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New Computation Methods for Geometrical Optics

  • Book
  • © 2014

Overview

Authors:
  1. Psang Dain Lin

    1. Dept. of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan

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  • Employs homogeneous coordinate notation to compute the first-and second-order derivative matrices of various optical quantities
  • Written for researchers, designers and graduate students
  • Serves as an important mathematical tool for automatic optical design

Part of the book series: Springer Series in Optical Sciences (SSOS, volume 178)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Homogeneous Coordinate Notation

    • Psang Dain Lin
    Pages 1-16

  3. Skew-Ray Tracing at Boundary Surfaces

    • Psang Dain Lin
    Pages 17-48

  4. Modeling an Optical System

    • Psang Dain Lin
    Pages 49-86

  5. Paraxial Optics for Axis-Symmetrical Systems

    • Psang Dain Lin
    Pages 87-113

  6. The Jacobian Matrix of a Ray with Respect to System Variable Vector

    • Psang Dain Lin
    Pages 115-161

  7. Point Spread Function and Modulation Transfer Function

    • Psang Dain Lin
    Pages 163-186

  8. Optical Path Length and Its Jacobian Matrix with Respect to System Variable Vector

    • Psang Dain Lin
    Pages 187-202

  9. The Wavefront Shape, Irradiance, and Caustic Surface in an Optical System

    • Psang Dain Lin
    Pages 203-237

  10. Back Matter

    Pages 239-239
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Keywords

About this book

This book employs homogeneous coordinate notation to compute the first- and second-order derivative matrices of various optical quantities. It will be one of the important mathematical tools for automatic optical design. The traditional geometrical optics is based on raytracing only. It is very difficult, if possible, to compute the first- and second-order derivatives of a ray and optical path length with respect to system variables, since they are recursive functions. Consequently, current commercial software packages use a finite difference approximation methodology to estimate these derivatives for use in optical design and analysis. Furthermore, previous publications of geometrical optics use vector notation, which is comparatively awkward for computations for non-axially symmetrical systems.

Authors and Affiliations

  • Dept. of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan

    Psang Dain Lin

About the author

Dr. PD Lin is a distinguished Professor of Mechanical Engineering at the National Cheng Kung University, Taiwan, where he has been since 1989. He earned his BS and MS from that university in 1979 and 1984, respectively. He received his Ph.D. in Mechanical Engineering from Northwestern University, USA, in 1989. He has served as an associate editor of Journal of the Chinese Society of Mechanical Engineers since 2000. His research interests include geometrical optics and error analysis in multi-axis machines.

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