Geometric Optics

Theory and Design of Astronomical Optical Systems Using Mathematica®

  • Antonio Romano

Table of contents

  1. Front Matter
    Pages i-x
  2. Antonio Romano
    Pages 25-47
  3. Antonio Romano
    Pages 91-100
  4. Antonio Romano
    Pages 101-125
  5. Antonio Romano
    Pages 127-144
  6. Antonio Romano
    Pages 145-155
  7. Antonio Romano
    Pages 157-170
  8. Antonio Romano
    Pages 171-190
  9. Antonio Romano
    Pages 191-200
  10. Antonio Romano
    Pages 201-217
  11. Back Matter
    Pages 1-5

About this book


This book—unique in the literature—provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica®.

The newly presented approach to third-order aberration theory adopted is based on Fermat’s principle and the use of particular optical paths—not rays—termed stigmatic paths, allowing for easy derivation of third-order formulae. This approach enables readers to understand and handle the formulae required to design optical combinations without resorting to the much more complex Hamiltonian formalism and Seidel's relations.

Additional features and topics:

* Presentation of the third-order design of cameras and telescopes with the aid of Mathematica eliminates the need for tedious computer calculations

* Mathematica notebooks accompanying each optical combination analyzed in the book are available for download at

* Discussion and analysis of specific optical devices: Newtonian and Cassegrain telescopes; Schmidt, Wright, Houghton, and Maksutov cameras; and other optical combinations, such as the Klevtsov telescope and the Baker–Schmidt flat-field camera

* Additional supplementary material available at the publisher's website

* Many worked-out examples and exercises

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


Hamiltonian formulation of the optical systems LED Lagrangian formulation of the optical systems Mathematica Newton Optics astronomical optics astronomy computing simulation geometric optics partial differential equations programming stigmatic paths third-order aberration theory

Authors and affiliations

  • Antonio Romano
    • 1
  1. 1.e Applicazioni “R. Caccioppoli”, Università degli Studi di NapoliDipartimento di MatematicaNapoliItaly

Bibliographic information