Algorithm for implementing an ABCD ray matrix wave-optics propagator

In prior work we described a 5x5 ray matrix formalism and how to integrate the effects that are not modeled in wave-optics with the ray matrix model. In this paper we describe how to complete the integration of the two techniques by modifying the Siegman ABCD ray matrix decomposition. After removing the separable effects like image rotation and image inversion, we break the 5x5 ray matrix into two 2x2 sections (a.k.a. the ABCD matrices) that correspond to the two axes orthogonal to the propagation. We then present a general algorithm that breaks any arbitrary ABCD matrix into four simple wave-optics steps. The algorithm presented has sufficient generality to handle image planes and focal planes. This technique allows for rapid and accurate wave-optics modeling of the propagation of light through complex optical systems comprised of simple optics.