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.

Develops from first principles modern geometric optics and its rich symmetry structure in hamiltonian form The relation of these geometric methods to wave models is also shown There is no other monograph that covers in depth this subject which is of growing importance for practical modeling in optics Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt

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