Skip to main content
SpringerLink
Log in

Advanced Geometrical Optics

  • Book
  • © 2017

Overview

Authors:
  1. Psang Dain Lin

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

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Computes the first- and second-order derivative matrices of skew ray and optical path length
  • Offers an important mathematical tool for automatic optical design
  • A valuable resource for researchers, designers, and graduate students
  • Includes supplementary material: sn.pub/extras

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xxiv
    Download chapter PDF

  2. A New Light on Old Geometrical Optics (Raytracing Equations of Geometrical Optics)

    1. Front Matter

      Pages 1-2
      Download chapter PDF

    2. Mathematical Background

      • Psang Dain Lin
      Pages 3-28

    3. Skew-Ray Tracing of Geometrical Optics

      • Psang Dain Lin
      Pages 29-69

    4. Geometrical Optical Model

      • Psang Dain Lin
      Pages 71-114

    5. Raytracing Equations for Paraxial Optics

      • Psang Dain Lin
      Pages 115-142

    6. Cardinal Points and Image Equations

      • Psang Dain Lin
      Pages 143-165

    7. Ray Aberrations

      • Psang Dain Lin
      Pages 167-183

  3. New Tools for Optical Analysis and Design (First-Order Derivative Matrices of a Ray and its OPL)

    1. Front Matter

      Pages 185-186
      Download chapter PDF

    2. Jacobian Matrices of Ray R̄i with Respect to Incoming Ray R̄i–1 and Boundary Variable Vector X̄i

      • Psang Dain Lin
      Pages 187-218

    3. Jacobian Matrix of Boundary Variable Vector X̄i with Respect to System Variable Vector X̄sys

      • Psang Dain Lin
      Pages 219-243

    4. Prism Analysis

      • Psang Dain Lin
      Pages 245-265

    5. Prism Design Based on Image Orientation

      • Psang Dain Lin
      Pages 267-294

    6. Determination of Prism Reflectors to Produce Required Image Orientation

      • Psang Dain Lin
      Pages 295-307

    7. Optically Stable Systems

      • Psang Dain Lin
      Pages 309-318

    8. Point Spread Function, Caustic Surfaces and Modulation Transfer Function

      • Psang Dain Lin
      Pages 319-351

    9. Optical Path Length and Its Jacobian Matrix

      • Psang Dain Lin
      Pages 353-369

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

    1. Front Matter

      Pages 371-372
      Download chapter PDF

    2. Wavefront Aberration and Wavefront Shape

      • Psang Dain Lin
      Pages 373-403

    3. Hessian Matrices of Ray R̄i with Respect to Incoming Ray R̄i-1 and Boundary Variable Vector X̄i

      • Psang Dain Lin
      Pages 405-423
Back to top

Keywords

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.

Reviews

“Professor Lin has greatly expanded the breadth and scope of using matrix representation in geometrical optics. … Advanced Geometrical Optics could be used in teaching graduate and advanced-undergraduate students and is enthusiastically recommended for those interested in geometrical optics, optical design, and optimization.” (R. Barry Johnson, Contemporary Physics, Vol. 58 (3), April, 2017)


“This book is concerned with the study of geometrical optics using a matrix method. … Since the author intends to make this book a useful reference for geometrical optics courses oriented to graduate and senior undergraduate students, many illustrative examples are presented. Overall, this is an interesting book modernizing the classical subject of geometrical optics.” (Jichun Li, zbMATH, Vol. 1366.78001, 2017) 

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 Department at 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. He has published over 80 papers and supervised over 60 MS and 11 Ph.D. students. His research interests include geometrical optics and error analysis in multi-axis machines. In geometrical optics, he employs homogeneous coordinate notation to compute the first- and second-order derivative matrices of various optical quantities. It is one of the important mathematical tools for automatic optical design.

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation