Optical phase space, Wigner representation, and invariant quality parameters

Wigner's quasi probability and related functional and operator methods of quantum mechanics have recently played an important role in optics. We present an account of some of these developments. The symmetry structures underlying the ray and wave approaches to paraxial optics are explored in some detail, and the manner in which the Wigner phase-space representation captures the merits of both approaches is brought out. A fairly self-contained analysis of the second or intensity moments of general astigmatic partially coherent beams and of their behavior under transmission through astigmatic first-order optical systems is presented. Geometric representations of the intensity moments that render the quality parameters or polynomial invariants manifest are discussed, and the role of the optical uncertainty principle in assigning unbeatable physical bounds for these invariants is stressed. Measurement of the ten intensity moments of an astigmatic partially coherent beam is considered. (C) 2000 Optical Society of America [S0740-3232(00)03112-4] OCIS codes: 030.1640, 030.6600, 080.2720, 350.5500, 260.0260.