Advanced Geometrical Optics

Psang Dain Lin
Department of Mechanical Engineering
National Cheng Kung University
Springer-Singapore, 2016, ISBN 978-981-10-2298-2, ISBN 978-981-10-2299-9 (eBook)

Abstract

Part One of the book reviews the basic principles and theories of skew-ray tracing, paraxial optics and primary aberrations. Much of the material is likely to be known to the readers. However, it serves as essential reading in laying down a solid foundation for the modeling work presented in Parts Two and Three of the book. Part Two derives the Jacobian matrices of a ray and its optical path length. Although this issue is also addressed in other books and publications, the authors generally fail to consider all of the variables of a non-axially symmetrical system. The modeling work presented in Part Two thus provides a more robust framework for the analysis and design of non-axially symmetrical systems such as prisms. Importantly, Part Two also presents a new method for determining the point spread function and modulation transfer function of an optical system such that the image quality can be evaluated accurately. Part Three 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 of determining an appropriate search direction when tuning the system variables in the system design process.

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 are also extended to the Ministry of Science and Technology of Taiwan for the generous financial support provided every year to the author in developing the methodologies and underlying concepts presented in this book.

中文摘要

過去幾何光學都使用「向量」當數學工具，向量是比較簡單易懂，但當光學邊界很複雜時，向量會較笨拙。為了克服此些困難，我就用「齊次座標」當成數學工具，對「歪斜光線」與「光程」作第一階微分與第二階微分。本書共分三部分，第一部分是幾何光學的基本理論，包函歪斜光線的追蹤、近軸光線的學理與應用、像差的介紹。雖然很多讀者已經很了解第一部分所敘述的內容，但其卻是第二部分與第二部分的基礎。第二部分是在闡述「歪斜光線」與「光程」的第一階微分(即Jacobian矩陣），我並且將該矩陣應用於光學系統最佳化、調變函數、點擴散函數、波前曲面、焦散面、照度的計算，都得到很好的效果。第三部分是在闡述「歪斜光線」與「光程」的第二階微分(即Hessian矩陣)，該兩種矩陣是光學最佳化設計的基礎，我提供很多例子作說明，證明此兩種矩陣是幾何光學的重要工具。

最後，我將本書獻給成功大學與成大機械系，因為它優越的環境，讓我得以完成此書。並且感謝科技部每年的經費補助。