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

摘要

We consider the propagation of both fully coherent and partially coherentcomplex scalar fields, through linear shift-invariant imaging systems. Thestate of such imaging systems is characterized by a countable infinity ofaberration coefficients, the values for which can be viewed as coordinates foran infinity of orthogonal axes that span the "aberration space" into which theoutput propagates. For fully coherent complex scalar disturbances, we study thepropagation of the field through the imaging system, while for partiallycoherent disturbances it is the two-point correlation functions whosepropagation we study. For both systems we write down generalized propagators inboth real and Fourier space, differential equations for evolution throughaberration space, transport equations, and Hamilton-Jacobi equations. Ageneralized form of the Wolf equations is an important special case of ourformalism.