Advanced Geometrical Optics PDF
Preview Advanced Geometrical Optics
Progress in Optical Science and Photonics Series Editor: Javid Atai Psang Dain Lin Advanced Geometrical Optics Progress in Optical Science and Photonics Volume 4 Series editor Javid Atai ThepurposeoftheseriesProgressinOpticalScienceandPhotonicsistoprovidea forum to disseminate the latest research findings in various areas of Optics and its applications. The intended audience is physicists, electrical and electronic engineers, applied mathematicians, and advanced graduate students. More information about this series at http://www.springer.com/series/10091 Psang Dain Lin Advanced Geometrical Optics 123 PsangDain Lin Department ofMechanical Engineering National Cheng KungUniversity Tainan Taiwan ISSN 2363-5096 ISSN 2363-510X (electronic) Progressin Optical Science andPhotonics ISBN978-981-10-2298-2 ISBN978-981-10-2299-9 (eBook) DOI 10.1007/978-981-10-2299-9 LibraryofCongressControlNumber:2016947036 ©SpringerScience+BusinessMediaSingapore2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerScience+BusinessMediaSingaporePteLtd. Preface The study of geometrical optics dates back to ancient Greek and Egyptian times. However,geometricalopticsremainsfirmlyrootedintheuseofparaxialopticsand skew-ray tracing equations. For many years, it has been known that the first- and second-order derivative matrices (i.e., Jacobian and Hessian matrices) of merit functions provide highly effective tools for the analysis and design of optical systems. However, computing these derivative matrices analytically is extremely challenging since ray-tracing equations are inherently recursive functions. To overcome this limitation, this book proposes a straightforward computational schemeforderivingtheJacobianandHessianmatricesofarayanditsopticalpath length using homogeneous coordinate notation. The book represents both a modernization and an extension of my last book, NewComputationMethodsforGeometricalOptics,publishedin2013bySpringer Singapore.PartIofthebookreviewsthebasicprinciplesandtheoriesofskew-ray tracing,paraxialopticsandprimaryaberrations.Muchofthematerialislikelytobe knowntothereaders.However,itservesasessentialreadinginlayingdownasolid foundation for the modeling work presented in Parts II and III of the book. Part II derives the Jacobian matrices of a ray and its optical path length. Although this issueisalsoaddressedinotherbooksandpublications,theauthorsgenerallyfailto consider all of the variables of a non-axially symmetrical system. The modeling work presented in Part II thus provides a more robust framework for the analysis anddesignofnon-axiallysymmetricalsystemssuchasprismsandhead-updisplay. Importantly, Part II also presents a new method for determining the point spread functionandmodulationtransferfunctionofanoptical system suchthattheimage quality can be evaluated accurately. Part III of the book proposes a computational scheme for deriving the Hessian matrices of a ray and its optical path length. The validity of the proposed method is demonstrated using various optical systems for illustration purposes. It is shown that the Hessian matrix approach overcomes the limitations of traditional finite difference methods and provides an effective means ofdetermininganappropriatesearchdirectionwhentuningthesystemvariablesin the system design process. vii viii Preface This book is intended to be used as a reference book for introductory graduate and senior undergraduate geometrical optics courses. With this in mind, the text containsnumerousillustrativeexamplesaimedathelpingthereaderunderstandthe underlying theories and concepts of the related modeling work and proposed methods. It is noted that while aspherical lenses are common in the geometrical optics field nowadays, the book focuses deliberately on the simpler case offlat or sphericalboundarysurfacesinordertomoreclearlyconveythemainconceptsand ideas. However, once students and self-taught practitioners have mastered the fundamentals described in this edition, they will find no problem in applying the related equations to the more complex case of aspherical lenses. This book is dedicated to all the faculty and staff at the Department of Mechanical Engineering, National Cheng Kung University, Taiwan. Without their support and encouragement, this book would never have been possible. Special thanks arealso extendedtotheMinistry ofScience andTechnologyofTaiwanfor the generous financial support provided every year to the author in developing the methodologies and underlying concepts presented in this book. I am indebted to Dr. Chung Yu Tsai of Formosa University in Taiwan for his many stimulating discussions on the subject of prism analysis and design. My thanks also go to Dr. Chien-Sheng Liu, Che-Wei Chang, Ying-Yan Hsu, and Chia-KueiHsufortheirhelpinverifyingtheequations,figures,andnotationsused throughout the text. Any shortcomings or errors in the book are my responsibility, and mine alone. Finally, I would like to thank Patrick Wyton for his efforts in proofreading the text. Tainan, Taiwan Psang Dain Lin Acknowledgements To my former advisor Kornel F. Ehmann To my wife Chiung-Jung Huang and In memory of my past wife Su-Chin Wang ix Contents Part I A New Light on Old Geometrical Optics (Raytracing Equations of Geometrical Optics) 1 Mathematical Background .... .... .... .... .... .... ..... .... 3 1.1 Foundational Mathematical Tools and Units... .... ..... .... 3 1.2 Vector Notation ... ..... .... .... .... .... .... ..... .... 5 1.3 Coordinate Transformation Matrix .. .... .... .... ..... .... 7 1.4 Basic Translation and Rotation Matrices.. .... .... ..... .... 9 1.5 Specification of a Pose Matrix by Using Translation and Rotation Matrices.... .... .... .... .... .... ..... .... 15 1.6 Inverse Matrix of a Transformation Matrix.... .... ..... .... 16 1.7 Flat Boundary Surface ... .... .... .... .... .... ..... .... 17 1.8 RPY Transformation Solutions. .... .... .... .... ..... .... 19 1.9 Equivalent Angle and Axis of Rotation .. .... .... ..... .... 20 1.10 The First- and Second-Order Partial Derivatives of a Vector... .... ..... .... .... .... .... .... ..... .... 22 1.11 Introduction to Optimization Methods ... .... .... ..... .... 26 References. .... .... .... ..... .... .... .... .... .... ..... .... 28 2 Skew-Ray Tracing of Geometrical Optics .... .... .... ..... .... 29 2.1 Source Ray... .... ..... .... .... .... .... .... ..... .... 29 2.2 Spherical Boundary Surfaces .. .... .... .... .... ..... .... 32 2.2.1 Spherical Boundary Surface and Associated Unit Normal Vector... .... .... .... .... .... ..... .... 32 2.2.2 Incidence Point .. .... .... .... .... .... ..... .... 34 2.2.3 Unit Directional Vectors of Reflected and Refracted Rays... .... .... .... .... ..... .... 37 xi
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