmaybehelpfulforfurtherunderstandingofimagingmechanismswithincurrenthigh�resolutionoptical�imagingtechniques.Basedonthevertex�propagator,acoordinate�tracingmodelisdevelopedtosearchprobabilitiesforleast�scatteredphotonstraversinginascatteringmedium.Integralexpressionsforphotonexperiencinganytimescatteringeventsareobtained.ComparedwiththemethodsbasedonbothgeometricaltracingandMonteCarlosimulation,ourmodelissimplerandeasierforprogramming.Keywords�scattering;turbidmedia;imagingalgorithm;biomedicalopticsCLCN:O242.2;TN012����DocumentCode:�A����doi:10.3788/CJL20093610.25101�IntroductionUnderstandingoftheinteractionoflightwithintissueatacellularlevelwillpromotethedevelopmentofopticaldiagnostictechniques.Opticaltechniquesarepotentiallycapableofrapid,non�invasiveassessmentoftissuepathology.Inthepastyears,anumberoftechniqueshavebeendevelopedthatrelyinsomemannersonmeasuringthescatteringpropertiesoftissuetodetermineitsphysiologicalstate.Thesetechniquesrangefromdirectimagingmethodssuchasconfocalmicroscopy[1],opticalcoherencetomography(OCT)[2],andphotoacousticimaging[3],torelativelyindirectapproachesincludingelastic�scatteringspectroscopy[4]andphotonmigration[5].OCTuseslowcoherenceinterferometrytoproduceatwo�dimensionalimageofopticalscatteringfrombothinternaltissuemicrostructures[6~8]andblood[9,10].Themainproblemwithlighttomographyofbiologicaltissues,whicharehighlylight�scatteringmedia,isretrievinginformationaboutthepropertiesandthestructuresofthetissuefromthestaticanddynamiccharacteristicsofoutgoinglight.Totackletheproblem,itisnecessarytoassumeatheoreticalmodelofthescatteringmediumandformulatemathematicallyalight�propagationproblemtobesolvedanalyticallyornumerically.Obviously,MonteCarlosimulationtechniquescanbeusedtotracestochasticallythelightpropagatinginthemedium[11],butitistimeconsuming.Thereareafewgeneraltheoreticalapproachesavailableforconsideringlightpropagationinscatteringmaterials,e.g.,light�transporttheory[12],light�diffusionapproximation[12~15],multifluxradiativetransfertheory[12,16~18],probabilisticrandom�walktheory[19~21],andphotonpathanalysis[22,23].Forleast�scatteredphotonsthatarriveatadetectorthroughaturbidmediumliketissue,Jacquesetal.[24]introducedapathintegraldescriptiontopredicttheearly�arrivingphotonstothedetector.Wangetal.[25]introducedatheorybasedonthevertex/propagatormodeltofindtheleast�scatteredphotonsprobabilitiesbytracingphotonsgeometrically.However,thegeometricalexpressionofphotonhistoryistoocomplexto...