U.K.Pergamon Press Ltd.,Headington Hill Hall,U.8.A.Elmaford,New York 10523.U.S.A.CANADAAUSTRALIAPergamon Press (Aust-)Pty.Ltd.,P.O.Box 544,FEDERAL REPUBLICOF GERMANYJAPANBRAZIL1-7-1 Nishiahinjuku.Shinjuku-ku,Tokyo 160,JapanPEOPLE'S REPUBLICOF CHINACopyright 1980 Max Born and Emil WoifFirst edition 1959Sixth edition 1980Born,MaxI.Title II.Wolf,EmilPREFACE TO THE FIRST EDITIONTHg idea of writing this book was a result of frequent enquiries about the possibilityof publishing in the English language a book on opties written by one of us*more thantwenty-five years ago.A preliminary survey of the literature showed that numerousresearches on almost every aspect of optics have been carried out in the interveningyears,so that the book no longer gives a comprehensive and balanced picture of thefield.In consequence it was felt that a translation was hardly appropriate;insteada 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 importantdevelopments which took place since the publication of Optik were incorporated,thebook would become impracticably large.It was,therefore,deemed necessary torestrict its scope to a narrower fieid.Optik 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 thefull connection between optics and atomie physics were not discussed;nor did theold book consider the effects of light on our visual sense organ-the eye.Theseaubjects can be treated more appropriately in connection with other fields such asrelativity,quantum mechanics,atomic and nuclear physics,and physiology.In thisbook not only are these subjects excluded,but also the classical molecular optics whichwas the subject-matter of almost half of the German book.Thus our discussion isrestricted to those optical phenomena which may be treated in terms of MAxWELL'sphenomenological theory.This includes all situations in which the atomistic structureof matter plays no decisive part.The connection with atomic pbysics,quantummechanics,and physiology is indicated only by short references wherever necesaary.The fact that,even after this limitation,the book is much larger than Optik,givessome indication about the extent of the researches that have been carried out inclassical optics in recent times.We have aimed at giving,within the framework just outlined,a reasonably com.plete pieture of our present knowledge.We have attempted to present the theory insuch a way that practically all the results can be traced back to the basie equations ofMAXWELL's electromagnetic theory,from which our whole consideration starts.formally,in terms of the usual material constants.A more physical approach to thequestion of influence of matter is developed in Chapter II:it is shown that in thepresence of an external incident field,each volume element of a material mediummay 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 ofconsiderable physical significance and its power is illustrated in a later chaptertreated in this way by A.B.BRATTA and W.J.NoBLE:Chapter XII was contributedA considerable part of Chapter III is devoted to showing how geometrical opticsfollows from MAxWELL's wave theory as a limiting case of short waveiengths.Inaddition to discussing the main properties of rays and wave-fronts,the veetorialMAx BoRN,Optik (Berlin,Springer,1933).PREFACE TO THE FIRST EDITIONconsidered.A detailed discussion of the foundations of geometrical optics seemed tous desirable in view of the important developments made in recent years in the relatedfield of microwave optics (optics of short radio waves).These developments wereoften stimulated by the close analogy between the two fieids and have providednew experimental techniques for testing the predictions of the theory.We found itconvenient to separate the mathematical apparatus of geometrical optics-thecaleulus 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),geometrical optics,clasaical mechanics,and electron optics,when these subjects aropresented 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.Thoughthese 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 mannerthe many diverse aspects of the subjeet.It is,of course,possible to derive some of themay be for the solution of individual problems,it cannot have more than illustrativevalue in a book concerned with a systematic development of a theory from a fewsimple postulates.The defect of optical images (the influence of aberrations)may be studied eitherby geometrical optics(appropriate when the aberrations are large),or by diffractiontheory (when they are sufficiently small).Since one usually proceeds from quitedifferent starting points in the two methods of treatments,a comparison of resultshas in the past not always been easy.We have attempted to develop a more unifiedtreatment,based on the concept of the deformation of wave-fronts.In the geometricalanalysis of aberrations (Chapter V)we have found it possible and advantageous toThe chapter on diffraction theory of aberrations (Chapter IX)gives an aocount ofthe NrJBOgR-ZERNIKs theory and also includes an introductory section on theimaging of extended objeets,in coherent and in incoherent illumination,based on theChapter VI,contributed by Dr.P.A.WAYMAN,gives a brief description of themain image-forming optical systems.Its purpose is to provide a framework forthose 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 withinterferometers.Some of the theoretical sections have their nucleus in the corre.sponding seetions of Optik,but the chapter has been completely re-written by Dr.and with some of its applications.In addition to the usual topics,the chapter includesa detailed discussion of the central problem of optical image formation-the analysisof the three-dimensional light distribution near the geometrical focus.An account isalso given of a less familiar alternative approach to diffraction,based on the notion(and therefore completely coherent)light,produced by point sources.ChapterX