Handbook of Optical Systems [Vol 2 - Physical Image Formation] -.pdf

1、Handbook of Optical SystemsEdited byHerbert GrossVolume 2:Physical Image FormationWolfgang Singer,Michael Totzeck,Herbert GrossHandbook of Optical SystemsEdited by Herbert GrossVolume 2:Physical Image FormationHandbook of Optical SystemsEdited byHerbert GrossVolume 1:Fundamentals of Technical Optics

2、Volume 2:Physical Image FormationVolume 3:Aberration Theory and Correction of Optical SystemsVolume 4:Survey of Optical InstrumentsVolume 5:Metrology of Optical Components and SystemsVolume 6:Advanced Physical OpticsHandbook of Optical SystemsEdited byHerbert GrossVolume 2:Physical Image FormationWo

3、lfgang Singer,Michael Totzeck,Herbert GrossHerbert GrossHead of Optical Design DepartmentCarl Zeiss AG,Oberkochen,Germanye-mail:Grosszeiss.deWolfgang SingerDepartment LIT-TDCarl Zeiss SMTAG,Oberkochen,Germanye-mail:singerzeiss.deMichael TotzeckDepartment LIT-TDCarl Zeiss SMTAG,Oberkochen,Germanye-ma

4、il:m.totzeckzeiss.de&All books published by Wiley-VCH are carefully pro-duced.Nevertheless,authors,editors,and publisherdo not warrant the information contained in thesebooks,including this book,to be free of errors.Read-ers are advised to keep in mind that statements,data,illustrations,procedural d

5、etails or other items mayinadvertently be inaccurate.Library of Congress Card No.:applied forBritish Library Cataloguing-in-Publication DataA catalogue record for this book is available from theBritish Library.Bibliographic information published byDie Deutsche BibliothekDie Deutsche Bibliothek lists

6、 this publication in theDeutsche Nationalbibliografie;detailed bibliographicdata is available in the Internet at.?2005 WILEY-VCH Verlag GmbH&Co.KGaA,WeinheimAll rights reserved(including those of translation intoother languages).No part of this book may be repro-duced in any form nor transmitted or

7、translated intomachine language without written permission fromthe publishers.Registered names,trademarks,etc.used in this book,even when not specifically markedas such,are not to be considered unprotected by law.Printed in the Federal Republic of Germany.Printed on acid-free paper.Cover Design4t Ma

8、tthes+Traut WerbeagenturGmbH,DarmstadtTypesettingK?hn&Weyh,Satz und Medien,FreiburgPrintingDruckhaus Darmstadt GmbH,DarmstadtBookbindingLitges&Dopf Buchbinderei GmbH,DarmstadtISBN3-527-40378-7(Vol.2)ISBN3-527-40382-5(Set)Wolfgang SingerWolfgang Singer was born in 1964 and studied Phy-sics at the Uni

9、versity of Erlangen.He received hisPh.D.at the Institute of Applied Optics in 1995 witha thesis on microoptics,propagation theory andtomography.He spent his post doctorate at the Insti-tute de Microtechnique in Neuchatel,where he devel-oped diffractive diffusors for DUV illumination sys-tems.From 19

10、96 to 1998,he was assistant at theInstitute of Applied Optics at the University of Stutt-gart.Since 1998,he has been with Carl Zeiss SMTAG,working in the department of optical design andsimulation for lithographic optics.His work includestolerancing of objectives and the design of illumina-tion syst

11、ems of EUV systems.He became principalscientist and was engaged at the scientific trainingprogramme at Carl Zeiss.His special interests areimaging theory and partial coherence,and he haswritten his own simulation software.He holds 50patents and has published about 30 papers and con-tributions to tex

12、tbooks.Michael TotzeckMichael Totzeck was born in 1961.He received hisdiploma degree in Physics in 1987 and his Ph.D.in1989,both from the Technical University of Berlin,where he also did his habilitation in 1995.In 1991 hewas awarded the Carl-Ramsauer-Award of the AEGAG for his Ph.D.thesis on near f

13、ield diffraction.From 1995 to 2002,he headed a group on high reso-lution microscopy at the Institute of Applied Opticsin Stuttgart,working by experimental,theoretical andnumerical means on optical metrology at the resolu-tion limit.He has been with the Carl Zeiss SMT AGsince 2002,working in the depa

14、rtment for opticaldesign.His current research topic is electromagneticimaging with high-NA optical systems.He has pub-lished 40 papers on diffraction theory,near-fieldoptics,high-resolution microscopy,interferometry,metrology,optical singularities,polarization-opticsand physics education.Herbert Gro

15、ssHerbert Gross was born in 1955.He studied Physicsat the University of Stuttgart and joined Carl Zeiss in1982.Since then he has been working in the depart-ment of optical design.His special areas of interestare the development of simulation methods,opticaldesign software and algorithms,the modellin

16、g oflaser systems and simulation of problems in physicaloptics,and the tolerancing and the measurement ofoptical systems.Since 1995,he has been heading thecentral optical design department at Zeiss.He servedas a lecturer at the University of Applied Sciences atAalen and at the University of Lausanne

17、,and gaveseminars for the Photonics Net of Baden W?rttem-berg as well as several company internal courses.In1995,he received his PhD at the University of Stutt-gart on a work on the modelling of laser beam propa-gation in the partial coherent region.He has pub-lished several papers and has given man

18、y talks at con-ferences.1Introduction12Paraxial Imaging53Interfaces614Materials1115Raytracing1736Radiometry2297Light Sources2698Sensor Technology and Signal Processing3239Theory of Color Vision37910Optical Systems42511Aberrations48512Wave Optics52313Plano-optical Components56914Gratings64715Special

19、Components69316Optical Measurement and Testing Techniques759VIIContents of Volume IIntroductionXIX17The Wave Equation117.1Introduction217.2From Maxwell to Helmholtz217.2.1Maxwells Equations and the Inhomogeneous Wave Equation217.2.2Wave Equation in Homogeneous Media and the Scalar WaveEquation417.2.

20、3The Dispersion Relation of the Harmonic Wave Solution617.3Elementary Waves in Free Space917.3.1The Electromagnetic Plane Wave917.3.2Spherical Wave1117.3.3Dipole Wave1117.3.4Radiated Field of a Harmonic Current Distribution1317.3.5A Note on Plane and Spherical Waves1317.4Energy,Irradiance and Intens

21、ity1417.5The Angular Spectrum1717.5.1Spatial Frequency Representation1717.5.2Transformation of the Three-dimensional Spectrum into TwoDimensions1917.5.3Free-space Propagation of Transverse Fields2017.5.4Periodic Fields with Discrete Spectra2217.5.5Boundary Conditions and the Spatial Frequency Spectr

22、um2317.5.6Vector Field Representation by Spatial Frequencies2417.6Evanescent Waves2617.7Approximative Solutions to the Wave Equation2817.7.1Geometrical Optics and the Eikonal Equation2817.7.2Paraxial Wave Equation2917.7.3Transport of Intensity3017.7.4Gaussian Beams3117.7.5Ray Equivalent of Gaussian

23、Beams3617.7.6Gaussian Beams in Two Dimensions3717.8Literature39IXContents18Scalar Diffraction4118.1Introduction4218.2Kirchhoff Diffraction Integral4418.2.1Inconsistency of the Kirchhoff Diffraction Integral4818.31stand 2ndRayleighSommerfeld Diffraction Integral4818.4Two-dimensional Diffraction5018.5

24、Huygens Principle5218.6Fourier Space Formulation5418.7Examples of Scalar Diffraction Patterns5718.7.1Diffraction Fields Behind Slits5718.7.2Diffraction by a Rectangular Aperture5918.8Fresnel Diffraction6018.8.1Computation6118.8.2Validity6218.9Collins Fresnel Diffraction Integral6418.9.1Definition641

25、8.9.2Example6718.10Fraunhofer Diffraction6918.11Grating Diffraction7118.11.1Ronchi Grating7118.11.2The Sinusoidal Phase Grating and Surface Fabrication Errors7618.12Scalar Diffraction at Dielectric Objects7918.13Babinets Principle8218.14Scalar Scattering8518.15Boundary Diffraction Waves8918.15.1Geom

26、etrical Theory of Diffraction9018.15.2An Empirical Boundary Diffraction Wave9418.16Literature9619Interference and Coherence9919.1Basic Principles10019.1.1Introduction10019.1.2Two-beam Interference and Double Slit Diffraction10219.1.3Contributions of Different Points of the Light Source10519.1.4The H

27、igh-frequency Term10719.1.5The Low-frequency Term10819.1.6Different Light Source Points with Statistical Phase10919.2Mathematical Description of Coherence11319.2.1Coherence Function11319.2.2Wigner Distribution Function11619.2.3Moments of the Wigner Distribution Function12019.2.4Smoothing of the Wign

28、er Distribution Function and DiffractionFocus12119.2.5Wigner Distribution Function of Coherent Fields12219.2.6Ambiguity Function123ContentsX19.2.7The Characterizing Functions in their Context12519.3Temporal Coherence12619.3.1Superposition of Signals with Different Frequency12619.3.2Spectral Distribu

29、tion of a Light Source12719.3.3Bandwidth-limited Signals12819.3.4Axial Coherence Length13019.3.5Thermal Light Sources13319.3.6Temporal Coherence in the Michelson Interferometer13419.4Spatial Coherence13519.4.1Introduction13519.4.2Propagation of the Coherence Function13819.4.3Van Cittert-Zernike Theo

30、rem14019.4.4The Coherence Function of a Circular Source14019.4.5Coherence Function behind a Double Slit14319.4.6Propagation of the Wigner Distribution Function14619.5Gaussian Schell Beams14919.5.1Definition of Gaussian Schell Beams14919.5.2Coherence and Wigner Functions of Gaussian SchellBeams15419.

31、5.3Basis Mode Expansion of Partial Coherent Fields15619.6Statistical Optics and Speckle15919.6.1Photon Statistics15919.6.2The Speckle Effect16119.6.3Speckle Parameters and Surface Structure16319.6.4Computation of Speckle Effects16519.6.5Speckle Reduction16919.7Array Homogenizer17219.7.1Setup of the

32、System17219.7.2Pupil Filling17519.7.3Coherence Effects17619.7.4Example Calculation17719.8Miscellaneous17919.8.1General Coherence Length17919.8.2General Degree of Coherence18219.8.3Coherence and Polarization18319.9Literature18420The Geometrical Optical Description and Incoherent Imaging18720.1Introdu

33、ction18820.2Characteristic Functions18920.2.1Geometrical Optics and the Wave Equation18920.2.2The Characteristic Functions19120.2.3Geometrical-optical imaging19420.2.4The Canonical Pupil19620.2.5A Note on Diffractive Optical Elements199ContentsXI20.3The Ideal Wave-optical Image of a Point and Geomet

34、rical-optical ImageFormation20020.3.1The Scalar Luneburg Integral20020.3.2Energy Discussions for Optical Imaging20420.3.3The Airy Disc20620.3.4Incoherent Resolution21020.4Aberrations of Optical Systems21120.4.1The Small-aberration Limit:The Strehl Ratio21120.4.2Expansion of the Wave-front Error into

35、 Zernike Polynomials21220.4.3Point Images for Different Aberrations21720.4.4Distortion,Defocus and Astigmatism21920.4.5Spherical Aberrations Z9,Coma Z7and Z822020.4.6Line of Sight22120.4.7Wave Aberrations for Annular Pupils22420.4.8Extended Zernike Expansion22720.5HelmholtzLagrange Invariant and Pha

36、se-space Description23120.5.1The Phase Space23120.5.2The Resolution Limit in the Space Domain and in the Spatial FrequencyDomain23420.5.3The SpaceBandwidth Product23620.6Literature23721The Abbe Theory of Imaging23921.1Introduction24021.2Phenomenological Description of Imaging24421.2.1The Explanation

37、 of Image Formation According to Abbe and the AbbeResolution24421.2.2The Information About an Object Contained in an Image24921.2.3Koehler Illumination and the Visibility25221.2.4The Siedentopf Illumination Principle25521.2.5Imaging with Different Colours25921.2.6Aplanatic Correction and Geometrical

38、 Optics26021.3The Mathematical Description of Fourier Optical Imaging26221.3.1Imaging with Uncorrelated Light Sources26221.3.2Consideration of Magnification26721.4Coherence in Imaging26921.4.1The Coherent Image26921.4.2Incoherent Imaging27221.4.3One-Dimensional Incoherent Imaging27321.4.4Systems wit

39、h Rotational Symmetry27521.4.5Conditions for Incoherent,Partially Coherent and CoherentImaging27721.4.6Imaging with Correlated Light Sources28021.5Literature281ContentsXII22Coherence Theory of Optical Imaging28322.1Introduction28422.2Theoretical Description of Partially Coherent Image Formation28422

40、.2.1Hopkins Transmission Cross Coefficient28422.2.2Image Fidelity28722.2.3Hopkins Formalism for Periodic Objects28822.2.4Aberrations in the Linear Grating Image29322.3The Coherence Function and the Coherence Transfer Function29622.4The Phase Space Description30022.4.1Transformation of Coherence and

41、Wigner Distribution Function30022.4.2Propagation of the Wigner Distribution Function in Free Space30322.4.3Compilation of the Transformations30722.5Optical Imaging in the Presence of Aberrations30922.5.1Linear Systems and Classification of Aberrations30922.5.2Random Non-stationary Aberrations:Stray

42、Light and Flare31422.6Literature31723Three-dimensional Imaging31923.1Introduction32023.2The Ewald Sphere and the Generalized Pupil32123.2.1The Ewald Sphere32123.2.2The Generalized Aperture and the Three-dimensional Point-spreadFunction32223.3The Three-dimensional Transfer Function32723.3.1Born Appro

43、ximation and the Laue Equation32723.3.2D?ndlikers Representation and the Shape of the Three-dimensionalTransfer Function33023.3.3Resolution,Depth Resolution and Depth of Focus33523.3.43D-Transfer Functions in Microscopy33823.3.5Magnification and a Comment on Absolute Instruments34023.4Selected Examp

44、les of the Three-Dimensional Transfer Function34323.4.1Transfer Function for Incoherent Imaging with r=134323.4.2Partial Coherent Image Examples34423.4.3?Tayloring of the 3D-Transfer Function34623.4.5Influence of Aberrations35123.5Literature35224Image Examples of Selected Objects35524.1Introduction3

45、5624.2Two-point Resolution35624.2.1Incoherent Versus Coherent Two-point Resolution35624.2.2Image of a Double Slit for Coherent and Incoherent Illumination36024.2.3Phase Shift and Oblique Illumination36424.3The Image of an Edge36524.3.1The Coherent Image of an Amplitude and Phase Edge365ContentsXIII2

46、4.3.2The Incoherent Image of an Amplitude Edge36924.3.3Partially Coherent Edge Image37024.3.4The Determination of the Optical Transfer Function from the EdgeImage37524.4The Line Image37624.4.1The Line Image of a Rotational-symmetrical Lens37624.4.2Coherent Line or Slit Image37724.4.3Incoherent Line

47、or Slit Image38024.5The Grating Image38124.5.1The Coherent Linear Grating Image38124.5.2The Coherent Grating Image with Aberrations38424.5.3The Influence of the Coherence Parameter r on the Grating Image38624.5.4Influence of the Shape of the Effective Light Source on the GratingImage38924.5.5Wigner

48、Distribution Function for Gratings,Talbot Effect andPropagation-invariant Fields39424.6Pinhole Imaging and Quasi-point Sources39924.6.1Introduction39924.6.2Incoherent Image of a Circular Object40024.6.3Quasi-point Source40224.6.4Pinhole with Coherent Illumination40424.6.5Pinhole with Partial Coheren

49、t Illumination40524.6.6Defocusing Planes and Deconvolution40624.7Literature40725Special System Examples and Applications40925.1Introduction41025.2Point-spread Functions for Annular Pupils41025.2.1Introduction41025.2.2Annular Pupils,Central Obscuration and Pupil Filters41125.3Point-spread Functions o

50、f Non-uniform Illuminated Pupils41625.3.1Introduction41625.3.2General Gaussian Apodization41725.3.3Gaussian Profile with Truncation41825.4Engineering of the Point-spread Function by Pupil Masks42325.4.1Introduction42325.4.2Characterization of the Three-dimensional Point-spread Function42325.4.3Chara