Table Of ContentImaging Optics
Thiscomprehensiveandself-containedtextpresentsthefundamentalsofopticalimagingfromtheviewpointofbothray
andwaveoptics,withinasinglevolume.Comprisingthreedistinctparts,itopenswithanintroductiontoelectromagnetic
theory,includingelectromagneticdiffractionproblemsandhowtheycanbesolvedwiththeaidofstandardnumerical
methodssuchasRCWAorFDTD.Thesecondpartisdevotedtothebasictheoryofgeometricalopticsandthestudyof
opticalaberrationsinherentinimagingsystems,includinglarge-scaletelescopesandhigh-resolutionprojectionlenses.
Adetailedoverviewofstate-of-the-artopticalsystemdesignprovidesreaderswiththenecessarytoolstosuccessfully
use commercial optical design software. The final part explores diffraction theory and concludes with vectorial wave
propagation,imageformationandimagedetectioninhigh-apertureimagingsystems.Thewide-rangingperspectiveof
thisimportantbookprovidesresearchersandprofessionalswithacomprehensiveandrigoroustreatiseonthetheoretical
andappliedaspectsofopticalimaging.
Joseph Braat is Emeritus Professor of Optics at the Delft Technical University, The Netherlands, and a Fellow of
the Royal Netherlands Academy of Arts and Sciences. Previously he was based at the Philips Research Laboratories
in Eindhoven where he worked on optical disc systems for video and audio recording and on high-resolution optical
lithography.Hisfurtherresearchinterestsarediffractiontheory,astronomicalimagingandopticalmetrology.
PeterTo¨ro¨kisProfessorofOpticalPhysicsattheNanyangTechnologicalUniversity,SingaporeandatImperialCollege
London, UK. His research is focused on the theory of diffraction, focusing and microscopy, with particular emphasis
on confocal microscopy, spectroscopic imaging and polarisation. Throughout the years he has taught vector calculus,
electromagnetism,opticalimagingandopticaldesigntheory.
Imaging Optics
JOSEPH BRAAT
DelftTechnicalUniversity,TheNetherlands
¨ ¨
PETER TOROK
NanyangTechnologicalUniversity,Singapore
ImperialCollegeofScience,TechnologyandMedicine,London
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781108428088
DOI:10.1017/9781108552264
©JosephBraatandPeterTo¨ro¨k2019
Thispublicationisincopyright.Subjecttostatutoryexception
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noreproductionofanypartmaytakeplacewithoutthewritten
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Firstpublished2019
PrintedintheUnitedKingdombyTJInternationalLtd,PadstowCornwall
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ISBN978-1-108-42808-8Hardback
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CONTENTS v
Contents
Preface pageix
Acknowledgements xi
I Electromagnetic Theory in the Optical Domain
1 ElectromagneticWavePropagationinIsotropicMedia 3
1.1 Introduction 3
1.2 Maxwell’sEquationsasExperimentalLaws 3
1.3 Maxwell’sEquationsintheOpticalDomain 9
1.4 ElectromagneticEnergyDensityandEnergyTransport 10
1.5 PotentialFunctionsandtheElectromagneticFieldVectors 13
1.6 HarmonicSolutionsandtheHelmholtzEquation 18
1.7 GaussianBeams 35
1.8 WavePropagationatanInterfacebetweenTwoMedia 51
1.9 TransmissionandReflectioninaStratifiedMedium 68
1.10 MultilayerReflectionandTransmissionCoefficients 72
1.11 TheScatteringMatrixandtheImpedanceMatrixFormalism 81
1.12 StratifiedMediumwithLaterallyModulatedPeriodicSublayers 87
2 WavePropagationinAnisotropicMedia 107
2.1 Introduction 107
2.2 HarmonicElectromagneticWavesinanAnisotropicMedium 108
2.3 PlaneWaveSolutionsinUniaxialandBiaxialMedia 112
2.4 SolutionoftheHelmholtzEquationinanAnisotropicMedium 117
2.5 EnergyTransportinaMediumwithLinearAnisotropy 124
2.6 EigenvalueEquationsInvolvingtheRayVectorsˆ 127
2.7 TheFunctionsv (kˆ),n (kˆ),v(sˆ)andn(sˆ) 133
p p r r
2.8 ConicalRefraction 138
2.9 OpticalActivity 143
2.10 WavePropagationinanAnisotropicMediumIncludingRotation 146
2.11 EnergyPropagationinaGeneralAnisotropicMedium 149
2.12 ReflectionandRefractionatanInterfaceinAnisotropicMedia 154
3 SurfaceWaves,MetamaterialsandPerfectImaging 160
3.1 EigenmodesofaMetal–DielectricInterface 161
3.2 WavePropagationinMetamaterials 168
3.3 TheConceptofthePerfectLens 179
vi CONTENTS
II Geometrical Theory of Optical Imaging
4 FoundationsofGeometricalOptics 191
4.1 Introduction 191
4.2 GeometricalOpticsDerivedfromMaxwell’sEquations 193
4.3 CharacteristicFunctionofanOpticalSystem 202
4.4 AngleCharacteristicFunctionofaSingleSurface 207
4.5 TheFirst-orderAngleCharacteristicandtheParaxialDomain 210
4.6 StigmaticImagingandtheAngleCharacteristicFunction 212
4.7 ConstructionoftheAngleCharacteristicFunctionofaSystem 214
4.8 IsoplanatismandAplanatismofanOpticalSystem 217
4.9 TheDefinitionofTransverseandWavefrontDeviation 223
4.10 ParaxialOpticsandtheMatrixAnalysisofOpticalSystems 230
4.11 RadiometryandPhotometry 257
5 AberrationAnalysisofOpticalSystems 266
5.1 Introduction 266
5.2 ClassificationofAberrations 276
5.3 CalculationoftheSeidelAberrationCoefficients 292
5.4 AberrationofaThinLens 309
5.5 SeidelAberrationsofaPlane-parallelPlate 320
5.6 ChromaticAberration 324
5.7 FiniteRay-tracing 338
5.8 TotalAberrationataSingleSurface;FormulasofHopkinsandWelford 357
5.9 Aperture-andField-dependentAberrationFunctionofanImagingSystem 359
5.10 ParaxialandFiniteRay-tracinginInhomogeneousMedia 372
5.11 PolarisationRay-tracinginAnisotropicMedia 378
6 AnalyticDesignandOptimisationofOpticalSystems 383
6.1 Introduction 383
6.2 AnalyticAberration-freeDesignofanOpticalSystem 384
6.3 MeritFunctionofanOpticalSystem 395
6.4 OptimisationofOpticalSystems 399
6.5 OpticalTolerancing 413
7 DesignMethodsforOpticalImagingSystems 425
7.1 Introduction 425
7.2 TheAchromaticDoublet 426
7.3 ThePhotographicLandscapeLens 432
7.4 ThePortraitLens 443
7.5 Flat-fieldImagingSystems 451
7.6 TheAstronomicalTelescope 474
7.7 MicroscopeOptics 496
7.8 AsphericObjectivesforOpticalDiscSystems 504
7.9 Large-fieldProjectionSystemswithDiffraction-limitedQuality 523
III Diffraction Theory of Optical Imaging
8 VectorialandScalarTheoryofDiffractionandFocusing 545
8.1 FoundationofVectorDiffraction 545
CONTENTS vii
8.2 BoundaryValueProblemsinDiffraction 559
8.3 TheDebye–WolfandRelatedDiffractionTheories 562
8.4 ScalarDiffractionTheories 568
8.5 TheValidityoftheDebye–WolfTheory 580
9 TheAberratedScalarandVectorPoint-spreadFunction 582
9.1 Introduction 582
9.2 PupilFunctionExpansionUsingZernikePolynomials 584
9.3 ThePoint-spreadFunctionandtheNijboer–ZernikeDiffractionTheory 591
9.4 TheExtendedNijboer–ZernikeDiffractionTheory 609
9.5 VectorPoint-spreadFunctionandtheENZDiffractionTheory 614
9.6 EnergyandMomentumDensityandTheirFlowComponents 640
10 FrequencyAnalysisofOpticalImaging 657
10.1 Introduction 657
10.2 OpticalTransferFunctionofaClassicalWide-fieldImagingSystem 660
10.3 FrequencyTransferbyaScanningImagingSystem 710
10.4 TheThree-dimensionalTransferFunction 725
10.5 LightScatteringandFrequencyTransfer 767
11 TheoryofVectorImaging 782
11.1 VectorRayTracing–TheGeneralisedJonesMatrixFormalism 783
11.2 VectorialPoint-spreadFunction 787
11.3 FocusingofPartiallyCoherent,PartiallyPolarisedLight 794
11.4 PropertiesofHigh-numerical-apertureImagingSystems 804
11.5 High-apertureScanningLightMicroscopesImagingaPointObject 814
11.6 TheoryofMultiphotonFluorescenceMicroscopes 832
11.7 ExtensionoftheImagingTheorytoMoreComplicatedOpticalSystems 847
11.8 ImagingofArbitraryObjects 855
AppendixA FourierAnalysis,ComplexNotationandVectorFormulas 860
AppendixB PhaseandGroupVelocityofaWavePacket 879
AppendixC TheKramers–KronigDispersionRelations 882
AppendixD ZernikePolynomials 888
AppendixE MagneticallyInducedOpticalRotation(FaradayEffect) 907
AppendixF VectorPoint-spreadFunctioninaMultilayerStructure 913
AppendixG V.S.Ignatowsky:DiffractionbyaLensofArbitraryAperture 919
*
References 945
AuthorIndex 959
SubjectIndex 963
