foueieroptics课件c8analogopticalinfomationprocessing

Chapter8AnalogOpticalInformationProcessing,FourieranalysisapplicationsbothintherealmofimagingandininformationprocessingSuchapplicationsrestontheabilitytoperformgenerallineartransformationsofinputdata,8.1Significanceofinformationprocessing,ImprovementofvarioustypesofimaginginstrumentsPhase-contrastmicroscope,opticalfilteringVastamountofdatamayoverpowertheeffectivenessofthehumanobserverTheabilitytoperformgenerallineartransformationsenablesFourieropticstoplayacrucialroleinthereductionoflargequantitiesofdatacharacterrecognitiontoplacebodyofdatainaformcompatiblewithhumanobserverprocessingsynthetic-apertureradardata,8.1.1TheAbbe-PorterExperiments,InthebackfocalplaneofthelensappearstheFourierspectrumoftheperiodicmeshIntheimageplanethevariousFouriercomponentspassedbythelensarerecombinedtoformareplicaofthemesh,Photographofthespectrumofthemeshandtheimageoftheoriginalmesh,Spatialfiltering_1,Insertinganarrowslitinthefocalplanetopassonlyasinglerowofspectralcomponents,Spatialfiltering_2,Whentheslitisrotatedby90topassonlythespectralcolumn,theimageisseentocontainonlyhorizontalstructure,8.1.2Phasevisibilityproblem,ManyobjectsofinterestinmicroscopyarelargelytransparentWhenlightpassesthroughsuchanobject,thepredominanteffectisthegenerationofaspatiallyvaryingphaseshiftThiseffectisnotdirectlyobservablewithaconventionalmicroscopeandasensorthatrespondstolightintensity,1.StainingThisrequiresadditionalpreparationanditalsokillsthecell2.Interferometrictechniques3.Centraldarkgroundmethod2-3techniquessufferfromasimilardefecttheobservedintensityvariationsarenotlinearlyrelatedtothephaseshift,DefectofmethodsbeforeZernike,Conditionofsmallphaseshift,Supposethatatransparentobject,withamplitudetransmittance,Anecessaryconditiontoachievelinearitybetweenphaseshiftandintensityisthatthevariablepartoftheobject-inducedphaseshift,besmallcomparedwith2radians,hasnozero-frequencyspectralcomponent,Zernikesanalysis,ThebackgroundisbroughttofocusontheopticalaxisinthefocalplaneThediffractedlight,arisingfromhigherspatialfrequencies,isspreadawayfromtheopticalaxisZernikeproposedthataphase-changingplatebeinsertedinthefocalplanetomodifythephaserelationbetweenthefocusedanddiffractedlight,Zernikesmethod,Thephase-changingplatecanconsistofaglasssubstrateonwhichasmalltransparentdielectricdothasbeendepositedThedotiscenteredontheopticalaxisinthefocalplaneandhasathicknessandindexofrefractionsuchthatitretardsthephaseofthefocusedlightbyeither/2or3/2radiansrelativetothephaseretardationofthediffractedlight,ZernikePhase-ContrastMicroscope_1,Intheformercasetheintensityintheimageisreferredtoaspositivephasecontrast,Thelattercaseisreferredtoasnegativephasecontrast,Phase-ContrastMicroscope,1.Condenserannulus2.Objectplane3.Phaseplate4.Primaryimageplane,Phasecontrastimageofaepithelialcell,8.1.3ImprovementofPhotographs,UndesireddefectsinphotographsarisefromcorrespondingdefectsintheopticaltransferfunctionoftheincoherentimagingsystemthatproducedthemByinsertionofappropriateattenuatingandphase-shiftingplatesinthefocalplane,acompensatingfiltercouldbesynthesizedtoatleastpartiallyremovetheundesireddefects,Examplesofphotographyimprovement,Smalldetailsintheimagecouldbestronglyemphasizedifthelow-frequencycomponentsoftheobjectspectrumweresimplyattenuatedRemovalofimageblurPeriodicstructureassociatedwiththehalftoneprocessusedinprintingphotographscouldbesuppressedbyasimplespatialfilter,Halftone,Halftoneisthereprographictechniquethatsimulatescontinuoustoneimagerythroughtheuseofdots,varyingeitherinsize,inshapeorinspacing,Removalofimageblur,TheoriginalimagingsystemwasbadlydefocusedThecorrespondingopticaltransferfunction,Compensatingfilter,8.2IncoherentOpticalInformationProcessingSystems,AdvantagesGeneralfreedomofincoherentsystemsfromcoherentartifactsdustspecks,specklephenomenonTheydonotrequirethemorecomplexandexpensiveinputdeviceslikeSLMsMoresimpleandcheaperOriginoftheadvantagesCertainredundancylightfromasinglepixelorresolvablespotofaninputpassesthroughthesystemviamanyspatiallyseparatechannels,duetotheextendednatureoftheincoherentsource,DisadvantagesofIncoherentSystem,NonaturalopticalwaytosubtracttwointensitypatternslightintensityisalwaysnonnegativeWithnofrequencyplaneThemanipulationofthespectrumofaninputmustthereforeresorttolessdirectmethodsIncoherentsystemsoftenmusthaveaheavyintrusionofelectronicsattheiroutputinordertoachieveaflexibilitycomparablewiththatofcoherentsystems,CategoriesofIncoherentSystems,Systemsbasedongeometricalopticsignorethediffractionphenomenonsufferfromlimitationsontheachievablespace-bandwidthproductSystemsbasedondiffractionDiscretesystemsThefirsttwocategoriesofsystemsaredesignedtoaccommodatespatiallycontinuousinputs,8.2.1SystemsBasedonGeometricalOptics,TheyalmostinvariablyuseoneformofgeometricalprojectionofoneimageontoanotherIfatransparencywithintensitytransmittance1isimagedontoasecondtransparencywithintensitytransmittance2,thentheintensityateachpointimmediatelybehindthesecondtransparencyis12,Opticalsetupforintegralofproduct_1,Aphotodetectormeasuresthetotalintensitytransmittedthroughthepair,yieldingaphotocurrentI,Opticalsetupforintegralofproduct_2,Itmaybedesiredtochangeoneoftheinputsrapidlyseparate1from21mustbeinsertedinaninvertedgeometrytocompensatefortheinversionintroducedbyL2,Two-dimensionalconvolution,Letthetransparency1beintroducedwithouttheinversionreferredtoearlier,sothat,1ismovedinthenegativexdirectionwithspeedvforgivenym,Convolutionwithoutmotion,Theintensitydistributionacrossthedetectormaybewritten,Impulseresponsesynthesiswithamisfocusedsystem,Limitations,ThegeometryofthesystemmustbechoseninsuchawaythatdiffractioneffectsareentirelynegligibleStructureontheinputtransparenciesgetsfinerandfinerlessandlessofthelightobeythelawsofgeometricalopticssystemsbecomelessandlessaccurateSpace-bandwidth-productoftheinputfunctionislimited,8.2.2Systemsthatincorporatetheeffectsofdiffraction,ItispossibletodesignincoherentopticalinformationprocessingsystemsthattakefullaccountofthelawsofdiffractionThetwomajordifficultiesencounteredinattemptingtoperformgeneralfilteringoperationswithincoherentlightThepoint-spreadfunctionsthatcanbesynthesizedmustbenonnegativeandrealrestrictsthegeneralityoftheoperationsDeficiencyofmethodsforfindingthesimplestpupil-planemasktogeneratethedesiredintensitypoint-spreadfunction,Example:Bandpassfiltering,Interestingoperationscanbeperformedevenundertheconstraintsmentionedtwo-pupilOTFsynthesisProblem:thelargelow-frequencycomponentsthatarealwayspresentinincoherentimagesmustberemovedGoal:provideameansforperformingbandpassfilteringusingincoherentlightIncoherentprocessingmustbesupplementedwithsomeotherformofprocessing,eitherelectronicorcoherentopticalprocessing,SynthesisofOpticalTransferFunction(OTF)_1,Opticalsystemwiththepupiloftwo-openings,OriginalOTF,PhaseshiftedOTF,SynthesisofOpticalTransferFunction(OTF)_2,SubtractthetwoimageintensitiescollectedwiththetwoOTFsbyanelectronicsystem,TheeffectivetransferfunctionforthedifferenceimageisthedifferenceofthetwoOTFsusedincollectingthoseimagesbandpassfilter,Implementofphaseshift,ThephaseplatecanbereplacedbyaphasemodulatorAlternativelythetwoincoherentimagescanbetranslatedbyspatiallightmodulatorsintocoherentimages,andtheamplitudesofthosecanbeaddedwitha180phasedifferenceinaninterferometertoachievesubtraction,Summary,Evenwithelectronicsubtraction,itisoftenfoundthatthelow-frequencycomponentsbeingsubtractedareverystrongcomparedwiththehigh-frequency,andimperfectionsinthesubtractionoperationmayleaveimageartifactsornoiseIncoherentopticalinformationprocessingisoftensimplerthancoherentopticalprocessingIngeneraltheincoherentoneismuchlessflexibleintermsoftheoperationsthatcanbeachievedbycoherentone,8.3CoherentOpticalInformationProcessingSystems,FilteringoperationscanbesynthesizedbydirectmanipulationofthecomplexamplitudeInthissectionweoutlinethesystemarchitecturesusedforcoherentopticalinformationprocessingPointoutsomeofthedifficultiesencounteredinattemptingtosynthesizegeneralcomplexfilters,8.3.1CoherentSystemArchitectures,Coherentsystems,beinglinearincomplexamplitude,arecapableofrealizingoperationsoftheform,Threedifferentsystemconfigurationscanrealizetheoperation3lenses(4fsystem)2lenses_OnelensperformsbothFTandimaging2lenses_OnelensperformsbothlightcollectingandFT,4ffilteringarchitecture_1,Therearefourseparatedistancesoflengthfseparatingtheinputplanefromtheoutputplane,4ffilteringarchitecture_2,Inputtransparencyg(x1,y1)withspectrumG(x2/(f),y2/(f)DesiredfilterH(x2/(f),y2/(f)isinsertedplaneP2ThefieldbehindthefilteristhusGHTheoutputappearsinvertedinplaneP3duetoasequenceoftwoFouriertransformsTheinversioncanberemediedbyreversingthefinalcoordinatesystem(x3,y3)Disadvantage:vignettingcanoccurduringthefirstFouriertransformoperation,OnelensperformsbothFTandimaging_1,LensL2nowperformsboththeFouriertransformingandtheimagingoperationsSpectrumoftheinputappearsintherearfocalplaneP2,andimageappearsinplaneP3withunitymagnification,OnelensperformsbothFTandimaging_2,ThespectrumoftheinputhasassociatedwithitaquadraticphasefactorRecall:inputPlacedinFrontoftheLensThequadraticphasefactoris(d=2f;u,vx2,y2),OnelensperformsbothFTandimaging_3:Disadvantages,TheinputisnowtwicethedistancefromlensL2,andthereforethevignettingwillbeevenworseIfthetransferfunctionHisofhighspace-bandwidthproductwiderhmoreobjectpointsrelatewithimagepointRecallOutputofthissystemmustberegardedasafilteredversionofthefunction(,x1,y1,z1=2f)ratherthansimplyof,OnelensperformsbothlightcollectingandFT_1,LensL1nowservesasbothalensforcollectingthelightfromthepointsourceSandasaFouriertransforminglens,OnelensperformsbothlightcollectingandFT_2,ThemagnificationofthisimagingoperationasshownisunityThissystemhasnovignettingproblemsThequadraticphasefactoracrosstheinputplane(mentionedabove)iscanceledbytheconvergingilluminationDisadvantage:thesystemisnowoflength6fratherthan5f,Anamorphicprocessors_1,Astackedarrayofone-dimensionalinputsyieldsastackedarrayofone-dimensionalspectra,Anamorphicprocessors_2,CombinationofL2andL3performsadoubleFTintheydirectionandasingleFTinthexdirectionAnarrayofone-dimensionalspectraappearinplaneP2.L4removesphasefactorThelenspairL5andL6returntheoriginalfunctionstothespacedomain,Conventionalfilters,TheconventionalmeansforrealizingagiventransferfunctionhadbeentheinsertionofindependentamplitudeandphasemasksinthefrequencyplaneAllsuchmethodsarerathercumbersome,andcouldbesuccessfullyemployedonlywhenthedesiredpatternofphasecontrolwasrathersimple,Reachableregionsofthefrequencyplane,(a)apurelyabsorbingfilter(b)anabsorbingfilterandbinaryphasecontrol(c)apurephasefilter(d)afilterthatachievesarbitarydistributionsofabsorbtionandphasecontrol,8.3.2ConstraintsonFilterRealization,Forevenaverysimpleimpulseresponse,thecorrespondingtransferfunctionwasdifficulttocalculatefartoocomplicatedtobesynthesizedbytheserathersimpletechniquesThemostseverelimitationisthedifficultyofsimultaneouslycontrollingtheamplitudeandphasetransmittances,8.4VanderLugtfilter,In1963,A.B.VanderLugtoftheUniversityofMichigansRadarLaboratoryproposedanddemonstratedthetechniqueThisfiltercaneffectivelycontrolboththeamplitudeandphaseofatransferfunction,inspiteofthefactthattheyconsistonlyofpatternsofabsorptionItlargelyovercomethelimitationstocoherentprocessingsystemsmentionedabove,8.4.1Recordingthefrequency-planemaskforaVanderLugtfilter,ThefilterissynthesizedwiththehelpofaninterferometricsystemTheamplitudetransmittanceofthemaskP1isproportionaltothedesiredimpulseresponseh,Fieldinx2-y2plane,Thetiltedplanewaveincidentfromtheprismproduces,Fourierspectrumofh,wherethespatialfrequency=sin/,Intensityinx2-y2plane_1,Intensityinx2-y2plane_2,IfthecomplexfunctionHhasanamplitudedistributionAandaphasedistribution,thentheexpressionforIcanberewrittenintheform,Otheropticalsystemsforrecordingmask_1,ModifiedMach-Zehnderinterfereometer,Otheropticalsystemsforrecordingmask_2,ModifiedRayleighinterferometer,Amplitudetransmittanceofthemask,Theexposedfilmisdevelopedtoproduceatransparency,ThethirdtermoftheamplitudetransmittanceisproportionaltoHandthereforeexactlytheformrequiredtosynthesizeafilterwithimpulseresponseh,8.4.2ProcessingtheInputData_1,Oncethefrequency-planemaskhasbeensynthesized,itmaybeinsertedinanyofthethreeprocessingsystemsshownpreviously.Tobespecific,wefocusonthe4fsystemLettheinputtobefilteredisg(xl,yl),incidentonthefrequency-planemaskisacomplexamplitudedistribution,ProcessingtheInputData_2,Thefieldstrengthtransmittedbythemask,ThefieldstrengthinP3plane,ProcessingtheInputData_3,Thethirdoutputtermyieldsaconvolutionofhandg,centeredatcoordinates(0,-f)inthe(x3,y3)plane,ProcessingtheInputData_4,Thefourthtermyieldsacrosscorrelationofgandh*,centeredatcoordinates(0,f)inthe(x3,y3)plane,Aboutthefirstandsecondterms,Thetwotermsareofnoparticularutilityintheusualfilteringoperations,arecenteredattheoriginofthe(x3,y3)planeIfthereferencewaveisintroducedatasufficientlysteepangle,theconvolutionandcrosscorrelationtermswillbedeflectedsufficientlyfaroff-axistobeviewedindependently,Widthsofvariousterms,IfthemaximumwidthofhintheydirectionisWhandthatofgisWg,thenthewidthsofthevariousoutputtermsareasfollows,Locationsofthevarioustermsoftheprocessoroutput,Conditionsoftermsseparateeachother,Fromthefigureitisclearthatcompleteseparationwillbeachievediforequivalently,if,8.4.3CharacteristicsoftheVanderLugtFilter,Whenaspecifiedimpulseresponseisdesired,thetaskoffindingtheassociatedtransferfunctioniseliminatedGenerallycomplicatedcomplex-valuedtransferfunctionissynthesizedwithasingleabsorbingmaskTheVanderLugtfilterremainsverysensitivetotheexactpositionofthefrequencyplanemaskTherecordingofthemodulatedhigh-frequencycarrierrequiresahigher-resolutionfilm,8.5JointTransformCorrelator,DifferingfromtheVanderLugtfilter,boththedesiredimpulseresponseandthedatatobefilteredarepresentedsimultaneouslyduringtherecordingprocess,RecordingthefilterObtainingthefilteredoutput,Fieldsinvariousplanesduringrecording,Thefieldtransmittedthroughthefrontfocalplane,wheretheseparationbetweenthecentersofthetwoinputsisYThefieldintherearfocalplaneofthelens,Filtertransparency,Intensityontherecordingplane,Thetransparencyisassumedtohaveanamplitudetransmittancethatisproportionaltotheintensitythatexposedit,Outputamplitude,Takingaccountofscalingfactorsandcoordinateinversions,thefieldintherearfocalplaneofL4is,Againitisthethirdandfourthtermsoftheexpressionfortheoutputthatareofmostinterest,Usefulterms,Bothoftheseexpressionsarecrosscorrelationsofthefunctionsgandh,Oneoutputiscenteredatcoordinates(0,-Y)andtheotheratcoordinates(0,Y),Conditionstoobtainaconvolution,Itisnecessarythathanggbeintroducedintherecordingsetupwithamirrorreflectionaboutitsownorigine.g.,h(x1,y1-Y/2)h(-x1,-y1+Y/2)Theresultwillbetwooutputterms,centeredat(0,Y)and(0,-Y)intheoutputplane,eachofwhichisaconvolutionofgandh.Onetermisidenticalwiththeother,butreflectedabouttheopticalaxis,Separationofthecorrelationorconvolutionterms,IfWhrepresentsthewidthofhandWgisthewidthofg,bothmeasuredintheydirectiondirection,thenseparationofthedesiredtermscanbeshowntooccurif,NoprecisealignmentisnecessaryforthejointtransformcorrelatorAdvantageousforreal-timesystemsReductionofthespace-bandwidthproduct,8.6Applicationtocharacterrecognition,AparticularapplicationofopticalinformationprocessingthathasbeenofinterestformanyyearsisfoundinthefieldofcharacterrecognitionThecarrier-frequencyfiltersynthesismethodsareparticularlywellsuitedforthisapplication,8.6.1MatchedFilter,Alinearspace-invariantfilterissaidtobematchedtoasignals(x,y)ifitsimpulseresponseh(x,y)isgivenby,Ifaninputg(x,y)isappliedtoafiltermatchedtos(x,y),thentheoutputv(x,y)is,OpticalinterpretationofmatchedFiltering_1,TheaboveequationisrecognizedtobethecrosscorrelationfunctionofgandsSupposethatafiltermatchedtotheinputsignals(x,y),OpticalinterpretationofmatchedFiltering_2,Fouriertransformationoftheimpulseresponseshowsthattherequiredtransferfunctionis,Whenthesignalsispresentattheinput,thefieldtransmittedbythefilterisproportionaltoSS*Thislatterquantityisentirelyreal,whichisbroughttoabrightfocusbythefinaltransforminglensThusthepresenceofthesignalscanconceivablybedetectedbymeasuringtheintensityatthefocalpoint,8.6.2Character-RecognitionProblem,TheinputgmayconsistofanyoneofNpossiblealphanumericcharacters,representedbysl,s2,.,sNTheparticularcharacterpresentistobedeterminedbytheprocessorTheidentificationprocesscanberealizedbyapplyingtheinputtoabankofNfilters,eachmatchedtooneofthepossibleinputcharacters,Blockdiagramoftherecognitionmachine,ProcessofCharacter-Recognition,Theinputissimultaneously(orsequentially)appliedtotheNmatchedfilterswithtransferfunctionsS1*,S2*,.,SN*TheresponseofeachfilterisnormalizedbythesquarerootofthetotalenergyinthecharactertowhichitismatchedThesquaredmodulioftheoutputs|v1|2,|v2|2,.,|vN|2arecomparedattheparticularpointswheretheirmaximumoutputswouldbeanticipated,TheoremoftheRecognition,Iftheparticularcharacterisactuallypresentattheinputthentheparticularoutput|vk|2willbethelargestoftheNresponses,ProofoftheRecognitionTheorem_1,Fromtheequation,thepeakoutput|vk|2ofthecorrectmatchedfilterisgivenby,ProofoftheRecognitionTheorem_2,Ontheotherhand,theresponse|vn|2(nk)ofanincorrectmatchedfilterisgivenby,FromSchwarzsinequality,wehave,ProofoftheRecognitionTheorem_3,Itfollowsdirectlythat,withequalityifandonlyif,Itisevidentthatthematchedfilterdoesprovideonemeansofrecognizingwhichcharacter,ofasetofpossiblecharacters,isactuallybeingpresentedtothesystem,Othercategoriesofpatternrecognition,DetectionofthepresenceorabsenceofasingleknownobjectinalargerimageSuchaproblemisclosertowhatthematchedfilterisknowntodowellRecognitionregardlessofpossiblechangesoforientationandscalesizeofthetarget,8.6.3OpticalSynthesisofaCharacter-RecognitionMachine,ThematchedfilteroperationcanreadilybesynthesizedbymeansofeithertheVanderLugttechniqueorthejointtransformtechnique.HereisdirectedattheVanderLugt-typesystemByrestrictingattentiontotheproperregionoftheoutputspace,thematchedfilteroutputisreadilyobserved,Photographsoffilteringeffect,FilteringEffect,(a)TheimpulseresponseofaVanderLugtfilterwhichhasbeensynthesizedforthecharacterP(b)Theresponseofthematchedfilterportionoftheoutp