Geometric Optics on Phase Space / Edition 1

Geometric Optics on Phase Space / Edition 1

by Kurt Bernardo Wolf
     
 

ISBN-10: 3540220399

ISBN-13: 9783540220398

Pub. Date: 08/26/2004

Publisher: Springer Berlin Heidelberg

Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase

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Overview

Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.

Product Details

ISBN-13:
9783540220398
Publisher:
Springer Berlin Heidelberg
Publication date:
08/26/2004
Series:
Theoretical and Mathematical Physics Series
Edition description:
2004
Pages:
376
Product dimensions:
9.21(w) x 6.14(h) x 0.88(d)

Table of Contents

Preliminary ToC: Optical Phase Space, Hamiltonian Systems and Lie Algebras.- Lie Groups of Optical Transformation.- The Paraxial Regime.- Hamiltonian Aberrations.

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