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Psang Dain Lin

Advanced Geometrical Optics

Progress in Optical Science and Photonics Volume 4

Series editor Javid Atai

The purpose of the series Progress in Optical Science and Photonics is to provide a 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

Psang Dain Lin Department of Mechanical Engineering National Cheng Kung University Tainan Taiwan

ISSN 2363-5096 ISSN 2363-510X (electronic) Progress in Optical Science and Photonics ISBN 978-981-10-2298-2 ISBN 978-981-10-2299-9 (eBook) DOI 10.1007/978-981-10-2299-9 Library of Congress Control Number: 2016947036 © Springer Science+Business Media Singapore 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part 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 or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 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 authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd.

Preface

The study of geometrical optics dates back to ancient Greek and Egyptian times. However, geometrical optics remains firmly rooted in the use of paraxial optics and 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 scheme for deriving the Jacobian and Hessian matrices of a ray and its optical path length using homogeneous coordinate notation. The book represents both a modernization and an extension of my last book, New Computation Metho