Wigner tools in optical system analysis, design, and simulation

Numerous papers have been written on the various roles the Wigner distribution function (WDF) can play in optics. The purpose of this paper is to show two applications of the WDF in the analysis, design, and simulation of optical systems. One system provides a vehicle for reducing the computational load in the numerical simulation of the propagation of optical wave fields. The WDF analysis of this system yields insight into methods that might be used in simplifying optical system simulations generally. The second system is intended for the sample-based recording of coherence functions associated with the propagated wave field produced by a three-dimensional, spatially-incoherent object. The WDF analysis, combined with a closely-related ambiguity-function analysis, provides the basic for non-stationary sampling conditions that can be used to determine the minimum number of samples required for the coherence function characterization.