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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 http://extra.springer.com/978-0-8176-4871-8 * 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.

Astronomical instruments -- Design and construction. --- Geometrical optics -- Mathematics. --- Mathematica (Computer program language). --- Optical instruments -- Design and construction. --- Geometrical optics --- Astronomical instruments --- Optical instruments --- Mathematica (Computer program language) --- Physics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Light & Optics --- Applied Mathematics --- Mathematics --- Design and construction --- Mathematics. --- Design and construction. --- Astronomy --- Instruments, Astronomical --- Optics, Geometrical --- Instruments --- Physics. --- Mathematical models. --- Geometry. --- Astronomy. --- Astrophysics. --- Cosmology. --- Microwaves. --- Optical engineering. --- Optics, Lasers, Photonics, Optical Devices. --- Astronomy, Astrophysics and Cosmology. --- Physics, general. --- Mathematical Modeling and Industrial Mathematics. --- Microwaves, RF and Optical Engineering. --- Optical engineering --- Domain-specific programming languages --- Physical instruments --- Scientific apparatus and instruments --- Space optics --- Optics --- Euclid's Elements --- Hertzian waves --- Electric waves --- Electromagnetic waves --- Geomagnetic micropulsations --- Radio waves --- Shortwave radio --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Lasers. --- Photonics. --- Mechanical engineering --- Models, Mathematical --- Simulation methods --- Astronomical physics --- Cosmic physics --- New optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators