Linear systems approach to simulation of optical diffraction

The diffractive processes within an optical system can be simulated by computer to compute the diffraction-altered electric-field distribution at the output of the system from the electric-field distribution at the input. In the paraxial approximation the system can be described by an ABCD ray matrix whose elements in turn can be used to simplify the computation such that only a single computational step is required. We describe two rearrangements of such computations that allow the simulation to be expressed in a linear systems formulation, in particular using the fast-Fourier-transform algorithm. We investigate the sampling requirements for the kernel-modifying function or chirp that arises. We also use the special properties of the chirp to determine the spreading imposed by the diffraction. This knowledge can be used to reduce the computation if only a limited region of either the input or the output is of interest.