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.
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From the reviews:
"This book is addressed to scientists, engineers, and advanced students. ... The author has been a prolific researcher in this field ... and much of this work is covered in the book. The main emphasis in the book is the application of Lie groups/Lie algebra techniques to various models of geometrical optics." (Philip Huddleston, Mathematical Reviews, 2005g)
"This book is devoted to the Hamiltonian (geometric) model of the light. ... the exposition is quite clear and pedagogical and can be recommended for both a lecture course and a self study because each Part/Chapter opens with its own Introduction. The text is supplemented by a representative list of important papers and books on the subject and an Index which is exhaustive and very well organized." (Ivailo Mladenov, Zentralblatt MATH, Vol. 1057 (8), 2005)
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