Abstract

The simulation of 2-D quasimonochromatic partially coherent imaging and spatial filtering systems is computationally intensive. One approach separates the effects of the object from the system. A 4-D function that fully describes the effects of the source and pupil can be calculated, stored, and subsequently applied to as many different objects as desired. This method may be useful if a large number of objects are to be examined for a given source and pupil. The calculation of the 4-D function, referred to here as the C-function, generally requires the evaluation of a triple correlation and is numerically intensive. Previous workers have devised numerical algorithms that exploit properties of specific source and pupil shapes, such as circular symmetry, to reduce the computational load. We employ singular value outer- product decompositions on the 2-D sources and pupils, effectively reducing the problem to the analysis of a number of 1-D systems. The C-functions for 1-D systems are functions of two variables. Each 1-D source component interacts with every pupil component to yield these reduced-dimension C-functions. The 4-D C-function of interest is obtained by a sum of outer products of these 2-D C-functions. If the effective ranks of the matrices representing the source and pupil are sufficiently small, this approach can be computationally efficient.

© 1989 Optical Society of America