Cross spectral density propagation through optical systems

Abstract

Huygens Fresnel principle as generalized to include diffraction by optical systems that can be characterized by an ABCD ray-transfer matrix is used to describe propagation of coherent modes representing cross spectral densities in Wolrs new theory of partial coherence. A mathematical method we introduced in a previous paper for the free space propagation of circularly symmetric cross spectral densities is modified to include propagation through axisymmetric optical systems. where pi, qj, p~, q~ are cartesian coordinates in the plane z = 0, a~ and O~~p~, q~) are the eigenvalues and the eigenfunctions of the integral equation +o~ +o~ dPl d~l W0~Pl, ~l,P2, ~2) On~Pl, ~l) ~n °n~P2, ~2), (~) -o~ -o~ O~~p~, q~) are taken to be orthonormafized, I.e.