U.K.
`
`.
`
`U.S.A.
`
`CANADA
`
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`
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`
`_
`FEDERAL REPUBLIC
`OF GERMANY
`JAPAN
`"
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`Pergamon Press Ltd., Headington Hill Hall,
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`Per-gamer: Press, Qismmen Hotel, Beijing,
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`- C
`
`oPyright © 1980 Max Born and Emil Wolf
`
`Alt Righter Reserved. No pan of this publication may be
`reproduced. stored in a retrieval system or transmitted in
`any form or by any means:
`electronic,
`electrostatic,
`magnetic tape, mechanieai, photocopying,
`recording or
`otherwise, without permiesion
`in writing from the
`publishers.
`
`First. edition 1959
`Second (revised) edition 1964
`Third (revised) edition 1965
`Fourth (revised) edition 1970
`Fifth (revised) edition 1975
`Reprinted 1975. 1977
`Sixth edition 1980
`Reprinted (with corrections) 1983
`Reprinted 1984
`Reprinted (with corrections} 1986
`
`Library of Congress Cataloging in Publication Data
`. Born, Mex
`'
`-
`Principles of optic5,—6th ed. (with corrections).
`1. Optics
`11. Wolf, Emil
`1. Title
`Q0351
`80-41470
`535
`ISBN 0438-0264824 hardcover
`ISBN 0-08-02648b6 flexicover
`
`Printed in Great Britain by A. Wheaten It Co. Ltd" Enter
`
`Petitioner Ciena Corp. et al.
`
`Exhibit 1038-1
`
`

`

`PREFACE TO THE FIRST EDITION
`
`THE idea of writing this book was a result of frequent enquiries about the possibility
`of publishing in the English language a book on optics written by one of us“ more than
`twenty—five years ago. A preliminary survey of the literature showed that numerous
`researches on almost every aspect of optics have been carried out in the intervening
`' years, so that the book no longer gives a comprehensive and balanced picture of the
`field. In consequence it was felt that a translation was hardly appropriate;
`instead
`a substantially new book was prepared, which we are now placing before the reader.
`In planning this book it soon became apparent that even if only the most important
`developments which took place since the publication of Optik were incorporated, the
`book would become impracticably large.
`It was,
`therefore, deemed necessary to
`restrict its scope to a narrower field. Optiic itself did not treat the whole of optics.
`The optics of moving media, optics of X-rays and y rays, the theory of spectra and the
`full connection between optics and atomic physics were not discussed; nor did the
`old book consider the effects of light on our visual sense Organ—the eye. These
`subjects can be treated more appropriately in connection with other fields such as
`relativity, quantum mechanics, atomic and nuclear physics, and physiology.
`In this
`book not only are these subjects excluded, but also the classical molecular optics which
`was the subject-matter of almost half of the German book. Thus our discussion is
`restricted to those optical phenomena which may be treated in terms of MAXWELL‘s
`phenomenological theory. This includes all situations in which the atomistic structure
`of matter plays no decisive part. The connection with atomic physics, quantum
`mechanics, and physiology is indicated only by short references wherever necessary.
`The fact that, even after this limitation, the book is much larger than Optil'c, gives
`some indication about the extent of the researches that have been carried out in
`classical optics in recent times.
`We have aimed at giving, within the framework just outlined, a reasonably com-
`plete picture of our present knowledge. We have attempted to present the theory in
`such a way that practically all the results can be traced back to the basic equations of
`MaxwuLL's electromagnetic theOry, from which our whole consideration starts.
`In Chapter I the main preperties of the electromagnetic field are discussed and the
`sheet of matter on the propagation of the electromagnetic disturbance is described
`formally, in terms of the usual material censtants. A more physical approach to the
`question of influence of matter is developed in Chapter II: it is shown that in the
`presence of an external incident field, each volume element of a material medium
`may be assumed to give rise to a secondary (scattered) wavelet and that the combina-
`tion of these wavelets leads to the observable, macroscopic field. This approach is of
`considerable physical significance and its power is illustrated in a later chapter
`(Chapter XIII—in connection with the diffraction of light by ultrasonic waves, first
`treated in this way by A. B. Bums and W. J. NOBLE; Chapter XII was contributed
`by Prof. BHATIA himself.
`A considerable part of Chapter III is devoted to showing how geomelfl'iml optics
`follows from MswaLL’s wave theory as a limiting case of short wavelengths.
`In
`addltlon to discussing the main properties of rays and wave-fronts, the vectorial
`
`‘ Max BORN, Optilc (Berlin, Springer, 1933}.
`
`V
`
`Petitioner Ciena Corp. et al.
`
`Exhibit 1038-2
`
`

`

`vi
`
`PREFACE TO THE rins'r EDITION
`
`aspects of the problem (propagation of the directions of the field vectors) are also
`considered. A detailed discussion of the foundations of geometrical Optics seemed to
`us desirable in view of the important developments made in recent years in the related
`field of microwave optics (optics of short radio waves). These developments were
`often stimulated by the close analogy between the two fields and have provided
`new experimental techniques for testing the predictions of the theory. We found it
`convenient
`to separate the mathematical apparatus of geometrical optics-«the
`calculus of variations—~from the main text; an appendix on this subject (Appendix I)
`is based in the main part on unpublished lectures given by D. HILBER’I‘ at Gettingen- "
`University in the early years of this century. The following appendix (Appendix II),
`contributed by Prof. D. Gases, shows the close formal analogy that exists between
`geometrical Optics, classical mechanics, and electron optics, when these subjects are
`presented in the language of the calculus of variations.
`We make no apology for basing our treatment of geometrical theory of imaging
`(Chapter IV) on HAMILTon’s classical methods of characteristic functions. Though
`these methods have found little favour in connection with the design of optical instru-
`ments, they represent nevertheless an essential tool for presenting in a unified manner
`the many diverse aspects of the subject. It is, of course, possible to derive some of the
`results more simply from ad toe assumptions; but, hmvever valuable such an approach
`may be for the solution of individual problems, it cannot have more than illustrative
`value in a book concerned with a systematic development of a theory-from a. few
`simple postulates.
`The defect of optical images (the influence of aberrations} may be studied either
`by geometrical optics (appropriate when the aberrations are large), or by difiraction
`theory (when they are sufficiently small). Since one usually proceeds from quite
`different starting points in the two methods of treatments, a comparison of results
`has in the past not always been easy. We have attempted to develop a more unified
`treatment, based on the concept of the deformation of wave-fronts. In the geometrical
`analysis of aberrations (Chapter V) we have found it possible and advantageous to
`follow, after a slight modification of his eikona], the old method of K. SCHWARZSCHILD.
`The chapter on diifraetion theory of aberrations (Chapter IX) gives an account of
`the NIJBOERZERNIKE theory and also includes an introductory section on the
`imaging of extended objects, in coherent and in incoherent illumination, based on the
`techniques of Founrnn transforms.
`Chapter VI, contributed by Dr. P. A. WAYMAN, gives a brief description of the
`main image-forming optical systems.
`Its purpose is to provide a framework for
`those parts of the book which deal with the theory of image formation.
`Chapter VII is concerned with the elements of the theory of interference and with
`interferOmeters. Some of the theoretical sections have their nucleus in the corre-
`
`sponding sections of Optik, but the chapter has been completely re-written by Dr.
`W. L. WILCOCK, who has also considerably broadened its scope.
`Chapter VIII is mainly concerned with the anssEL-KIRUHHOFF diffraction theory
`and with some of its applications. In addition to the usual topics, the chapter includes
`a detailed discussion of the central problem of optical image formation—the analysis
`of the three-dimensional light distribution near the geometrical focus. An account is
`also given of a less familiar alternative approach to diffraction, based on the notion
`0f the boundary diffraction wave of T. Y0 UNG.
`. The cl’lapters so far referred to are mainly concerned with perfectly monochromatic
`{and therefore UGmpletely coherent) light, produced by point sources. Chapter X
`deals Wlth the more realistic case of light produced by sources of finite extension and
`
`Petitioner Ciena Corp. et al.
`
`Exhibit 1038-3
`
`

`

`PREFACE TO THE FIRST EDITION
`
`vii
`
`covering a finite frequency range. This is the subject of partial coherence, Where
`considerable progress has been made in recent years. In fact, a systematic theory of
`interference and dili‘raction with partially coherent light has now been developed.
`This chapter also includes an account of the closely related subject of partial polariza-
`tion, from‘the standpoint cf_-C(iherence theory.
`Chapter XI deals with rigorous diffraction theory, a field that has witnessed a
`tremendous development over the period of the last twenty years} stimulated largely
`by advances in the ultra-shortwave radio techniques. This chapter was contributed
`by Dr. P. C. CLEMMOW who also prepared Appendix III, which deals with the
`mathematical methods of steepest descent and stationary phase.
`The last two chapters, Optics of Metals (Chapter XIII) and Optics of Crystals
`(Chapter XIV} are based largely on the corresponding chapters of Optik, but were
`revised and extended with the help of Prof. A. M. Tamoaand Dr. A. B... STOKES
`respectively. These two subjects are perhaps discussed in less detail than might
`seem appropriate. However, the Optics of metals can only be treated adequately
`with the help of quantum mechanics of electrons, which is outside the scope of this
`book.
`In crystal Optics the centre of interest has gradually shifted from visible
`radiation to X-rays, and the progress made in recent years has been of a technical
`rather than theoretical nature.
`
`Though we have aimed at producing a book which in its methods of presentation
`and general approach would be similar to Optz'k, it will be evident that the present
`book is neither a translation of Optiic, nor entirely a compilation of known data. As
`regards our own share in its production, the elder co-author (M. B.) has contributed
`that material from Optik which has been used as a basis for some of the chapters in
`the present treatise, and has taken an active part in the general planning of the
`11001: and in numerous discussions concerning disputable points, presentation, etc.
`Most of the compiling, writing, and checking of the text was done by the younger
`co-author (E. W.).
`Naturally we have tried to use systematic notation throughout the book. But in a
`_ book that covers such a wide field, the number of letters in available alphabets is far
`too limited. We have, therefore, not always been able to use the mostelegant notation
`but we hope that we have succeeded, at least, in avoiding the use in any one section
`of the same symbol for different quantities.
`In general we use vector notation as customary in Great Britain. After much
`reflection we rejected the use of the nabla operator alone and employed also the
`customary “div”, “grad”, and “curl". Also, We did not adopt the modern electro-
`technical units, as their main advantage lies in connection with purely electromagnetic
`measurements, and these play a negligible part in our discussions; moreover, we
`hope, that if ever a second volume (Molecular and Atomic Optics) and perhaps a'third
`volume (Quantum Optics) is written, the C.G.S. system, as used in Theoretical Physics,
`will have returned to favour. Although, in this system of units, the magnetic per-
`meability p, of most substances differs inappreciably from unity at optical frequencies,
`we have retained it in some of the equations. This has the advantage of greater
`symmetry and makes it possible to derive “dual” results by making use of the
`symmetry properties of MAXWEIL'S equations. For time periodic fields we have used.
`in complex representation, the factor exp (— imt) throughout.
`We have not attempted the task of referring to all the relevant publications. The
`
`'.The import-ant review article by C. J. Boownaur, Rep. Progr. Phys. {Lender-n Physical
`1
`bOCIety). 17 (lilo-Ll, 35, records more than 500 papers published in the period lQilLlQE-i.
`
`Petitioner Ciena Corp. et al.
`
`Exhibit 1038-4
`
`

`

`viii
`
`PREFACE TO THE FIRST EDITION
`
`references that are given, and which, we hope, include the most important papers, are
`to help the reader to gain some orientation in the literature; an omission of any
`particular reference should not be interpreted as due to our lack of regard for its merit.
`In conclusion it is a pleasure to thank many friends and colleagues for advice and
`help. In the first place we wish to record our gratitude to Professor D. Genoa for useful
`advice'and assistance in the early stages of this project, as well as for providing
`a draft concerning his ingenious method of reconstructed wave-fronts (§ 8.10). We
`are also greatly indebted to Dr. F. ABELES, who prepared a draft, which is the back-
`bone of § 1.6, on the propagation of electromagnetic waves through stratified media,
`a field to which he himself has made a substantial contribution. We have also
`benefited by advice on this subject from Dr. B. H. BILLINGS.
`We are much indebted to Dr. H. H. Harms, Dr. R. A. Savanna, Dr. W. T.
`WELFDRD and Dr. G. WYLLIE for critical comments and valuable advice, and to
`them and also to Dr. G. BLACK, Dr. H. J. J. Bunnies, Dr. N. CHAKO, Dr. F. D. KAHN,
`Mr. A. NISBET, Dr. M. Ross and Mr. R. M. SELLITro for scrutinizing various sections
`of the manuscript. We are obliged to Polaroid Corporation for information concerning
`dichroie materials. Dr. F. D. KAHN helped with proof-reading and Dr. P. ROMAN and
`Mrs. M. PODOLANSKI with the preparation of the author index.
`The main part of the writing was done at the Universities of Edinburgh and
`Manchester. The last stages were completed whilst one of the authors (E. W.) was
`a guest at the Institute of Mathematical Sciences, New York University. We are
`grateful to Professor M. KLINE, Head of its Division of Electromagnetic Research,
`for his helpful interest and for placing at our disposal some of the technical facilities
`of the Institute.
`
`We gratefully acknowledge the loan of original photographs by Professor M. FRANQON
`and Dr. M. Caesar (Figs. 7.4, 7.26, 7.28, 7.60, 14.24, 14.26), Professor H. LIPSON
`and his co-workers at the Manchester College of Science and Technology (Figs. 8.10,
`8.12, 8.15), Dr. 0. W. RICHARDS (Figs. 8.34, 8.35), and Professor F. ZERNIKE and
`Dr. K. NIENEUIS (Figs.- 9.4, 9.5, 9.8, 910, 9.11). Figure 7.66 is reproduced by courtesy
`'of the Director of the Mount Wilson and Palomar Observatories. The blocks of
`
`Fig. 7.42 were kindly loaned by Messrs. Hilger and Watts, Ltd., and those of Figs.
`7.64 and 7.65 by Dr. K. W. MEISSNER.
`_
`Financial assistance was provided by Messrs. Industrial Distributors Ltd., London,
`and we wish to acknowledge the generosity of the late Sir ERNEST OPPsNHEIMnn,
`its former head.
`
`Finally, it is a pleasure to thank our publishers and in particular Mr. E. J. BUCKLEY,
`Mr. D. M. Lawn and also Dr. P. ROSBAUD, who as a former Director of Pergamon
`Press was closely associated with this project in its early stages, for the great care
`they have taken in the production of the book. It is a pleasure to pay tribute also
`to the printers, Pitman Press of Bath, for the excellence of their printing.
`
`Bad Pyrmont and Manchester
`January 1959
`
`MK BORN
`Em “Fol-Ja-
`
`Petitioner Ciena Corp. et al.
`
`Exhibit 1038-5
`
`

`

`PREFACE TO THE SECOND EDITION
`
`ADVANTAGE has been taken in the preparation of a. new edition of this work to make a.
`number of corrections of errors and misprints, to make a few minor additions and to
`include some new references.
`
`Since the appearance of the first edition almost exactly three years ago, the first
`optical masers (lasers) have been developed. By means of these devices very intense
`and highly coherent light beams may be produced. 1Whilst it is evident that optical
`masers will prove of considerable value not only for optics but also for other sciences
`and for technology. no account of them is given in this new edition. For the basic
`principles of maser action have roots outside the domain of classical electromagnetic
`theory on which considerations of this book are based. We have. however. included
`a few references to recent researches in which light generated by optical masers was
`utilized or which have been stimulated by the potentialities of these new optical
`devices.
`
`We wish to acknowledge our gratitude to a number of readers who drew our
`attention to errors and misIn-ints. We are also obliged to Dr. B. Kanczswsxi and
`Mr. C. L. MEIITA for assistance with the revisions.
`
`Bad Pyrmonl and Rochester
`November 1962
`
`M.B.
`ELW.
`
`PREFACE TO THE SIXTH EDITION
`
`THIS edition differs from its immediate predecessor chiefly in that it contains
`corrections of a small number of errors and misprints.
`-
`
`Roam,
`September 1985
`
`_
`
`'
`
`' ew.
`
`PC em Ed. — a-
`
`ix
`
`Petitioner Ciena Corp. et al.
`
`Exhibit 1038-6
`
`

`

`'
`
`-.
`
`.
`
`.__
`_.
`-
`.
`HISTORICAL INTRODUCTION
`
`C O N T E N T S
`
`I
`
`II BASIC PROPERTIES OF THE ELECTROMAGNETIC FIELD
`
`1.1. The Electromagnetic Field
`1.1.1. Maxwell’s equations
`1.1.2. Material equations
`1.1.3. Boundary conditions at a surface of discontinuity
`1.1.4. The energy law of the electromagnetic field
`
`1.2. The Wave EquatiOn and the Velocity of Light
`1.3. Scalar Waves
`
`1.3.1. Plane waves
`
`1.3.2. Spherical waves
`1.3.3. Harmonic Waves. The phase velocity
`1.3.4. Wave packets. The group velocity
`1.4. Vector Waves
`
`1.4.1. The general electromagnetic plane wave
`1.4.2. The harmonic electromagnetic plane wave
`(a) Elliptic polarization
`(1)) Linear and circular polarization
`(c) Characterization of the state of polarization by Stokes
`parameters
`1.4.3. Harmonic vector waves of arbitrary form
`1.5. Reflection and Refraction of a Plane Wave
`
`_
`
`1.5.1. The laws of reflection and refraction
`--1.5.2. Fresnel formulae
`
`1.5.3. The reflectivity and transmissivity; polarization on reflection
`and refraction
`1.5.4. Total reflection
`
`1.6. Wave Pmpagation in a Stratified Medium. Theory of Dielectric Films
`1.6.1. The basic differential equations
`1.6.2. The characteristic matrix of a stratified medium
`(a) A homogeneous dielectric film
`(b) A stratified medium as a pile of thin homogeneous films
`1.6.3. The reflection and transmission coefi’icients
`1.6.4. A homogeneous dielectric film
`1.6.5. Periodically stratified media
`
`II. ELECTROMAGNETIC POTENTIALS AND POLARIZATION
`
`2.1. The Electrodynamic Potentials in the Vacuum
`2.1.1. The vector and scalar potentials
`2.1.2. Retarded potentials
`
`no:
`xxi
`
`1
`
`1
`1
`2
`4
`7
`
`10
`l-i
`
`14
`
`15
`15
`18
`23
`
`23
`24
`25
`28
`
`30
`32
`36
`
`36
`33
`
`41
`47
`
`51
`52
`55
`5'?
`53
`59
`61
`65
`
`71
`
`72
`72
`74
`
`xi
`
`Petitioner Ciena Corp. et al.
`
`Exhibit 1038-7
`
`

`

`xii
`
`CONTENTS
`
`2.2. Polarization and Magnetization
`
`2.2.1. The potentials in terms of polarization and magnetization
`22.2. Hertz vectors
`
`2.2.3. The field of a linear electric dipole
`
`2.3. The Lorentz—Lorenz Formula and Elementary Dispersion Theory
`
`'
`
`2.3.1. The dielectric and magnetic susceptibilities
`2.3.2. The effective field
`
`the Lorentz~Lorenz formula
`2.3.3. The mean polarizability:
`2.3.4. Elementary theory of dispersion
`. 2.4. Prepagation of Electromagnetic Waves Treated by Integral Equations
`2.4.1. The basic integral equation
`2.4.2. The Ewald~03een extinction theorem and a rigorous derivation
`of the Lorentz—Lorenz formula
`
`2.4.3. Refraction and reflection of a plane wave, treated with the help
`of the Ewald—Oseen extinction theorem
`
`III. FOUNDATIONS OF GEOME‘I‘RICAL OPTICS
`
`3.1. Approximation for Very Short Wavelengths
`
`3.1.1. Derivation of the eikonal equation
`3.1.2. The light rays and the intensity law of geometrical optics
`3.1.3. Propagation of the amplitude vectors
`3.1.4. Generalizations and the limits of validity of geometrical optics
`
`3.2. General Properties of Rays
`
`,
`
`3.2.1. The differential equation of light rays
`3.2.2. The laws of refraction and reflection
`
`3.2.3. Ray cengruences and their focal properties
`
`_ 3.3. Other Basic Theorems of Geometrical Optics
`3.3.1. Lagrange’s integral invariant
`3.3.2. The principle of Format
`3.3.3. The theorem of Malus and Dupin and some related theorems
`
`IV. GEOMETRICAL THEORY OF OPTICAL IMAGING
`
`4.1. The Characteristic Functions of Hamilton
`
`4.1.1. The point characteristic
`4.1.2. The mixed characteristic
`
`4.1.3. The angle characteristic
`4.1.4. Approximate form of the angle characteristic of a refracting
`surface of rerolution
`
`4.1.5. Approximate form of the angle characteristic of a reflecting
`surface of revolution
`
`4.2. Perfect Imaging
`4.2.1. General theorems
`
`4.2.2. Maxwell’s “fish-eye”
`4.2.3. Stigmatic imaging of surfaces
`
`P1015
`
`76
`
`76
`79
`
`81
`
`84
`
`84
`85
`
`87
`90
`98 '
`99
`
`100
`
`104
`
`109
`
`109
`
`110
`113
`117
`119
`
`121
`
`121
`124
`
`126
`
`127
`127
`128
`130
`
`133
`
`133
`
`133
`135
`
`137
`
`138
`
`141
`
`143
`143
`
`147
`149
`
`Petitioner Ciena Corp. et al.
`
`Exhibit 1038-8
`
`

`

`CONTENTS
`
`4.3. Projective Transformation {Collineation} with Axial Symmetry
`4.3.1. General formulae
`
`4.3.2. The telescopic case
`4.3.3. Classification of projective transformations
`4.3.4. Combination of projective transformations
`
`4.4. Gaussian Optics
`
`4.4.1. Refracting surface of revolution
`4.4.2. Reflecting surface of revolution
`4.4.3. The thick lens
`4.4.4. The thin lens
`
`4.4.5. The general centred system
`
`4. 5. Stigmatic Imaging with Wide-angle Pencils
`4.5.1. The sine cenditien
`4.5.2. The Herschel condition
`
`4.6. Astigmatic Pencils of Rays
`
`4.6.1. Focal properties of a thin pencil
`4.6.2. Refraction of a. thin pencil
`4.7. Chromatic Aberration. Dispersion by a. Prism '
`4.7.1. Chromatic aberration
`
`'
`
`4.7.2. Dispersion by a prism
`
`4.8. Photometry and Apertures
`4.8.1. Basic concepts of photometry
`4.3.2. Stops and pupils
`4.8.3. Brightness and illumination of images
`
`4.9. Ray Tracing
`4.9.1. Oblique meridional rays
`4.9.2. Pars-xiii] rays
`4.9.3. Skew rays
`
`4.10. Design of Aspheric Surfaces
`
`4.10.1. Attainment of axial stigmatism
`4.10.2. Attainment of aplanatism
`
`V. GEOMETRICAL THEORY OF ABERRATIONS
`
`5.1. Wave and Ray Aberrations; the Aberration Function
`5.2. The Perturbation Eikonal of Schwarzschild
`
`5.3. The Primary (Seidel) Aberrations
`
`5.4. Addition Theorem for the Primary Aberrations
`
`xiii
`P101
`
`150
`151
`
`154
`154
`155
`
`157
`
`15”:
`160
`161
`163
`
`1'54
`
`166
`167
`169
`
`169
`
`169
`171
`1'74
`174
`
`177
`
`181
`181
`186
`188
`
`_ 190
`- 191
`' 193
`194
`
`197
`
`197
`200
`
`“203
`
`9.03
`‘20?
`
`211
`
`218
`
`5.5. The Primary Aberration Coefficients of a General Centred Lens System 220
`
`5.5.1. The Seidel formulae in terms of two pal-axial rays
`5.5.2. The Seidel formulae in terms of one paraxial my
`5.5.3.
`l’etzvai's theorem
`
`5.6. Example: The Primary Aberrations Of 3. Thin Lens
`
`'
`
`5.7. The Chromatic Aberration of a General Centred Lens System
`
`220
`224
`225
`
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`Petitioner Ciena Corp. et al.
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`Exhibit 1038-9
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`xiv
`
`CONTENTS
`
`VI. IMAGE-FORMING INSTRUMENTS
`
`6.1. The Eye
`
`6.2. The Camera
`6.3. The Refracting Telescope
`
`I
`
`6.4. The Reflecting Telescope
`
`6.5. Instruments of Illumination
`
`,
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`6.6. The Microscope
`
`FAG].
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`VII. ELEMENTS OF THE THEORY OF INTERFERENCE AND
`INTERFEROMETERS
`
`7.1. Introduction
`
`7.2. Interference of Two Monochromatic Waves
`
`7.3. Two-beam Interference: Division of Wave-front
`
`7.3.1. Young’s experiment
`7.3.2. Fresnel’s mirrors and similar: arrangements
`7.3.3. Fringes with quasi-monochromatic and white light
`7.3.4. Use of slit sources; visibility of fringes
`7.3.5. Application to the measurement of optical path difference:
`Rayleigh interferometer
`7.3.6. Application to the measurement ofangular dimensions ofsources '.
`the Michelson stellar interferometer
`
`the
`
`7.4. Standing Waves
`
`7.5. Two-beam Interference: Division of Amplitude
`
`..
`7.5.1. Fringes with a plane parallel plate
`7.5.2. Fringes with thin films;
`the Fizeau interferometer -
`7.5.3. Localization of fringes
`7.5.4. The Michelson interferometer
`
`7.5.5. The Twyman—Green and related interferometers
`7.5.6. Fringes with two identical plates:
`the Jamin interferometer
`and interference microscopes
`the Bates wave-front
`7.5.7. The Mach—Zehnder
`interferometer;
`'
`shearing interferometer
`7.5.8. The coherence length; the application of two-beam interference
`to the study of the fine structure of spectral lines
`
`7.6. Multiple-beam Interference
`7.6.1. Multiple-beam fringes with a plane parallel plate
`7.6.2. The Fabry—Perot interferometer
`7.6.3. The application of the Fabry—Perot interferometer to the study
`of the fine structure of spectral lines
`7.6.4. The application of the Fabry—Perot interferometer to the com-
`parison of wavelengths
`7.6.5. The Lummer—Gehrcke interferometer
`7.6.6. Interference filters
`
`7.6.7. Multiple-beam fringes with thin films
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`Petitioner Ciena Corp. et al.
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`Exhibit 1038-10
`
`

`

`CONTENTS
`
`7.6.8. Multiple-beam fringes with two plane parallel plates
`(a) Fringes with monochromatic and quasi-monochromatic light
`(b) Fringcs of superposition
`- 7.7. The Comparison of Wavelengths with the Standard Metre
`
`VIII. ELEMENTS OF THE THEORY OF DIFFRACTION
`
`8.1. Introduction
`
`8.2. The Huygens-Fresnel Principle
`
`8.3. Kirchhofi’s Diffraction Theory
`
`8.3.1. The integral theorem of Kirchhoff
`8.3.2. Kirchhofi’s diffraction theory
`8.3.3. Fraunhofer and Fresnel difiraction
`
`8.4. Transition to a Scalar Theory
`
`8.4.1. The image field due to a monochromatic oscillator
`8.4.2. The total image field
`
`8.5. Fraunhofer Difiraction at Apertures of Various Forms
`8.5.1. The rectangular aperture and the slit
`8.5.2. The circular aperture
`8.5.3. Other forms of aperture
`
`'
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`8.6. Fraunhofer Diffraction in Optical Instruments
`
`8.6.1. Diffraction gratings
`(a) The principle of the diffraction grating
`(b) Types of grating
`(c) Grating spectrograph;
`8.6.2. Resolving power of imageuforming systems
`8.6.3. Image formation in the microscope
`(a) Incoherent illumination
`(b) Coherent illumination—Abbe’s theory
`(c) Coherent illumination—“Zernike’s phase contrast method of
`observation
`
`8.7. Fresnel Difiraction at a Straight Edge
`8.7 .1. The diffraction integral
`8.7.2. Freenel’s integrals
`8.7.3. Fresnel diffraction at a straight edge
`
`8.8. The Three-dimensional Light Distribution near Focus
`8.8.1. Evaluation of the difiraction integral
`in terms of Lommel
`functions
`8.8.2. The distribution of intensity
`(3-) Intensity in the geometrical focal plane
`(b) Intensity along the axis
`(e) Intensity along the boundary of the geometrical shadow
`8.8.3. The integrated intensity
`8.8.4. The phase behaviour
`
`8.9. The BOundary Diflraction Wave
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`XV
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`1'10]
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`Petitioner Ciena Corp. et al.
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`Exhibit 1038-11
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`

`

`xvi
`
`oos‘rnn'rs
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`8.10. Gabor’s Method of Imaging by Reconstructed Wave-fronts
`(Holography)
`
`8.10.1. Producing the positive hologram
`8.10.2. The reconstruction
`
`IX. THE DIFFRACTION THEORY OF ABERRATIONS
`
`9.1. The Diffraction Integral in the Presence of Aberrations
`
`9.1.1. The diffraction integral
`9.1.2. The displacement theorem. Change of reference sphere
`9.1.3. A relation between the intensity and the average deformation
`of wave-fronts
`
`9.2. Expansion of the Aberration Function
`
`9.2.1. The circle polynomials of Zernike
`9.2.2. Expansion of the aberration function
`
`9.3. Tolerance Conditions for Primary Aberrations
`
`9.4. The bitiraction Pattern Associated with a. Single Aberration
`9.4.1. Primary Spherical aberration
`9.4.2. Primary coma
`9.4.3. Primary astigmatism
`
`9.5. Imaging of Extended Objects
`9.5.1. Coherent illumination
`9.5.2. Incoherent illumination
`
`X. INTERFERENCE AND DIFFRACTION WITH PARTIALLY
`COHERENT LIGHT
`
`10.1. Introduction
`
`10.2. A Complex Representation of Real Polychromatic Fields
`
`10.3. The CorrelationFunctions of Light Beams
`
`10.3.1. Interference of two partially coherent beams. The mutual
`coherence function and the complex degree of coherence
`10.3.2. Spectral representation of mutual coherence
`
`10.4. Interference and Difiraction with Quasi-monochromatic Light
`
`10.4.1. Interference with quasi-monochromatic light. The mutual
`intensity
`10.4.2. Calculation of mutual intensity and degree of coherence for
`light
`from an extended incoherent quasi-monochromatic
`source
`
`{a} The Van Cittert—Zernike theorem
`0)) Hopkins’ formula
`10.4.3. An example
`10.4.4. Propagation of mutual intensity
`
`PLGI
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`453
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`Petitioner Ciena Corp. et al.
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`Exhibit 1038-12
`
`

`

`CONTEHTS
`
`xvii
`1’10!
`
`10.5. Some Applications
`10.5.1. The degree of coherence in the image of an extended incoherent
`quasi-monochromatic source
`_
`10.5.2. The influence of the condenser on resolution in amicroscope
`(a) Critical illumination
`_
`.
`'
`(b) Kohler's illumination
`10.5.3. Imaging with partially coherent quasi-monochromatic illumi-
`526
`' nation
`I.
`(a) Transmission of mutual intensity through an optical system 526
`(b) Images of transilluminated objects
`528
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`522.
`522
`52-1
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`£
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`10.6. Some Theorems Relating to Mutual Coherence
`
`10.6.1. Calculation of mutual coherence for light from an incoherent
`source
`
`10.6.2. Propagation of mutual coherence
`
`10.7. Rigorous Theory of Partial Coherence
`
`10.7.1. Wave equations for mutual coherence
`10.7.2. Rigorous formulation of the propagation law for mutual
`coherence
`
`10.7.3. The coherence time and the effective Spectral width
`
`10.8. Polarization Properties of Quasi-monochromatic Light
`
`10.8.1. The coherency matrix of a quasi-monochromatic plane wave
`(3.) Completely unpolarized light (Natural light)
`(b) Completely polarized light
`10.8.2. Some equivalent representations. The degree of polarization of
`a light wave
`10.8.3. The Stokes parameters of a quasi-monochromatic plane wave
`
`X1. RIGOROUS DIFFRACTION THEORY
`
`-
`
`11.1. Introduction
`
`11.2. Boundary Conditions and Surface Currents
`
`11.3. Diffraction by a Plane Screen: Electromagnetic Form of Babinet’s
`Principle
`
`11.4. Twodimensional Diffraction by a Plane Screen
`11.1.1. The scalar nature of tw0~dinicnsi0nal electromagnetic fields
`11.4.2. An angular spectrum of plane waves
`11.4.3. Formulation in terms of dual integral equations
`
`.
`
`11.5. Two-dimensional Diffraction of a Plane Wave by a Half-plane
`11.5.1. Solution of the dual integral equations for Epolarization
`11.5.2. Expression of the solution in terms of Fresnel integrals
`11-5.3. The nature of the solution
`11.5.1. The solution for Iii-polarization
`11.5.5. Some numerical calculations
`11.5.6. Comparison with approximate theory and with experimental
`results
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`560
`561)
`561 _
`564
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`56:3
`565
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`570
`51-1
`57-3
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`5??
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`Petitioner Ciena Corp. et al.
`
`Exhibit 1038-13
`
`

`

`xviii
`
`eonrnnws
`
`11.6. Three-dimensional Difiraction of a Plane Wave by a Half-plane
`
`11.7. Diffraction of a Localized Source by a Half-plane
`
`11.7.1. A line-current parallel to the difiracting edge
`11.7.2. A dipole
`.
`
`11.8. Other Problems
`
`'
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`.-
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`;
`__
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`_
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`H
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`11.8.1. Two parallel half-planes
`11.8.2. An infinite (stack of parallel, staggered half-planes
`11.8.3. A strip
`11.8.4. Further problems
`
`11.9. Uniqueness of Solution
`
`XII. DIFFRACTION OF LIGHT BY ULTRASONIC WAVES
`
`the Phenomenon and Summary of
`12.1. QualitatiVe Description of
`Theories Based on Maxwell’s Differential Equations
`
`12.1.1. Qualitative description of the phenomenon
`12.1.2. Summary of theories based on Maxwell's equations
`
`12.2. Diffraction of Light by Ultrasonic Waves as Treated by the Integral
`Equation M