Coherent optical extrapolation of 2-D band-limited signals: processor theory

Abstract

Given a truncated portion of a band-limited image with known x and y bandwidths, the extrapolation problem is to determine the signal over all x and y. An iterative extrapolation algorithm, recently proposed by Gerchberg, requires only the repeated operations of Fourier transformation and truncation. A coherent optical processor is presented that implements Gerchberg's iterative extrapolation algorithm in two dimensions. Iteration is performed by simple passive feedback.