  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.
