Abstract

On free propagation the cross-spectral density function obeys two Helmholtz equations. We show that under the paraxial approximation, both equations can conveniently be written as a single differential equation in terms of the sum and difference coordinates. Furthermore, we indicate that the formal solution to this single differential equation can be written as a differential operator, which converts the cross-spectral density function at the object plane into the cross-spectral density function at any other plane. This formalism is applied to give a coherence theory of the Lau effect at finite distances when using quasihomogeneous fields.

© 1987 Optical Society of America