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Keigo Iizuka Engineering Optics Fourth Edition
EngineeringOptics FourthEdition KeigoIizuka DepartmentofElectrical&Computer
Engineering
UniversityofToronto
Toronto,ON,Canada
ISBN978-3-319-69250-0ISBN978-3-319-69251-7(eBook) https://doi.org/10.1007/978-3-319-69251-7
LibraryofCongressControlNumber:2018961225
1st and2nd editions: © Springer-VerlagBerlinHeidelberg1985,1987
3rd edition: © SpringerScience+BusinessMedia,LLC2008
4th edition: © SpringerNatureSwitzerlandAG2019
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Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthis bookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernorthe authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardto jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations.
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PrefacetotheFourthEdition Startlingly,fastprogresshasbeenmadeinthe fieldofopticaldistancemeasurement.Itisarapidlygrowing fieldwithsignificantimprovementsinmeasurement accuracy,reliability,simplicity,andrange.Yettextbooktreatmentsofthe fieldare laggingbehindtherapiddevelopment.
Inthisedition,sixnewchaptershavebeenaddedonopticaldistancemeasurementfromChaps. 17 to 22.
Opticaldistancemeasurementisuniqueinthatitisnon-contactandcanbe invisibleusinginfraredlight.Opticalmeasurementsarevastrangedfromthe micro-measurementofretinaltissueinophthalmologytothedetectionofgravitationalwavesfromcoalescingblackholesindistantpartsoftheuniverse.Optical distancemeasurementisusedinawidevarietyof fields,includingremotesensing, surveying,robotics,machinevision,qualitycontrol,medicaldevices,thecamera industry,andevencomputergames.
Besidestheadditionofthenewchapters,someoftheexistingchapterswere revitalizedtokeeppacewithtechnologicaladvances.Theupdatedmaterialincludes opticaldisksinChap. 4,optical fi bercommunicationsinChap. 13,and3Dimaging inChap. 16.
Examplesandproblemsareincludedineachchapterforeasiercomprehension andelaborationofthesubjectmatter.
Allinall,itistheauthor ’shumbleattempttomakechallengestothecutting edgeofopticsa “lightjob”!
Mylongtimecolleague,Ms.MaryJeanGiliberto,hasmadeasignificantcontributiontobringingthemanuscripttoitspresentform.Isincerelyappreciateher tremendouseffortsanddevotion.
Iwouldliketoextendmygratitudetomywife,Yoko,whohasbeenaconstant sourceofencouragementthroughoutourmanyyearstogether.Shehasstoodbeside meineverythingIhaveundertaken.Shehasbeenmyinspirationandmotivation, andIamforevergratefulforherprofoundsupport.
Toronto,CanadaKeigoIizuka August2018
PrefacetotheThirdEdition Onmy1990sabbaticalleavefromtheUniversityofToronto,IworkedfortheNHK (JapanBroadcastingStation)ScienceandTechnologyLaboratory.Irecallmy initialvisittotheexecutive floorofNHK,aspaciousroomwithacommanding viewofmetropolitanTokyo.Icouldnothelpbutnoticehigh-definitiontelevisions (HDTVs)ineverycorneroftheroom.Atthattime,HDTVtechnologywasjust breakingintothemarketplace,andtherewas fiercecompetitionformass-producing HDTVs.WhenIenteredtheroom,theHDTVswereturnedononeaftertheotheras myhostproclaimed, “Thisisthefutureofthetelevision.Isn’tthequalityofthe picturesuperb?”
Ireplied, “Theyareindeedsuperb,butiftheHDTVimageswere3D,thatwould bereallyout-of-thisworld.”
Thehostcontinued, “3DHDTVisourfutureproject.”
Thatwasnearlytwentyyearsago,andmuchprogresshasbeenmadein3D imagingtechniquessincethen,andthisfutureisherewithus.Theamountof informationintheliteratureonthissubjectisnowsubstantial.Three-dimensional imagingtechniquesarenotmerelylimitedtothetelevisionindustry.Thebasic techniquesarealsousedintheautomobile,electronics,entertainment,andmedical industries.Inspiredbythisareaofgrowth,IaddedChap.16on3Dimaging,which startswithabriefhistoricalintroductionof3DimagingfromtheancientGreekera tomoderntimes.Thechapterthenexpandsonbasicprinciplesof13differenttypes of3Ddisplays.
Theerrataofthesecondeditionof EngineeringOptics,whichwerepreviously publishedonmyWebsite,havebeencorrectedinthisedition.
Afewnewproblemset-typequestionshavebeenaddedforteachingpurposes. Iwouldliketoexpressmysinceregratitudetomycolleagueandfellowengineer,Ms.MaryJeanGiliberto,forherexcellenteditingassistance.Thisbookand itspreviouseditionwouldnothavebeenpossiblewithouttheunconditionalcaring supportofmywifeandfamily.
Toronto,CanadaKeigoIizuka October2007
PrefacetotheSecondEdition The firsteditionofthistextbookwaspublishedonlylastyear,andnow,thepublisherhasdecidedtoissueapaperbackedition.Thisisintendedtomakethetext moreaffordabletoeveryonewhowouldliketobroadentheirknowledgeofmodern problemsinoptics.
Theaimofthisbookistoprovideabasicunderstandingoftheimportant featuresofthevarioustopicstreated.Adetailedstudyofallthesubjectscomprising the fieldofengineeringopticswould fillseveralvolumes.Thisbookcouldperhaps belikenedtoasoup:Itiseasytoswallow,butsoonerorlaterheartiersustenanceis needed.Itismyhopethatthisbookwillstimulateyourappetiteandprepareyoufor thebanquetthatcouldbeyours.
Iwouldliketotakethisopportunitytothankthosereaders,especially Mr.BranislavPetrovicandMr.ThomasNimz,whosentmeappreciativelettersand helpfulcomments.Thesehaveencouragedmetointroduceafewminorchanges andimprovementsinthisedition.
Toronto,CanadaKeigoIizuka September1986
PrefacetotheFirstEdition “WhichareadoyouthinkIshouldgointo?” or “Whicharetheareasthathavethe brightestfuture?” arequestionsthatarefrequentlyaskedbystudentstryingto decideona fieldofspecialization.Myadvicehasalwaysbeentopickany fieldthat combinestwoormoredisciplinessuchasnuclearphysics,biomedicalengineering, optoelectronics,orevenengineeringoptics.Withtheever-growingcomplexityof today’sscienceandtechnology,manyaproblemcanbetackledonlywiththe cooperativeeffortofmorethanonediscipline.
Engineeringopticsdealswiththeengineeringaspectsofoptics,anditsmain emphasisisonapplyingtheknowledgeofopticstothesolutionofengineering problems.Thisbookisintendedbothforthephysicsstudentwhowantstoapplyhis knowledgeofopticstoengineeringproblemsandfortheengineeringstudentwho wantstoacquirethebasicprinciplesofoptics.
Thematerialinthebookwasarrangedinanorderthatwouldprogressively increasethestudent’scomprehensionofthesubject.Basictoolsandconcepts presentedintheearlierchaptersarethendevelopedmorefullyandappliedinthe laterchapters.Inmanyinstances,thearrangementofthematerialdiffersfromthe truechronologicalorder.
Thefollowingisintendedtoprovideanoverviewoftheorganizationofthe book.Inthisbook,thetheoryoftheFouriertransformswasusedwheneverpossible becauseitprovidesasimpleandclearexplanationformanyphenomenainoptics. Complicatedmathematicshavebeencompletelyeliminated.
Chapter1givesahistoricalprospectiveofthe fieldofopticsingeneral.Itis amazingthat,eventhoughlighthasalwaysbeenasourceofimmensecuriosityfor ancientpeoples,mostprinciplesofmodernopticshadtowaituntilthelateeighteenthcenturytobeconceived,anditwasonlyduringthemid-nineteenthcentury withMaxwell’sequationsthatmodernopticswasfullybroughttobirth.The centuryfollowingthateventhasbeenanexcitingtimeoflearningandatremendous growthwhichwehavebeenwitnessingtoday.
Chapter2summarizesthemathematicalfunctionswhichveryoftenappearin optics,anditisintendedasabasisforthesubsequentchapters.
Chapter3developsdiffractiontheoryandprovesthatthefar-fielddiffraction patternissimplytheFouriertransformofthesource(oraperture)function.This Fouriertransformrelationshipisthebuildingblockoftheentirebook(Fourieroptics).
Chapter4teststheknowledgeobtainedinChaps.2and3.Aseriesofpractical examplesandtheirsolutionsarecollectedinthischapter.
Chapter5developsgeometricalopticswhichisthecounterpartofFourieroptics appearinginChap.3.Thepowerofgeometricalopticsisconvincinglydemonstratedwhenworkingwithinhomogeneoustransmissionmediabecause,forthis typeofmedia,othermethodsaremorecomplicated.Variouspracticalexamples relatedto fiberopticsarepresentedsothatthebasicknowledgenecessaryfor fiber-opticalcommunicationinChap.13isdeveloped.
Chapter6dealswiththeFouriertransformableandimageformablepropertiesof alensusingFourieroptics.Thesepropertiesofalensareabundantlyusedinoptical signalprocessingappearinginChap.11.
Chapter7explainstheprincipleofthefastFouriertransform(FFT).Inorderto constructaversatilesystem,themeritsofbothanaloganddigitalprocessinghaveto becleverlyamalgamated.Onlythroughthishybridapproachcansystemssuchas computerholography,computertomography,orhologrammatrixradarbecome possible.
Chapter8coversbothcoherentandwhite-lightholography.Thefabricationof hologramsbycomputerisalsoincluded.Whileholographyispopularlyidenti fied withitsabilitytocreatethree-dimensionalimages,theusefulnessofholographyas ameasurementtechniquedeservesequalrecognition.Thus,holographyisusedfor measuringminutechangesandvibrations,asamachiningtool,andforprofilingthe shapeofanobject.
DescriptionsofmicrowaveholographyaregiveninChap.12asaseparatechapter. Knowledgeaboutthediffraction fieldandFFTwhicharefoundinChaps.3and6is usedasthebasisformanyofthediscussionsonholography.
Chapter9showsapictorialcookbookforfabricatingahologram.Experiencein fabricatingahologramcouldbeamemorableinitiationforastudentwhowishesto beapioneerinthe fieldofengineeringoptics.
Chapter10introducesanalysisinthespatialfrequencydomain.Thetreatmentof opticscanbeclassifi edintotwobroadcategories:Oneisthespacedomain,which hasbeenuseduptothischapter,andtheotheristhespatialfrequencydomain, whichisnewlyintroducedhere.ThesetwodomainsarerelatedbytheFourier transformrelationship.TheexistenceofsuchdualdomainsconnectedbyFourier transformsisalsofoundinelectronicsandquantumphysics.Needlesstosay,the finalresultsarethesameregardlessofthechoiceofthedomainofanalysis. ExamplesdealingwiththelensinChap.6areusedtoexplaintheprinciple.
Chapter11coversopticalsignalprocessingofvarioussorts.Knowledgeof diffraction,lenses,FFT,andholography,coveredinChaps.3,6,7,and8, respectively,isusedextensivelyinthischapter.Inadditiontocoherentandincoherentopticalprocessing,Chap.11alsoincludesasectionontomography.Many examplesaregiveninthischapterwiththehopethattheywillstimulatethereader ’s imaginationtodevelopnewtechniques.
Chapter12isaseparatechapteronmicrowaveholography.While Chap.8concernsitselfprimarilywithlightwaveholography,Chap.12extendsthe principlesofholographytothemicrowaveregion.Itshouldbepointedoutthat manyofthetechniquesmentionedherearealsoapplicabletoacousticholography.
Chapter13describes fiber-opticalcommunicationsystemswhichcombinethe technologiesofopticsandthoseofcommunications.Thetreatmentoftheoptical fiberisbasedonthegeometricalopticspointofviewpresentedinChap.5.Many ofthecomponentsdevelopedfor fiber-opticalcommunicationsystems findapplicationsinotherareasaswell.
Chapter14providesthebasicsnecessarytofullyunderstandintegratedoptics. Manyanintegratedopticsdeviceusesthefactthatanelectro-oracousto-optic materialchangesitsrefractiveindexaccordingtotheexternalelectric fieldor mechanicalstrain.Theindexofrefractionofthesematerials,however,depends uponthedirectionofthepolarizationofthelight(anisotropic),andtheanalysisfor theanisotropicmaterialisdifferentfromthatofisotropicmaterial.Thischapter dealswiththepropagationoflightinsuchmedia.
Chapter15dealswithintegratedoptics,whichisstillsucharelativelyyoung fieldthatalmostanyonewithdesireandimaginationcancontribute.
Mrs.MaryJeanGilibertoplayedanintegralroleinproofreadingandstylingthe Englishoftheentirebook.Onlythroughherdevotedpainstakingcontributionwas thepublicationofthisbookpossible.Iwouldliketoexpressmysincereappreciationtoher.
Mr.TakamitsuAokiofSonyCorporationgavemehisabundantcooperation.He checkedalltheformulasandsolvedallproblemsets.Hewasthusthemanbehind thesceneswhoplayedalloftheseimportantroles.
IamthankfultoDr.JunichiNakayamaofKyotoInstituteofTechnologyfor helpingmetoimprovevariouspartsofChap.10.IamalsogratefultoProfessor StefanZukotynskiandMr.DehuanHeoftheUniversityofTorontofortheir assistance.TheauthoralsowishestothankProfessorT.TamirofthePolytechnic InstituteofNewYork,Brooklyn,andDr.H.K.V.LotschofSpringer-Verlagfor criticalreadingandcorrectingthemanuscript.Mr.R.MichelsofSpringer-Verlag deservespraiseforhispainstakingeffortstoconvertthemanuscriptintobookform. MegumiIizukahelpedtocompiletheSubjectIndex.
Toronto,CanadaKeigoIizuka August1985
3.2Fresnel-KirchhoffDiffractionFormula
3.3Fresnel-Kirchhoff
4.3DiffractionfromaPeriodicArrayofSlits
5.1.3DerivativeinanArbitraryDirectionandDerivative NormaltoaSurface
5.2SolutionoftheWaveEquationinInhomogeneousMedia bytheGeometrical-OpticsApproximation
5.3PathofLightinanInhomogeneousMedium
5.4RelationshipBetweenInhomogeneityandRadius ofCurvatureoftheOpticalPath
5.5PathofLightinaSphericallySymmetricMedium
5.6PathofLightinaCylindricallySymmetricMedium
5.7SelfocFiber
5.7.1MeridionalRayinSelfocFiber
5.7.2SkewRayinSelfocFiber
5.8QuantizedPropagationConstant
5.8.1QuantizedPropagationConstantinaSlabGuide
5.8.2QuantizedPropagationConstantinOpticalFiber
5.9GroupVelocity
6.1DesignofPlano-ConvexLens
6.2ConsiderationofaLensfromtheViewpointofWave
6.3.1InputontheLensSurface
6.3.2InputattheFrontFocalPlane
6.3.3InputBehindtheLens
6.3.4FourierTransformbyaGroupofLenses
6.3.5EffectofLateralTranslationoftheInputImage ontheFourier-TransformImage
6.4ImageFormingCapabilityofaLensfromtheViewpoint ofWaveOptics
6.5EffectsoftheFiniteSizeoftheLens
6.5.1InfluenceoftheFiniteSizeoftheLens ontheQualityoftheFourierTransform
6.5.2InfluenceoftheFiniteSizeoftheLens
7.1WhatistheFastFourierTransform?
7.2FFTbytheMethodofDecimationinFrequency
7.3FFTbytheMethodofDecimationinTime
8.1PictorialIllustrationofthePrincipleofHolography
8.2AnalyticalDescriptionofthePrincipleofHolography
8.3RelationshipBetweentheIncidentAngleofthe ReconstructingBeamandtheBrightnessofthe ReconstructedImage
8.4WaveFrontClassi ficationofHolograms
8.4.1FresnelHologram
8.4.2FourierTransformHologram
8.4.4LenslessFourierTransformHologram
8.5HologramsFabricatedbyaComputer
8.6White-LightHologram
8.7SpecklePattern
8.8ApplicationsofHolography
8.8.1PhotographswithEnhancedDepthofField
8.8.2High-DensityRecording .....................
8.8.3OpticalMemoryforaComputer
8.8.4HolographicDisk ..........................
8.8.5LaserMachining ...........................
8.8.6ObservationofDeformationbyMeansofan InterferometricHologram
8.8.7DetectionoftheDifferenceBetweenTwo Pictures .................................
8.8.8ObservationofaVibratingObject
8.8.9GenerationofContourLinesofanObject
9LaboratoryProceduresforFabricatingHolograms
9.1IsolatingtheWorkAreafromEnvironmentalNoise
9.2NecessaryOpticalElementsforFabricatingHolograms
9.2.1OpticalBench
9.2.2Laser
9.2.3BeamDirector
9.2.4SpatialFilter
9.2.5BeamSplitter
9.2.6Photographic-PlateHolder
9.2.7Film ....................................
9.3PhotographicIllustrationoftheExperimentalProcedures forHologramFabrication ...........................
9.4ExposureTime
9.5Dark-RoomProcedures
9.5.1Developing
9.5.2StopBath
9.5.3Fixer
9.5.4WaterRinsing
9.5.6Bleaching
9.6ViewingtheHologram
10AnalysisoftheOpticalSystemintheSpatialFrequency Domain
10.1TransferFunctionforCoherentLight
10.1.1ImpulseResponseFunction ...................
10.1.2CoherentTransferFunction(CTF)
10.2SpatialCoherenceandTemporalCoherence
10.3DifferencesBetweentheUsesofCoherentandIncoherent
11.2BasicOperationsofComputationbyLight
11.2.1OperationofAdditionandSubtraction
11.3.1DecodingbyFourierTransform
11.3.2InverseFilters
11.3.4AFilterforRecoveringtheImagefrom aPeriodicallySampledPicture
12.1.2MethodBasedonChangesinColorInduced byMicrowaveHeating
12.1.3MethodbyThermalVision
12.1.4MethodbyMeasuringSurfaceExpansion
12.2MicrowaveHolographyAppliedtoDiagnostics andAntennaInvestigations
12.2.1 “SeeingThrough” byMeansofMicrowave Holography
12.2.2VisualizationoftheMicrowavePhenomena
12.2.3SubtractiveMicrowaveHolography
12.2.4HolographicAntenna
12.2.5AMethodofObtainingtheFar-FieldPattern fromtheNearFieldPattern ...................
12.3SideLookingSyntheticApertureRadar .................
12.3.1MathematicalAnalysisofSideLookingSynthetic ApertureRadar ............................
12.4HISSRadar .....................................
13.1AdvantagesofOpticalFiberSystems
13.1.1LargeInformationTransmissionCapability
13.1.2LowTransmissionLoss
13.1.3Non-metallicCable
13.2OpticalFiber
13.3DispersionoftheOpticalFiber
13.4FiberTransmissionLossCharacteristics
13.5.1PhotonicCrystalFiberConfinedbyTotal InternalReflection
13.7ReceiversforFiberOpticalCommunications
13.7.2AvalanchePhotodiode
13.7.3OpticalPowerBudgetandSignalBitRate
13.8TransmittersforFiberOpticalCommunications
13.9Connectors,Splices,andCouplers
13.9.1OpticalFiberConnector
13.9.2Splicing
13.9.3FiberOpticCouplers
15.3.1DirectionalCouplerSwitch
15.3.2Reversed Db DirectionalCoupler
15.3.3TunableDirectionalCouplerFilter
15.3.4YJunction
15.3.5Mach-ZehnderInterferometricModulator
15.3.6WaveguideModulator
15.3.7AcoustoopticModulator
15.4.1OpticallySwitchableDirectionalCoupler
15.4.2OpticalTriode
15.4.3OpticalANDandORGates
15.4.4OtherTypesofBistableOpticalDevices
15.4.5Self-focusingActioninNon-linearOptics
15.5ConsiderationofPolarization
15.6IntegratedOpticalLensesandtheSpectrumAnalyzer
15.6.1ModeIndexLens ..........................
15.6.2GeodesicLens ............................
15.6.3FresnelZoneLens
15.6.4IntegratedOpticalSpectrumAnalyzer
15.7MethodsofFabrication .............................
15.7.1FabricationofOpticalGuides .................
15.7.2FabricationofPatterns ......................
15.7.3SummaryofStripGuides
15.7.4SummaryofGeometriesofElectrodes
163DImaging
16.1HistoricalDevelopmentof3DDisplays
16.2PhysiologicalFactorsContributingto3DVision
16.3HowParallaxandConvergenceGeneratea3DEffect
16.3.1ProjectionType
16.3.2InterceptionType
16.4DetailsoftheMeansUsedforRealizingthe3DEffect
16.4.1MethodsBasedonPolarizedLight
16.4.2SuperDeep3DMovies ......................
16.4.3Wheatstone’sStereoscope ....................
16.4.4Brewster ’sStereoscope ......................
16.4.5Anaglyph ................................
16.4.6TimeSharingMethod
16.4.7HeadMountedDisplay(HMD)
16.4.8VolumetricMethods
16.4.9VarifocalMirror
16.4.10ParallaxBarrier
16.4.11HorseBlinderBarrierMethod
16.4.12LenticularSheetMethod
16.4.13IntegralPhotography(IP)
17.1ScheimpflugCondition
17.2Triangulation
17.2.1SingleSpotScanningMethod
17.2.2LineScanningMethod ......................
17.2.3StereoscopicCameraMethod
17.3MethodbyAnalyticGeometry
17.3.1ExpressionofaLineinSpace
17.3.2ComparisonBetweentheMethodofAnalytic GeometryandthatofTrigonometry
17.4DistanceMeasurementofanAutofocusCamera
17.4.1AutofocusbyTriangulation ...................
17.4.2AutofocusbyProjectionofaStructuredPattern
17.4.3AutofocusbyImageComparison ...............
17.4.4AutofocusbyPhaseDetection(withaBeam DirectionDiscriminator) .....................
17.4.5AutofocusbyPhaseDetection(withFocus Detector) ................................
17.4.6AutofocusbyDetectingtheImageContrast .......
17.5Trilateration
17.5.1PrincipleofTrilateration 586
18Structured-LightPatternProjectionMethods
18.1CalculatingtheProfi lefromtheProjectedStructured-Light Pattern 593
18.1.1CalculationbyTrigonometryorAnalytic Geometry
18.1.2CalculationfromtheDistortionoftheStripe 594
18.1.3CalculationfromtheShiftoftheSpaceCode
18.2VariousKindsofStructured-LightPatterns
18.2.1DiscretelyColoredStripes
18.2.2StripesCodedbyRandomCuts
18.2.3ContinuousColorPattern
18.2.4LinearlyIntensityModulatedMonochromatic Pattern ..................................
18.2.5SequentialFringePattern
18.3Phase-ShiftingMethodofanIntensity-ModulatedPattern
18.3.1SinusoidalPhase-ShiftingMethod 603
18.3.2PhaseShiftingMethodwithSimultaneous Projection 613
18.3.3FastSinusoidalPhaseShiftingMethod 614
18.3.4TrapezoidalIntensityModulatedStripes 618
18.4Moiré TopographyMethod 621
19LightBeamRangeFinders
19.1PulsedLidar
19.2FMLidar
19.2.1FMLidarofthe1stType
19.2.2FMLidarofthe2ndType
19.3PrincipleoftheStepFrequencyMethod
19.3.1DerivationoftheObjectDistancebyDFT
19.3.2ZoomingFunctionofStepFrequencyLidar
19.3.3StepFrequencyLidarofthe1stTypeApplied to3DLaserMicrovision ..................... 637
19.4StepFrequencyLidarofthe2ndTypeUsedasa
21Interferometry
21.1CoherentInterferometry
21.1.1OpticalPathDifferenceoftheTwoBeams 654
21.1.2PhaseDifferenceDuetoInternalandExternal Refl ection
21.1.3FieldIntensityoftheFringePattern ontheScreen
21.1.4GeneralBehavioroftheInterferenceFringe Pattern ..................................
21.1.5ApplicationsoftheMichelsonInterferometer
21.2LaserInterferometerforDetectingGravitationalWaves
21.3IncoherentInterferometry ............................
21.3.1IntuitiveExplanationofOpticalCoherence Tomography(OCT) ........................
21.3.2AMoreRigorousExpressionoftheOCTSignal ... 670
21.3.3ApplicationsofOCT 673
21.4InterferometryinRadioAstronomy 674
21.4.1FringeFunctionofRadioWaveInterferometry 674
21.4.2SynthesisofOneDimensionalRadioAstronomy Interferometry 677
21.4.3PrincipleofVeryLongBaseLineInterferometry
22DistanceMappingCameras
22.1Continuous-WaveTimeofFlight(CW-TOF)Range Camera
22.1.1CalculationofthePhaseoftheEnvelope oftheReceivedLight .......................
22.1.2BlockDiagramoftheCW-TOFRangeCamera 686
22.1.3PerformanceoftheCW-TOFRangeCamera 687
22.2Divcam(DivergenceRatioAxi-VisionCamera) 688
22.2.1DistanceCalculationofDivcam 689
22.2.2DivcamApplications 692
22.3Axi-VisionCamera ................................
22.3.1BasicPrincipleoftheAxi-VisionCamera
22.3.2DistanceCalculationofAxi-VisionCamera
22.3.3StructureoftheAxi-VisionCamera
22.3.4ApplicationoftheAxi-VisionCameratoDepth Keying ..................................
22.4Gain-ModulatedAxi-VisionCamera ....................
22.4.1PrincipleofOperationoftheGain-Modulated Axi-VisionCamera
22.4.2ComparisonsBetweentheGain-Modulated Axi-VisionCameraandanOrdinaryAxi-Vision Camera
ListofFigures Fig.1.1CuneiformtabletsexcavatedfromMesopotamia.The contentsaredevotedtothe floodepisode(BycourtesyofA. W.Sjörberg,UniversityMuseum,University ofPennsylvania)
2
Fig.1.2 a, b OnecandlepoweratthebeginningofGreekempire a evolvedto15cdpower, b attheendoftheempire 3
Fig.1.3Measurementoftheheightofapyramidbytheshadow ofastick .......................................... 3
Fig.1.4Reverseddirectionofarrowsaswellasreverseddesignation oftheincidentandreflectedangles ...................... 4
Fig.1.5Democritus(460–370B.C.)said “areplicaoftheobject isincidentupontheeyesandisimprintedbythemoisture oftheeye” ........................................ 5
Fig.1.6Inversionofmirrorimages ............................ 5
Fig.1.7Comermirrorwhichforms “correctimage” wasinventedby Hero(50?).Directionofthearrowsisstillwrong 6
Fig.1.8Ptolemy’sexplanationofCtesibiu’scoinandcup experiment
Fig.1.9Alhazen
Fig.1.10TelescopesmadebyGalileoGalilei(1564–1642). a Telescopeofwoodcoveredwithpaper, 1.36mlong;witha biconvexlensof26mmapertureand1.33mfocallength; planoconcaveeye-piece;magnifi cation,14times. b Telescope ofwood, coveredwithleatherwithgolddecorations:0.92m long;withabiconvexobjectiveof16mmusefulapertureand 0.96mfocallength;biconcaveeye-piece(alateraddition); magni fication,20times ...............................
Fig.1.11Descartes’ Vat ......................................
Fig.1.12Grimaldi’sexplanationofrefraction .....................
Fig.1.13Newton
Fig.1.14Newton
Fig.1.15Newton’sreflectortelescope ...........................
Fig.1.16Newton’srings ..................................... 16
Fig.1.17Huygens’ principle .................................. 17
Fig.1.18Michelson-Morleyexperimenttoexaminethedragbyaether wind ............................................. 20
Fig.1.19Photoelectriceffectexperiment: E ¼ 1
Fig.1.20 a, b Experimentalresultsofthephotoelectriceffect, a Photoelectriccurrentversusappliedpotentialswith wavelengthandintensityoftheincidentlightasparameters, b Energyneededtostopphotoelectricemissionversus frequency 22
Fig.1.21 a, b Compton’sexperiment. a Experimentalarrangement, b Changeofwavelengthwithangle 23
Fig.1.22Methodofchirpedpulseamplifi cation 26
Fig.2.1Energydistributionemanatingfromapointsourcewitha sphericalwavefront
Fig.2.2Geometryusedtocalculatethe fi eldattheobservation pointPduetoapointsourceS 31
Fig.2.3Energydistributionemanatingfromalinesource 32
Fig.2.4Positionvectorandthewavevectorofaplanewave propagatinginthe b k direction .......................... 33
Fig.2.5Determinationofthedirectionalsense(positiveornegative) ofawave ......................................... 35
Fig.2.6SummaryoftheresultsofExercise2.1
Fig.2.7Componentsofwavevectors k1 and k2
Fig.2.8 a, b Interferencepatternproducedbythevectorcomponents k″ a Geometry, b analogytoacorrugatedsheet 37
Fig.2.9De finitionofspatialfrequency 38
Fig.2.10Geometryusedtocalculatethe fi eldattheobservation pointPfromaonedimensionalslit 39
Fig.2.11 a Rectanglefunction P(x)and b itsFouriertransform 41
Fig.2.12 a, b The fielddistributiononanobservationscreenproduced byaonedimensionalslit. a Amplitudedistribution, b intensitydistribution 42
Fig.2.13 a Trianglefunction K(x)and b itsFouriertransform sinc2 f 43
Fig.2.14 a, b Curvesof a signfunctionsgn x and b itsFourier transform1=jpf ..................................... 44
Fig.2.15 a, b Curvesof a thestepfunctionH(x)and b itsFourier transform 1 2 d x ðÞþ 1=jpf ½ 45
Fig.2.16 a Analogyshowinghowthe d(x)functionhasconstantarea. b d(x)andanarbitraryfunction f(x) 46
Fig.2.17 a Shahfunctiongenerator, b shahfunctionIII(x) 47
Fig.2.18Convolutionofanarbitraryfunction g(x)withtheshah functionresultinginaperiodicfunctionof g(x) ............ 48
Fig.2.19Fourierexpansionoftheshahfunction ................... 48
Fig.2.20 a,b Fouriertransformincylindricalcoordinates. a Spatial domain, b spatialfrequencydomain ..................... 50
Fig.2.21 a Circlefunctioncirc(r)and b itsFouriertransform J1(2p .)/.
53
Fig.2.22DiagramshowinggeometryofExercise2.2(mirrorplaced atanangle c totheplaneperpendiculartothe opticalaxis) 54
Fig.2.23 a, b Maskswithtransmissiondistributions t(x) 58
Fig.2.24Semi-circularmask(seeProblem2.7) 58
Fig.3.1Avolume V completelyenclosedbyasurface S. Thevolume mustnotincludeanysingularitiessuchasPl,P2,P3, Pn 60
Fig.3.2Volume V ofintegration 61
Fig.3.3Theshapeofthedomainofintegrationconveniently chosenforcalculatingthediffractionpatternofanaperture usingtheKirchhoffintegraltheorem ..................... 63
Fig.3.4Multiplescatteringfromtheedgeoftheaperture ........... 64
Fig.3.5SpecialcaseofthesourceP2 beingplacednearthecenter oftheaperture,where SA isasphericalsurfacecentered aroundthesource.Theobliquityfactor ís(1+cos v) .......
65
Fig.3.6Geometryforcalculatingthediffractionpattern{u (xi, yi, zi)} onthescreenproducedbythesource{g(x0, y0,0)} ......... 67
Fig.3.7DiagramshowingtherelativepositionsoftheFresnel (near fi eld)andFraunhofer(far field)regions 67
Fig.3.8Geometryusedtocalculatethediffractionpattern duetoapointsourceusingtheFresnelapproximation (Exercise3.1)
71
Fig.3.9Geometryusedforcalculatingtheone-dimensional diffractionpattern 72
Fig.3.10Diffractionpatternduetoasquareaperture 75
Fig.3.11Cornu’sspiral(plotoftheFresnelintegralinthecomplex plane) ............................................ 76
Fig.3.12 a, b RelationshipbetweenthephasoronCornu’sspiral andthemagnitudeofthediffracted field. a Phasors representingthemagnitudeofthelight. b Themagnitude ofthe fieldvsposition(theFresneldiffractionpattern) ....... 77
Fig.3.13IllustrationofBabinet’sprinciple ....................... 78
Fig.4.1Geometryofdiffractionfromarectangularaperture ......... 80
Fig.4.2 a, b Diffractionpatternofarectangularaperture. a Amplitude. b Intensity .............................. 80
Fig.4.3 a, b Squarelightsourceobstructedbyasquare. a Geometry. b Antennawithcenterfeed(EMSystems, Inc.) ............................................. 81
Fig.4.4Diffractionpatternswithandwithouttheobstructing square ............................................ 81
Fig.4.5Apertureinatriangularshape 82
Fig.4.6Amplitudeandphasedistributionalong fx forthediffraction patternofatriangularaperture 83
Fig.4.7 a, b Aperturediffraction. a Photographofthediffraction patternofaright-angledtriangularaperture. b Diffraction duetoiris 84
Fig.4.8Semi-infiniteaperture 85
Fig.4.9Diffractionpatternofthesemi-infi niteaperturewith respectto fx 85
Fig.4.10 a–c Compositionofaslit. a Halfplaneshiftedby a/2 totheleft. b Halfplaneshiftedby a/2totheright. c Slit madeupoftwohalfplanes............................ 86
Fig.4.11Expressionofaslitusingstepfunctions .................. 87
Fig.4.12Mereadditionoftwohalfplanefunctions.Notethatitdoes notrepresentaslit.Thelawofsuperpositionisappliedtothe fieldbutnottotheboundaryconditions .................. 88
Fig.4.13One-dimensionalperiodicsource ....................... 89
Fig.4.14Convolutionof(sinc(af))*III(b/f)withsinc(cf) ........... 89
Fig.4.15Graphofac[sinc(af)III(bf)]*sine(cf) ................... 90
Fig.4.16Hornantennaarray 90
Fig.4.17Methodofdesigningtheantennaarray 91
Fig.4.18 a–c Compactopticaldisc(CD). a PhotographoftheCD. b ElectronmicroscopephotographoftheCDsurface (courtesyofPhilips). c CrosssectionoftheCD 92
Fig.4.19Diagramofthethree-beamtrackingmethodofaCD player 95
Fig.4.20 a–c Formationofanastigmaticbeambythecombination ofasphericalandcylindricallens. a Astigmaticbeam. b FocallengthFv intheverticalplane. c FocallengthFh inthehorizontalplane ............................... 96
Fig.4.21 a–c Changeoftheerrorsignalinaccordancewiththeposition oftheopticaldisc. a Discisinfocus. b Discistooclose.
c Discistoofar(BycourtesyofPhilips) ................. 97
Fig.4.22 a–c Principleoftheleftandrighttrackingbythethree-beam opticalpickuphead. a Trackdriftstotheleft. b Ontrack.
c Trackdriftstotheright ............................. 98
Fig.4.23 a–i Foucault’sknifeedge(left),imagecomparator(center), andopticalwedge(right)focussingmethods. a Thediscisin focus. b Thediscistooclose.Theknifeedge’sshadowison
theoppositesideoftheknifeedge. c Thediscistoofar.The knifeedge’sshadowisonthesamesideastheknifeedge. d Thediscisinfocus.Thecirclesareidentical. e Thediscis tooclose.Thelowercircleislarger. f Thediscistoofar.The uppercircleislarger. g Thediscisinfocus.Onebeamhits theborderbetweenAandB,andtheother,theborder betweenCandD. h Thediscistooclose.Thebeamsseparate moreandhitAandD. i Thediscistoofar.Thebeamscome closerandhitBandC
Fig.4.24 a, b Circularapertureanditsdiffractionpattern. a Circular aperture. b Diffractionpattern
Fig.4.25 a, b Transmissiondistributionofaonedimensionalzone plateexpressed a asafunctionof 2=kp p x0 and b asa functionof x ¼
Fig.4.26DistributionofthelighttransmittedthroughaFresnel zoneplate
Fig.4.27TwodimensionalFresnelzoneplate
Fig.4.28Thephotographsofthemachinedholesobtainedwithalaser beamfocusedbymeansofMZP[6]. a Anarrayofholes madeonachrome filmdepositedonasheetglass. b Two arraysofblindholesmadeonapolishedsurfaceofsteel
Fig.4.29 a, b Gammaraycamera. a Shadowofzoneplatecastby isotopetracer. b Reconstructionoftheimagebycoherent light
Fig.4.30Echelettegrating
Fig.4.31Debye-Searsspatiallightdeflector
Fig.4.32Modulatedzoneplate(MZP)formachiningtool
Fig.5.1Tangenttoacurve
Fig.5.2Tangentinpolarcoordinatesystem
Fig.5.3GeometryusedtoproveFrenet-Serretformula
Fig.5.4Explanationofthedirectionofdifferentiation
Fig.5.5Growthofanequi-phasefrontwiththeprogressoftime
Fig.5.6Pathoflightinamediumwhoserefractiveindexis variedonlyinthe x direction
Fig.5.7Pathoflightatvariouslaunchinganglesintoamedium whoserefractiveindexismonotonicallydecreasingwith increasing x 130
Fig.5.8PropagationpathoflightinsideaonedimensionalSelfoc slab ..............................................
Fig.5.9Suchanopticalpathisimpossibleifthemediumis sphericallysymmetric ................................
Fig.5.10Initiallaunchingconditionintoasphericallysymmetric medium ...........................................
Fig.5.11 a, b Lightpathinasphericallysymmetricmedium. In a thevaluesof c atthesame r areidentical. b shows thevalueof rmn(rm)foragivenlaunchingcondition ........
Fig.5.12Lightpathinamediumwith nðr Þ¼ 1= rp
Fig.5.13Geometryoftheopticalpathinacylindricallysymmetric medium(directioncosines) 141
Fig.5.14Determinationoftheregionofpropagationofameridional rayandaskewrayinaSelfoc fiberfromthesquarerootin (5.110)
Fig.5.15 a, b PathofthemeridionalrayinaSelfoc fi ber; a sideview, b endview.Asseenintheendview,theplaneofincidenceis perpendiculartothecircumference,justastherayintheslab isperpendiculartotheboundary ........................
Fig.5.16SkewrayinaSelfoc fiber ............................
Fig.5.17Explanationofthequantizationintheangleofincidence h ...
Fig.5.18Interferencebetweenthelightrays ......................
Fig.5.19Awavylineisdrawnonasideofapieceofnoodle,andthen wrappedaroundapieceofpencil.Thelinecanrepresentthe pathofaskewray ..................................
Fig.5.20Cross-sectionaldistributionoftheintensityforvariousmode numbers
Fig.5.21 k b diagramoftheSelfoc fiber 153
Fig.5.22Thelightpathinamediumwith n = b/(a ± x)isanarc ofacircle
Fig.5.23Directionoftheopticalpathexpressedindirectioncosines
Fig.6.1Designofthecurvatureofaplanoconvexlens 160
Fig.6.2Illustrationofthecauseoftheintensitynon-uniformity existinginaparallelbeamemergingfromaplanoconvex lens 161
Fig.6.3Phasedistributionofabeampassedthroughaplano-convex lens 161
Fig.6.4Apatternprojectedontoascreenthroughaconvexlenswhen theinputtransparency g(x0, y0)ispressedagainstthelensand thescreenisplacedat z = zi ........................... 163
Fig.6.5Fouriertransformbyaconvexlens;thecasewhentheinput transparency g(x0, y0)islocatedadistance d1 infrontofthe lensandthescreenisatthebackfocalplane .............. 164
Fig.6.6Fouriertransformbyaconvexlens;thecasewhentheinput transparency g(x0, y0)isplacedinthefrontfocalplane.When theinputtransparencyisplacedatthefrontfocalplanethe exactFouriertransform G(xi/k f, yi/k f)isobservedattheback focalplane 166
Fig.6.7Fouriertransformbyaconvexlens;inthecasewhenthe inputtransparency g(x0, y0)isplacedbehindthelens 166
Fig.6.8Fouriertransformperformedbyaconvergingbeamoflight. TheFouriertransformisobservedinaplanecontainingthe point P ofconvergence.Itdoesnotmatterhowthe convergentbeamisgenerated .......................... 169
Fig.6.9 a, b EffectofthelateraltranslationontheFouriertransform. a Theobjectisinthecenter; b theobjectislaterally translated.NotethatFouriertransformalwaysstaysonthe opticalaxis 170
Fig.6.10Theimageformingcapabilityofalensisexaminedfromthe viewpointofwaveoptics 171
Fig.6.11FormationoftheimageusingtwosuccessiveFourier transforms.Theoutputimageobtainedinthismanneris identicalwiththeinputimagenotonlyinmagnitudebutalso inphase 172
Fig.6.12Theoutputimagethroughalensofa finitesize.Someofthe higherspatialfrequencycomponentsdonotinterceptthelens resultinginalossofthehigherfrequencycomponentinthe outputimage ....................................... 173
Fig.6.13TheFouriertransformbyalensofa
nitesize ............ 174
Fig.6.14Theblurringduetothe finitenessofthediameter ofthelens ......................................... 175
Fig.6.15Influenceofthe finitenessofthelenssizeontheresolution ofoutputimage .....................................
Fig.6.16Thedesignofthesurfaceofameniscuslens ..............
Fig.6.17Maximumobtainablereductionratioofacamera withalensofa fi nitesize 180
Fig.6.18EliminationofthephasefactorassociatedwiththeFourier transformusingaconvexlens 181
Fig.6.19Opticalcomputingusingtwoconvexlenses 181
Fig.6.20Combinationofcylindricalandsphericallenses 181
Fig.6.21Electricalequivalentcircuitofanopticallenssystem 181
Fig.7.1Substantialreductioninnumberofcomputationsis demonstrated;OnecurvewithFTTtheotherwithordinary computation ....................................... 184
Fig.7.2Representationof Wk planeonthecomplexplane .......... 186
Fig.7.3Signal flowgraphrepresentingthecalculationof(7.12). Blackdotrepresentsthesummingofthetwonumbers transferredbythearrows ............................. 188
Fig.7.4SameasFig.7.3butfor(7.13).Adottedlinemeanstransfer thenumberafterchangingitssign.Anumberwrittenonthe sideofalinemeansthewrittennumberismultipliedbythe numberbroughtbytheline ............................ 189
Fig.7.5The4-pointDFTofthesamplepoints q0, q1, q2, q3 arefurther splitinto2-pointDFT 190
Fig.7.6SameasFig.7.5butfor r ’s ........................... 191
Fig.7.7Signal flowgraphof8-pointDFTbyamethodofdecimation infrequency ....................................... 191
Fig.7.8Signal flowgraphobtainedbyremovingtheframesand straighteningthelinesofFig.7.7(methodofdecimationin frequency) 192
Fig.7.9Signal flowgraphredrawnfromthatofFig.7.8withthe emphasisonusingitasanaidtowiretheFFTcomputer. (Methodofdecimationinfrequency) 193
Fig.7.10Signal flowgraphofthe firststageofthemethodof decimationintime;First,DFT Fl andDFT Hl arecalculated fromthesampledvaluesof g2k and g2k+1 andnext, Gl is foundbycombining Fl and Hl inthespeci fiedmanner 196
Fig.7.11Thesignal flowchartofthemethodofdecimationintime 197
Fig.7.12Signal flowgraphobtainedbyremovingtheframesand straighteningthelinesofFig.7.11(Methodofdecimation intime) ........................................... 197
Fig.7.13Signal flowgraphredrawnfromthatofFig.7.12withthe emphasisonusingitasanaidtowiretheFFTcomputer. (Methodofdecimationintime) ........................ 198
Fig.7.14Reductionofthenumberofvaluesof Wk tobestoredina ROM(ReadOnlyMemory) ........................... 199
Fig.7.15Findingthevaluesof G–l bytranslatingthespectrumnear theend ........................................... 200
Fig.7.16Sampledvaluesof gk =1 200
Fig.7.17Curveof gxðÞ¼
Fig.7.18Valueof gk 201
Fig.7.19Valueof g ’ k 201
Fig.7.20Valueof gk ........................................ 201
Fig.8.1 a,b Illustrationoftheprincipleofholography. a Fabrication ofhologram. b Reconstructionoftheimagefrom hologram .......................................... 204
Fig.8.2Arrangementofcomponentsforfabricatingahologram ...... 206
Fig.8.3Reconstructingoftheimagefromahologram ............. 208
Fig.8.4Imagesreconstructedfromahologram ................... 211
Fig.8.5Photographofthecross-sectionofaKodak469F holographicplatetakenbyanelectronmicroscope[3] 212
Fig.8.6Thereconstructionofanimagefromathickhologram.The samesourcewhichwasusedforthereferencebeamisused forthereconstructingbeam 212
Fig.8.7 a,b Theclassi ficationofhologramsaccordingtotheshapes ofthewavefront. a GeometriesforFouriertransform
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