Abstract

It was recently shown that there is a formal similarity between 1- and 2-D canonical operators.¹ This immediately generalizes all previous results in 2-D Fourier optics to nonorthogonal systems. In particular, the analysis of Nazarathy and Goodman² goes through as before with no change in the logic. The spatial dispersion relation now expresses p_z as a function of p_x and p_y, where p_i is the optical direction cosine in the ith direction. This leads to the linear scalar transfer function for Fourier optics in three dimensions. Similar results can be derived in related fields, such as for anisotropic Gaussian-Schell model sources.

© 1988 Optical Society of America