Propagation of fully-coherent and partially-coherent complex scalar fields in aberration space

TL;DR

This paper develops a comprehensive mathematical framework for propagating fully and partially coherent scalar fields through imaging systems characterized by infinite aberration parameters, unifying various propagation equations.

Contribution

It introduces a generalized formalism with propagators, differential, transport, and Hamilton-Jacobi equations for scalar fields in aberration space, extending Wolf equations.

Findings

Derived generalized propagators in real and Fourier space

Formulated differential and Hamilton-Jacobi equations for aberration space

Unified treatment of coherent and partially coherent field propagation

Abstract

We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration coefficients, the values for which can be viewed as coordinates for an infinity of orthogonal axes that span the "aberration space" into which the output propagates. For fully coherent complex scalar disturbances, we study the propagation of the field through the imaging system, while for partially coherent disturbances it is the two-point correlation functions whose propagation we study. For both systems we write down generalized propagators in both real and Fourier space, differential equations for evolution through aberration space, transport equations, and Hamilton-Jacobi equations. A generalized form of the Wolf equations is an important special case of our formalism.