Geometric Optics

Theory and Design of Astronomical Optical Systems Using Mathematica®

  • Antonio Romano
  • Roberto Cavaliere

Table of contents

  1. Front Matter
    Pages i-xii
  2. Antonio Romano, Roberto Cavaliere
    Pages 23-51
  3. Antonio Romano, Roberto Cavaliere
    Pages 53-89
  4. Antonio Romano, Roberto Cavaliere
    Pages 91-105
  5. Antonio Romano, Roberto Cavaliere
    Pages 107-118
  6. Antonio Romano, Roberto Cavaliere
    Pages 119-144
  7. Antonio Romano, Roberto Cavaliere
    Pages 145-161
  8. Antonio Romano, Roberto Cavaliere
    Pages 163-173
  9. Antonio Romano, Roberto Cavaliere
    Pages 175-195
  10. Antonio Romano, Roberto Cavaliere
    Pages 197-220
  11. Antonio Romano, Roberto Cavaliere
    Pages 221-245
  12. Antonio Romano, Roberto Cavaliere
    Pages 247-263
  13. Antonio Romano, Roberto Cavaliere
    Pages 265-271
  14. Back Matter
    Pages 273-289

About this book


This text, now in its second edition, presents the mathematical background needed to design many optical combinations that are used in astronomical telescopes and cameras.  It uses a novel approach to third-order aberration theory based on Fermat’s principle and the use of particular optical paths (called stigmatic paths) instead of rays, allowing for easier derivation of third-order formulae.  Each optical combination analyzed is accompanied by a downloadable Mathematica® notebook that automates its third-order design, eliminating the need for lengthy calculations.

The essential aspects of an optical system with an axis of rotational symmetry are introduced first, along with a development of Gaussian optics from Fermat’s principal.  A simpler approach to third-order monochromatic aberrations based on both Fermat’s principle and stigmatic paths is then described, followed by a new chapter on fifth-order aberrations and their classification.  Several specific optical devices are discussed and analyzed, including the Newtonian and Cassegrain telescopes; the Schmidt, Wright, Houghton, and Maksutov cameras; the Klevtsov telescope; the Baker-Schmidt flat-field camera; the Buchroeder camera; and, new in this edition,  the Baker-Nunn camera and optical combinations with sub-corrector and Petzval objectives.  Finally, the Lagrangian and Hamiltonian formulations of geometric optics and Seidel’s third-order aberration theory are presented, and a new chapter considers optics in anisotropic media.  Numerous diagrams, worked-out examples, and exercises for further practice of key concepts are included throughout the book.

Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. It can also be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica®, or geometric optics.


Geometric Optics Fermat's Principle Stigmatic Paths Optical Design Astronomical Optics Third-Order Aberration Theory

Authors and affiliations

  • Antonio Romano
    • 1
  • Roberto Cavaliere
    • 2
  1. 1.Università degli Studi di Napoli “Federico II”Dipartimento di Matematica e Applicazioni “R. Caccioppoli”NapoliItaly
  2. 2.Mercato San SeverinoItaly

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-43731-6
  • Online ISBN 978-3-319-43732-3
  • Series Print ISSN 2164-3679
  • Series Online ISSN 2164-3725
  • Buy this book on publisher's site