Advanced Geometrical Optics

  • Psang Dain Lin

Part of the Progress in Optical Science and Photonics book series (POSP, volume 4)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. A New Light on Old Geometrical Optics (Raytracing Equations of Geometrical Optics)

    1. Front Matter
      Pages 1-2
    2. Psang Dain Lin
      Pages 3-28
    3. Psang Dain Lin
      Pages 29-69
    4. Psang Dain Lin
      Pages 71-114
    5. Psang Dain Lin
      Pages 115-142
    6. Psang Dain Lin
      Pages 143-165
    7. Psang Dain Lin
      Pages 167-183
  3. New Tools for Optical Analysis and Design (First-Order Derivative Matrices of a Ray and its OPL)

  4. A Bright Light for Geometrical Optics (Second-Order Derivative Matrices of a Ray and its OPL)

  5. Back Matter
    Pages 459-460

About this book


This book computes the first- and second-order derivative matrices of skew ray and optical path length, while also providing an important mathematical tool for automatic optical design. This book consists of three parts. Part One reviews the basic theories of skew-ray tracing, paraxial optics and primary aberrations – essential reading that lays the foundation for the modeling work presented in the rest of this book. Part Two derives the Jacobian matrices of a ray and its optical path length. Although this issue is also addressed in other publications, they generally fail to consider all of the variables of a non-axially symmetrical system. The modeling work thus provides a more robust framework for the analysis and design of non-axially symmetrical systems such as prisms and head-up displays. Lastly, Part Three proposes a computational scheme for deriving the Hessian matrices of a ray and its optical path length, offering an effective means of determining an appropriate search direction when tuning the system variables in the system design process.


Skew-Ray Tracing Paraxial Optics Point Spread Function Modulation Transfer Function Prism design Hessian matrices Jacobian Matrix Homogeneous coordinate notation Optically Stable Systems Wavefront Aberrations

Authors and affiliations

  • Psang Dain Lin
    • 1
  1. 1.Dept. of Mechanical EngineeringNational Cheng Kung UniversityTainanTaiwan

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media Singapore 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Engineering
  • Print ISBN 978-981-10-2298-2
  • Online ISBN 978-981-10-2299-9
  • Series Print ISSN 2363-5096
  • Series Online ISSN 2363-510X
  • Buy this book on publisher's site
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