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Introduction+to+Fourier+Optics+2nd-Goodman.pdf

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IntroductiontoFourierOpticsSECONDEDITIONJosephWGoodmanStanfordUniversityTHEMcGRAWHILLCOMPANIES,INCNewYorkStLouisSanFranciscoAucklandBogotCaracasLisbonLondonMadridMexicoCityMilanMontrealNewDelhiSanJuanSingaporeSydneyTokyoTorontoABOUTTHEAUTHORJOSEPHWGOODMANreceivedtheABdegreeinEngineeringandAppliedPhysicsfromHarvardUniversityandtheMSandPhDdegreesinElectricalEngineeringfromStanfordUniversityHehasbeenamemberoftheStanfordfacultysince,andservedastheChairmanoftheDepartmentofElectricalEngineeringfromthroughDrGoodman'scontributionstoopticshavebeenrecognizedinmanywaysHehasservedasPresidentoftheInternationalCommissionforOpticsandoftheOpticalSocietyofAmerica(OSA)HereceivedtheFETermanawardoftheAmericanSocietyforEngineeringEducation(),theMaxBornAwardoftheOSAforcontributionstophysicaloptics(),theDennisGaborAwardoftheInternationalSocietyforOpticalEngineering(SPIE,),theEducationMedaloftheInstituteofElectricalandElectronicsEngineers(IEEE,),theFredericIvesMedaloftheOSAforoveralldistinctioninoptics(),andtheEstherHoffmanBellerMedaloftheOSAforcontributionstoopticseducation()HeisaFellowoftheOSA,theSPIE,andtheIEEEInhewaselectedtotheNationalAcademyofEngineeringInadditiontoIntroductiontoFourierOptics,DrGoodmanistheauthorofStatisticalOptics(JWileySons,)andtheeditorofInternationalTrendsinOptics(AcademicPress,)HehasauthoredmorethanscientificandtechnicalarticlesinprofessionaljournalsandbooksCONTENTSPrefaceIntroductionOptics,Information,andCommunicationTheBookAnalysisofTwoDimensionalSignalsandSystemsFourierAnalysisinTwoDimensionsDejinitionandExistenceConditionsTheFourierTransformasaDecompositionFourierTransformTheoremsSeparableFunctionsFunctionswithCircularSymmetry:FourierBesselTransformsSomeFrequentlyUsedFunctionsandSomeUsefulFourierTransformPairsLocalSpatialFrequencyandSpaceFrequencyLocalizationLinearSystemsLineurityandtheSuperpositionIntegralInvuriuntLinearSystems:TransferFunctionsTwoDimensionalSamplingTheoryTheWhittakerShannonSamplingTheoremSpacseBandwidthProducfProblemsChapterFoundationsofScalarDiffractionTheoryHistoricalIntroductionFromaVectortoaScalarTheorySomeMathematicalPreliminariesTheHelmholtzEquationGreen:sTheoremTheIntrgrulTheoremojHelmholtzandKirchhoflTheKirchhoffFormulationofDiffractionbyaPlanarScreenApplicutioncfrhrIntegralTheoremTheKirchhoffBoundaryConditiorzsTheL'resnelKirchhoffDffrclctionFormulaTheRayleighSomrnerfeldFormulationofDiffractionChoiceofAlternativeGreen:sFurzction~TheKuylcighSornmerfeld)iffructionFornzuluxviixiiContentsComparisonoftheKirchhoffandRayleighSommerfeldTheoriesFurtherDiscussionoftheHuygensFresnelPrincipleGeneralizationtoNonmonochromaticWavesDiffractionatBoundariesTheAngularSpectrumofPlaneWavesTheAngularSpectrumandItsPhysicalInterpretationPropagationoftheAngularSpectrumEffectsofaDiffractingApertureontheAngularSpectrumThePropagationPhenomenonasaLinearSpatialFilterProblemsChapterFresnelandFraunhoferDiffractionBackgroundITheIntensityofaWaveFieldTheHuygensFresnelPrincipleinRectangularCoordinatesTheFresnelApproximationPositivevsNegativePhasesAccuracyoftheFresnelApproximationTheFresnelApproximationandtheAngularSpectrumFresnelDiffractionBetweenConfocalSphericalSur$acesTheFraunhoferApproximationExamplesofFraunhoferDiffractionPatternsRectangularApertureCircularApertureThinSinusoidalAmplitudeGratingThinSinusoidalPhaseGratingExamplesofFresnelDiffractionCalculationsFresnelDiffractionbyaSquareApertureFresnelDiffractionbyaSinusoidalAmplitudeGratingTalbotImagesProblemsChapterWaveOpticsAnalysisofCoherentOpticalSystemsAThinLensasaPhaseTransformationITheThicknessFunctionTheParaxialApproximationThePhaseTransformationandItsPhysicalMeaningFourierTransformingPropertiesofLensesInputPlacedAgainsttheLensInputPlacedinFrontoftheLensInputPlacedBehindtheLensExampleofanOpticalFourierTransformContentsImageFormation:MonochromaticIlluminationTheImpulseResponseofaPositiveLensEliminatingQuadraticPhaseFactors:TheLensLawTheRelationBetweenObjectandImageAnalysisofComplexCoherentOpticalSystemsIAnOperatorNotationApplicationoftheOperatorApproachtoSomeOpticalSystemsProblemsChapterFrequencyAnalysisofOpticalImagingSystemsGeneralizedTreatmentofImagingSystemsAGeneralizedModelEffectsofDiffractionontheImagePolychromaticIllumination:TheCoherentandIncoherentCasesFrequencyResponseforDiffractionLimitedCoherentImagingTheAmplitudeTransferFunctionExamplesofAmplitudeTransferFunctionsFrequencyResponseforDiffractionLimitedIncoherentImagingTheOpticalTransferFunctionGeneralPropertiesoftheOTFTheOTFofanAberrationFreeSystemExamplesofDiffractionLimitedOTFsAberrationsandTheirEffectsonFrequencyResponseTheGeneralizedPupilFunctionEfSectsofAberrationsontheAmplitudeTransferFunctionEffectsofAberrationsontheOTFExampleofaSimpleAberration:AFocusingErrorApodizationandItsEffectsonFrequencyResponseComparisonofCoherentandIncoherentImagingFrequencySpectrumoftheImageIntensityTwoPointResolutionOtherEffectsResolutionBeyondtheClassicalDiffractionLimitUnderlyingMathematicalFundamentalsIntuitiveExplanationofBandwidthExtrapolationAnExtrapolationMethodBasedontheSamplingTheoremAnIterativeExtrapolationMethodPracticalLimitationsProblemsChapterWavefrontModulationWavefrontModulationwithPhotographicFilmThePhysicalProcessesofExposure,Development,andFixingDejinitionofTermsFilminanIncoherentxivContentsOpticalSystemFilminaCoherentOpticalSystemTheModulationTransferFunctionBleachingofPhotographicEmulsionsSpatialLightModulatorsPropertiesofLiquidCrystalsSpatialLightModulatorsBasedonLiquidCrystalsMagnetoOpticSpatialLightModulatorsDeformableMirrorSpatialLightModulatorsMultipleQuantumWellSpatialLightModulatorsAcoustoOpticSpatialLightModulatorsDiffractiveOpticalElementsBinaryOpticsOtherTypesofDifSractiveOpticsAWordofCautionProblemsChapterAnalogOpticalInformationProcessingHistoricalBackgroundTheAbbePorterExperimentsTheZemikePhaseContrastMicroscopeImprovementofPhotographs:MardchalTheEmergenceofaCommunicationsViewpointApplicationofCoherentOpticstoMoreGeneralDataProcessingIncoherentImageProcessingSystemsSystemsBasedonGeometricalOpticsSystemsThatIncorporatetheEffectsofDiffractionCoherentOpticalInformationProcessingSystemsCoherentSystemArchitecturesConstraintsonFilterRealizationTheVanderLugtFilterSynthesisoftheFrequencyPlaneMaskProcessingtheInputDataAdvantagesoftheVanderLugtFilterTheJointTransformCorrelatorApplicationtoCharacterRecognitionTheMatchedFilterACharacterRecognitionProblemOpticalSynthesisofaCharacterRecognitionMachineSensitivitytoScaleSizeandRotationOpticalApproachestoInvariantPatternRecognitionMellinCorrelatorsCircularHarmonicCorrelationSyntheticDiscriminantFunctionsImageRestorationTheInverseFilterTheWienerFiltecortheLeastMeanSquareErrorFilterFilterRealizationProcessingSyntheticApertureRadar(SAR)DataFormationoftheSyntheticApertureTheCollectedDataandtheRecordingFormatFocalPropertiesoftheContentsxvFilmTransparencyFormingaTwoDimensionalImageTheTiltedPlaneProcessorAcoustoOpticSignalProcessingSystemsBraggCellSpectrumAnalyzerSpaceIntegratingCorrelatorTimeIntegratingCorrelatorOtherAcoustoOpticSignalProcessingArchitecturesDiscreteAnalogOpticalProcessorsDiscreteRepresentationofSignalsandSystemsASerialMatrixVectorMultiplierAParallelIncoherentMatrixVectorMultiplierAnOuterProductProcessorOtherDiscreteProcessingArchitecturesMethodsforHandlingBipolarandComplexDataProblemsChapterHolographyHistoricalIntroductionTheWavefrontReconstructionProblemRecordingAmplitudeandPhaseTheRecordingMediumReconstructionoftheOriginalWavefrontLinearityoftheHolographicProcessImageFormationbyHolographyTheGaborHologramOriginoftheReferenceWaveTheTwinImagesLimitationsoftheGaborHologramTheLeithUpatnieksHologramRecordingtheHologramObtainingtheReconstructedImagesTheMinimumReferenceAngleHolographyofThreeDimensionalScenesPracticalProblemsinHolographyImageLocationsandMagnificationImageLocationsAxialandTransverseMagn$cationsAnExampleSomeDifferentTypesofHologramsFresnel,Fraunhofer,Image,andFourierHologramsTransmissionandReflectionHologramsHolographicStereogramsRainbowHologramsMultiplexHologramsEmbossedHologramsThickHologramsRecordingaVolumeHolographicGratingReconstructingWavefrontsfromaVolumeGratingFringeOrientationsforMoreComplexRecordingGeometriesGratingsofFiniteSizeDiffractionESficiencyCoupledModeTheoryxviContentsRecordingMaterialsSilverHalideEmulsionsPhotopolymerFilmsDichromatedGelatinPhotorefractiveMaterialsComputerGeneratedHologramsTheSamplingProblemTheComputationalProblemTheRepresentationalProblemDegradationsofHolographicImagesEffectsofFilmMTFEffectsofFilmNonlinearitiesEffectsofFilmGrainNoiseSpeckleNoiseHolographywithSpatiallyIncoherentLightApplicationsofHolographyMicroscopyandHighResolutionVolumeImageryInte$erometryImagingThroughDistortingMediaHolographicDataStorageHolographicWeightsforArtijicialNeuralNetworksOtherApplicationsProblemsChapterADeltaFunctionsandFourierTransformTheoremsAlDeltaFunctionsADerivationofFourierTransformTheoremsBIntroductiontoParaxialGeometricalOpticsBlTheDomainofGeometricalOpticsBRefraction,Snell'sLaw,andtheParaxialApproximationBTheRayTransferMatrixBConjugatePlanes,FocalPlanes,andPrincipalPlanesBEntranceandExitPupilsCPolarizationandJonesMatricesCDefinitionoftheJonesMatrixCExamplesofSimplePolarizationTransformationsCReflectivePolarizationDevicesBibliographyIndexPREFACEFourieranalysisisaubiquitoustoolthathasfoundapplicationtodiverseareasofphysicsandengineeringThisbookdealswithitsapplicationsinoptics,andinparticularwithapplicationstodiffraction,imaging,opticaldataprocessing,andholographySincethesubjectcoveredisFourierOptics,itisnaturalthatthemethodsofFourieranalysisplayakeyroleastheunderlyinganalyticalstructureofourtreatmentFourieranalysisisastandardpartofthebackgroundofmostphysicistsandengineersThetheoryoflinearsystemsisalsofamiliar,especiallytoelectricalengineersChapterreviewsthenecessarymathematicalbackgroundForthosenotalreadyfamiliarwithFourieranalysisandlinearsystemstheory,itcanserveastheoutlineforamoredetailedstudythatcanbemadewiththehelpofothertextbooksexplicitlyaimedatthissubjectAmplereferencesaregivenformoredetailedtreatmentsofthismaterialForthosewhohavealreadybeenintroducedtoFourieranalysisandlinearsystemstheory,thatexperiencehasusuallybeenwithfunctionsofasingleindependentvariable,namelytimeThematerialpresentedinChapterdealswiththemathematicsintwospatialdimensions(asisnecessaryformostproblemsinoptics),yieldinganextrarichnessnotfoundinthestandardtreatmentsoftheonedimensionaltheoryTheoriginaleditionofthisbookhasbeenconsiderablyexpandedinthissecondedition,anexpansionthatwasneededduetothetremendousamountofprogressinthefieldsincewhenthefirsteditionwaspublishedThebookcanbeusedasatextbooktosatisfytheneedsofseveraldifferenttypesofcoursesItisdirectedtowardsbothphysicistsandengineers,andtheportionsofthebookusedinthecoursewillingeneralvarydependingontheaudienceHowever,byproperlyselectingthematerialtobecovered,theneedsofanyofanumberofdifferentaudiencescanbemetThisPrefacewillmakeseveralexplicitsuggestionsfortheshapingofdifferentkindsofcoursesFirstaonequarteroronesemestercourseondiffractionandimageformationcanbeconstructedfromthematerialscoveredinChaptersthrough,togetherwithallthreeappendicesIftimeisshort,thefollowingsectionsofthesechapterscanbeomittedorleftasreadingfortheadvancedstudent:,,,andAsecondtypeofonequarteroronesemestercoursewouldcoverthebasicsofFourierOptics,butthenfocusontheapplicationareaofanalogopticalsignalprocessingForsuchacourse,IwouldrecommendthatChapterbelefttothereadingofthestudent,thatthematerialofChapterbebegunwithSection,andfollowedbySection,leavingtherestofthischaptertoareadingbythosestudentswhoarecuriousastotheoriginsoftheHuygensFresnelprincipleInChapter,SectionsandcanbeskippedChaptercanbeginwithEq()fortheamplitudetransmittancefunctionofathinlens,andcanincludealltheremainingmaterial,withtheexceptionthatSectioncanbeleftasreadingfortheadvancedstudentsIftimeisshort,ChaptercanbeskippedentirelyForthiscourse,virtuallyallofthematerialpresentedinChapterisimportant,asismuchofthematerialinChapterIfitisnecessarytoreducetheamountofmaterial,Iwouldrecommendthatthefollowingsectionsbeomitted:,,andItisoftendesirabletoincludesomesubsetofthematerialxviiiPrefaceonholographyfromChapterinthiscourseIwouldincludesections,,,,,,,andThethreeappendicesshouldbereadbythestudentsbutneednotbecoveredinlecturesAthirdvariationwouldbeaonequarteroronesemestercoursethatcoversthebasicsofFourierOpticsbutfocusesonholographyasanapplicationThecoursecanagainbeginwithSectionandbefollowedbySectionThecoveragethroughChaptercanbeidenticalwiththatoutlinedaboveforthecoursethatemphasizesopticalsignalprocessingInthiscase,thematerialofSections,,,andcanbeincludedInChapter,onlySectionisneeded,althoughSectionisausefuladditionifthereistimeChaptercannowbeskippedandChapteronholographycanbethefocusofattentionIftimeisshort,SectionsandcanbeomittedThefirsttwoappendicesshouldbereadbythestudents,andthethirdcanbeskippedInsomeuniversities,morethanonequarteroronesemestercanbedevotedtothismaterialIntwoquartersortwosemesters,mostofthematerialinthisbookcanbecoveredTheabovesuggestionscanofcoursebemodifiedtomeettheneedsofaparticularsetofstudentsortoemphasizethematerialthataparticularinstructorfeelsismostappropriateIhopethatthesesuggestionswillatleastgivesomeideasaboutpossibilitiesTherearemanypeopletowhomIoweaspecialwordofthanksfortheirhelpwiththisneweditionofthebookEarlyversionsofthemanuscriptwereusedincoursesatseveraldifferentuniversitiesIwouldinparticularliketothankProfsAASawchuk,JFWalkup,JLeger,PPichon,DMehrl,andtheirmanystudentsforcatchingsomanytypographicalerrorsandinsomecasesoutrightmistakesHelpfulcommentswerealsomadebyIErtezaandMBashaw,forwhichIamgratefulSeveralusefulsuggestionswerealsomadebyanonymousmanuscriptreviewersengagedbythepublisherAspecialdebtisowedtoProfEmmettLeith,whoprovidedmanyhelpfulsuggestionsIwouldalsoliketothankthestudentsinmyFourierOpticsclass,whocompetedfiercelytoseewhocouldfindthemostmistakesUndoubtedlythereareotherstowhomIowethanks,andIapologizefornotmentioningthemexplicitlyhereFinally,IthankHonMai,withoutwhosepatience,encouragementandsupportthisbookwouldnothavehavebeenpossibleJosephWGoodmanCHAPTERIntroductionOPTICS,INFORMATION,ANDCOMMUNICATIONSincethelates,thevenerablebranchofphysicsknownasopticshasgraduallydevelopedeverclosertieswiththecommunicationandinformationsciencesofelectricalengineeringThetrendisunderstandable,forbothcommunicationsystemsandimagingsystemsaredesignedtocollectorconveyinformationIntheformercase,theinformationisgenerallyofatemporalnature(egamodulatedvoltageorcurrentwaveform),whileinthelattercaseitisofaspatialnature(egalightamplitudeorintensitydistributionoverspace),butfromanabstractpointofview,thisdifferenceisarathersuperficialonePerhapsthestrongesttiebetweenthetwodisciplinesliesinthesimilarmathematicswhichcanbeusedtodescribetherespectivesystemsofinterestthemathematicsofFourieranalysisandsystemstheoryThefundamentalreasonforthesimilarityisnotmerelythecommonsubjectof"information",butrathercertainbasicpropertieswhichcommunicationsystemsandimagingsystemsshareForexample,manyelectronicnet

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