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`
`FEDERAL REPUBLIC
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`Pergamon Press Ltd., Headington Hill Hall,
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`CEP 04011, Siio Paulo, BrlliLi.l
`Pergamon Press, Qia.nmen Hotel, Be1jing,
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`
`Copyright© 1980 Max Born and Emil Wolf
`
`All Riyhu R~rved. No pan of thi.J publicalion may be
`r~produced, stored in a retrieval system or ~ransmitttd in
`,.,. by any means: electron~, ekaroatat~,
`any form
`magnet~ tape, nuchanical, photocopying, ree&rding
`from
`otherwise, wielwu~ permiosion
`in writing
`puhli8her8.
`
`()p'
`the
`
`First edition 1959
`Second (revised) edition 1964
`Third (revised) edition 1965
`Fourth (revised) edition 1970
`Fifth (Mvised) edition 1975
`Raprinted 1975, 1977
`Sixth edition 1980
`Reprinted (with corrections) 1983
`Reprinted 1984
`Reprinted (with corrections) 1986
`
`Library of Congn!:liS Cataloging in PublicaD.on Data
`Born, ~lax
`Principles of optics,-6th ed. (with corrections).
`L Optics
`IL Wolf, Emil
`I. Title
`QC35I
`80-41470
`535
`ISBN 0-08.026482·4 hardcover
`ISBN 0-08·026481·6 flexicover
`
`l'r;nted in Great Britain by A. ff'heaton .i· Cv. Ltd., E.utu
`
`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. Optik itself did not treat the whole of optics.
`The optics of moving media, optics of X-rays andy 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 a.lmost 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 Optik, gi'VeS
`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(cid:173)
`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
`MAXWELL's electromagnetic theory, from which our whole consideration starts.
`In Chapter I the main properties of the electromagnetic field are discussed and the
`effect of matter on the propagation of the electromagnetic disturbance is described
`formally, in terms of the usual material constants. 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 4
`tion of these wavelets leads to the observable, macroscopic field. This approach is of
`considerable physica_~ significance and its power is illustrated in a later chapter
`(Chapter xrrnn-Connection with the diffraction of light by ultrasonic waves, first
`treated in this way by A. B. BHATIA and \V. J. NoBLE; Chapter XII was contributed
`by Prof. BHATIA himself.
`A considerable part of Chapter III is devoted to showing how geometrical optics
`follows from MAXWELL'a wave theory as a limiting case of short wavelengths. In
`addition to discussing the main properties of rays and wave-fronts, the vectorial
`
`• M .. u: BoR:-<, Optik (Berlin, Springer, 1933).
`
`v
`
`Petitioner Ciena Corp. et al.
`Exhibit 1038-2
`
`

`
`vi
`
`PREFACE TO THE FIRST EDITION
`
`aspects of the problem (propagation of the directions of the field vectors) are aleo
`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 relat.ed
`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. HILBERT at Gottingen·
`University in the early years of this century. The following appendix {Appendix II),
`contributed by Prof. D. GABOR, 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 baaing 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 hoc assumptions; but, however 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 diffraction
`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 o!" aberrations {Chapter V) we have found it possible and advantageous to
`follow, after a slight modification of his eikonal, the old method ofK_ ScnwARZSCHILD_
`The chapter on diffraction theory of aberrations (Chapter IX) gives an account of
`the NI.JBOER-ZERNIKE theory and also includes an introductory section on the
`imaging of extended objects, in coherent and in incoherent illumination, based on the
`techniques of FOURIER 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(cid:173)
`sponding sections of Optik, but the chapter has been completely re-written by Dr.
`\V. L. WILCOCK, who has also considerably broadened its scope.
`Chapter VIII is mainly concerned with the FRES~EL-KmcrmoFF diffraction theory
`and with some of its applications. In addition to the usual tppics, 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, baserl on the notion
`of the boundary diffraction wn.ve ofT. YouNG.
`The chapters so far referred to are mainly concerned \vith perfectly monochromatic
`(and th.erefore completely coherent) light, produced hy point sources. Chapter X
`deals with 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
`
`cove_ring 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 diffraction with partially coherent light has now been developed.
`This chapter ~lso includes an account of the closely related subject of partial polariza(cid:173)
`tion, from-the standpoint of cOherence theory.
`Ch..1.pter 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. TAYLOR and Dr. A. R. 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 Optik, it will be evident that the present
`book is neither a translation of Optik, nor entirely a compib.tion 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
`book 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 most elegant notation
`hut '"e 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(cid:173)
`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 OptiC8) and perhaps a third
`volume (Q-uantum 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(cid:173)
`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 oL\la .. "{WELL's equations. For time periodic fields we have used.
`in complex representation, the factor exp (- iwt) throughout.
`\Ve have not attempted the task of referring to all the relevant publications. The
`
`• The important rO\'iow article by C. J. BouwKAMP, Rep. Progr. Phya. {London, Phvsi<;a.i
`Socioty), 17 (1U54), 35, records more than 500 papers published in the period 19.1.0-195"-.
`-
`
`Petitioner Ciena Corp. et al.
`Exhibit 1038-4
`
`

`
`viii
`
`PREFACE TO THE FIRST EDITION
`
`references that arc 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. GABOR 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(cid:173)
`bone of§ l.G, 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. HoPKINS, Dr. R. A. SILVERMAN, Dr. W. T.
`WELFORD and Dr. G. WYLLIE for critical comments and valuable advice, and to
`them and also to Dr. G. BLACK, Dr. H. J. J. BRAD DICK, Dr. N. CHAKO, Dr. F. D. KAHN,
`Mr. A. NISBET, Dr. M. Ross and Mr. R. M. SILLITI'o for scrutinizing various sections
`of the manuscript. We are obliged to Polaroid Corporation for information concerning
`dichroic materials. Dr. F. D.ILu!N helped with proof-rea.ding 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 II1Btitute of Mathematical Sciences, New York University.
`\Ve 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. FRA.Nt;ON
`and Dr. M. CAGNET (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. \V. RICHARDS (Figs. 8.34, 8.35), and Professor F. ZERNIKE and
`Dr. K. NIENHUIS (Figs. 9.4, 9.5, 9.8, 9.10, 9.11). Figure 7.66 is reproduced by courtesy
`of the Director of the Mount Wilson and Palom:u 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 a.~sistance was provided by lfessrs. Industrial Distributors J ... td., London,
`and we wish to acknowledge the generosity of the late Sir ERNEST OPPENHEIMER,
`its former hea.d.
`Finally, it is a pleasure to thank our publishers and in particular Mr. E. J. BucKLEY,
`Mr. D. M. LoWE 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 pa.y tribute also
`to the printers, Pitman Press of Bath, for the excellence of their printing.
`
`Bad Pyrmont and ManchuUr
`January 1959
`
`MAx BoRN
`EMIL WOLF
`
`Petitioner Ciena Corp. et al.
`Exhibit 1038-5
`
`

`
`PREFACE TO THE SECOND EDITION
`AovANT.WE has been taken in the preparation of a. new edition ofthis 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 appen.rance 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. \Vhilst 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 ma!ier action have roots outside the domain of cl:lssical electromagnetic
`theory on which considerations of this book arc based. \Ve 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 erronJ and misprints. We are also obliged to Dr. B. KARCZEWSKI a.nd
`Mr. C. L. MEHTA for assistance with the revisions.
`Bad Pyrmon' and RochuUr
`November 1962
`
`M.B.
`E.W.
`
`PREFACE TO THE SIXTH EDITION
`
`Tats edition differs from its immediate predecessor chiefly in that it contains
`corrections of a small number of errors and misprints.
`
`RriChultlr
`Stpltlmber 198J
`
`E.W.
`
`PC Olh Ed • . A"
`
`ix
`
`Petitioner Ciena Corp. et al.
`Exhibit 1038-6
`
`

`
`CONTENTS
`HISTORICAL INTRODUCTION
`I. 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
`(b) 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 Propagation 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 coefficients
`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. R.etarded potentials
`
`U.Oit
`xxi
`l
`1
`
`2
`4
`7
`10
`14
`14
`15
`16
`18
`23
`23
`24
`25
`28
`
`30
`32
`36
`36
`38
`
`41
`47
`51
`52
`55
`57
`58
`59
`61
`66
`71
`72
`72
`74
`
`xi
`
`Petitioner Ciena Corp. et al.
`Exhibit 1038-7
`
`

`
`xii
`
`CONTEN'rS
`
`2.2. Polarization and Magnetization
`2.2.1. The potentials in terms of polarization and magnetization
`· 2.2.2. Hertz vectors
`~.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
`2.3.3. The mean polarizability: the Lorentz-Lorenz formula
`2.3.4. Elementary theory of dispersion
`2.4. Propagation of Electromagnetic Waves Treated by Integral Equations
`2.4.1. The basic integral equation
`2.4.2. The Ewa.Id-Oseen 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
`
`PJ.OIC
`76
`76
`79
`81
`84
`84
`85
`87
`90
`98 ·
`99
`
`100
`
`I 04
`
`109
`III. FOUNDATIONS OF GEOMETRICAL OPI'ICS
`3.1. Approximation for Very Short Wavelengths
`109
`3.1.1. Derivation of the eikonal equation
`IIO
`113
`3.1.2. The light rays and the intensity law of geometrical optics
`3.1.3. Propagation of the amplitude vectors
`117
`3.1.4. Generalizations and the limits of validity of geometrical optics 119
`3.2. General Properties of Rays
`121
`3.2.1. The differential equation of light rays
`121
`3.2.2. The laws of refraction and reflection
`124
`3.2.3. Ray congruences and their focal properties
`126
`3.3. Other Basic Theorems of Geometrical Optics
`127
`3.3.1. Lagrange's integral invariant
`127
`3.3.2. The principle of Fermat
`128
`3.3.3. The theorem of Malus and Dupin and some related theoreml'l
`130
`
`IV. GEOMETRICAL THEORY OF OPI'ICAL 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 revolution
`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-eve"
`4.2.3. Stigmatic imaging of surfaces
`
`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 Pends
`4.5.1. The sine condition
`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 Pri1nn
`4. 7 .1. Chromatic aberration
`4.7.2. Dispersion by a prism
`4.8. Photometry and Apertures
`4.8.1. Basic concepts of photometry
`4.8.2. Stops and pupils
`4.8.3. Brightness and illumination of images
`4.9. Ray Tracing
`4.9.1. Oblique meridional rays
`4.9.2. Paraxla.l 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
`
`xiii
`
`PJ.o•
`150
`151
`154
`154
`155
`157
`157
`160
`161
`163
`164
`166
`167
`169
`169
`169
`171
`174
`174
`177
`181
`181
`186
`188
`190
`191
`193
`194
`197
`197
`!."!00
`
`:!03
`V. GEOMETRICAL THEORY OF ABERRATIONS
`5.1. Wave and Ray Aberrations; the Aberration Function
`:!03
`5.2. The Perturbation Eikonal of Schwarzschild
`207
`211
`5.3. The Primary (Seidel) Aberrations
`5.1:. Addition Theorem for the Primary Aberrations
`::!18
`5.5. The Primary Aberration Coefficients of a General Centred Lens System 220
`5.5.1. The Seidel formulae in terms of two paraxial rays
`220
`5.5.2. The Seidel formulae in terms of one paraxial ray
`224
`5.5.3. Petzval's theorem
`:.!25
`5,(). Example: The Primary .--\.berrations of a Thin Lens
`226
`5.7. The Chromatic Aberration of a General Centred Lens SyRtem
`230
`
`Petitioner Ciena Corp. et al.
`Exhibit 1038-9
`
`

`
`xiv
`
`CONTENT~
`
`VI. IMAGE-FORMING INSTRUMENTS
`~~-~~
`6.2. The Camera
`6.3. The Refracting Telescope
`6.4. The Reflecting Telescope
`6.5. Instruments of Illumination
`6.6. The Microscope
`
`-
`
`PAG.
`233
`
`· ·235
`239
`245
`250
`251
`
`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: the
`Rayleigh interferometer
`7 .3.6. Application to the measurement of angular dimensions of sources:
`the Michelsor. stellar interferometer
`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 .Michebon interferometer
`7 .5.5. The Twyman-Green and related interferometers
`7.5.6. }i'ringes with two identical plates: the Jamin interferometer
`and interference microscopes
`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 .G.5. The T .... ummer-Gehrcke interferometer
`7.6.6. Interference filters
`7.6.7. ::"llultiple-beam fringes with thin films
`
`the Bates wave-front
`
`256
`257
`257
`260
`260
`261
`264
`265
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`268
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`271
`277
`281
`281
`286
`291
`300
`302
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`306
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`312
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`316
`323
`323
`329
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`333
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`338
`3·11
`347
`351
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`Exhibit 1038-10
`
`

`
`CONTENTS
`
`XV
`
`PJ.G•
`360
`7 .6.8. Multiple-beam fringes with two plane parallel plates
`(a) Fringes with monochromatic and quasi-monochromatio light 360
`(b) Fringes of superposition
`364
`7.7. The Comparison of Wavelengths with the Standard Metre
`367
`
`VIII. ELEMENTS OF THE THEORY OF DIFFRAGriON
`8.1. Introduction
`8.2. The Huygens-Fresnel Principle
`8.3. Kirchhoff's Diffraction Theory
`8.3.1. The integral theorem of Kirchhoff
`8.3.2. Kirchhoff's diffraction theory
`8.3.3. Fraunhofer and Fresnel diffraction
`8.4. Transition to a. Sca.la.r Theory
`8.4.1. The image field due to a monochromatic oscillator
`8.4.2. The total image field
`8.5. Fraunhofer Diffraction 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
`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 spectrographs
`8.6.2. Resolving power of image-forming systems
`8.6.3. Image fonnation in the microscope
`(a) Incoherent illumination
`(b) Coherent illumination-Abbe's theory
`{c) Coherent illuroination-Zemike's phase contrast method of
`observation
`8.7. Fresnel Diffraction at a Straight Edge
`8.7 .1. The diffraction integral
`8.7.2. Fresnel'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 diffraction iil.tegral in terms of Lommel
`functions
`8.8.2. The distribution of intensity
`(a) Intensity in the geometrical focal plane
`(h) Intensity along the axis
`(c) Intensity along the boundary of the geometrical shadow
`8.8.3. The integrated intensity
`8.8.4. The phase behaviour
`8.0. The Boundary Diffraction Wave
`
`370
`370
`370
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`378
`382
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`392
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`445
`449
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`Exhibit 1038-11
`
`

`
`xvi
`
`OONTBNTS
`
`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 Zemike
`9.2.2. Expansion of the aberration function
`
`9.3. Tolerance Conditions for Primary Aberrations
`
`9.4. The Diffraction 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.l. Coherent illumination
`9.5.2. Incoherent illumination
`
`X. l:IITERFERENCE A.c'W 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 Diffraction 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 Va.n Cittert-Zernike theorem
`(b) Hopkins' formula
`10A.3. An example
`10.4.4. Propagation of mutual intensity
`
`PJ.(IIC
`
`453
`453
`455
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`459
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`460
`462
`462
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`463
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`513
`516
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`Exhibit 1038-12
`
`

`
`CONTENTS
`
`Xvii
`
`P.O.
`518
`
`518
`522
`52:'!
`524-
`
`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 a-miCroscope
`(a) Critical illumination
`{b) KOhler's illumination
`10.5.3. Imaging with partially coherent quasi-monochromatic illumi-
`526
`nation
`(a) Transmission of mutual intensity through an optical system 526
`(b) Images of transilluminated objects
`528
`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 \Vave
`(a) Completely unpolarized light (Natural light)
`(b) Completely polarized light
`10.8.2. Some equivalent representatiom. The degree of polarization of
`a light wave
`550
`10.8.3. The Stokes parameters of a quasi-monochromatic plane wave 554
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`532
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`532
`534
`535
`535
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`540
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`544
`548
`549
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`XI. RIGOROUS DIFFRACTION THEORY
`11.1. Introduction
`
`11.2. Boundary Conditions and Surfa.ce Currents
`
`11.3. Diffraction by a Plane Screen: Electromagnetic Form of Babinet's
`Principle
`
`11.-t Two-dimem>ional Diffraction by a. Plane Screen
`11.-tl. The scala.r nature of two-dimensional electromagnetic fields
`11.4.2. An angular spectrum ofphne waves
`11.4.3. Formulation in terms of dua.l 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 E.polarization
`11.5.2. E:,pre~sion of the solution in terms of Fresnel integ-ral::;
`11.5.3. The nature of the solution
`ll.5.-t The .'mlution for H-polarization
`ll.;),;). Some liUmel"ical f'alculation::;
`ll.3.tJ. Compari.-;on with approximate theory and with experimental
`results
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`55!)
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`5GO
`560
`5f)l
`564
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`565
`56.'5
`567
`570
`57-!
`57.)
`
`577
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`Petitioner Ciena Corp. et al.
`Exhibit 1038-13
`
`

`
`xviii
`
`OONTlDNTS
`
`11.6. Three-dimensional Diffraction 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