ALGEBRAIC DESIGN OF PARAXIAL DIFFRACTIVE ELEMENTS FOR GENERAL SPACE-VARIANT TRANSFORMS

Optical implementations of linear transforms are of high interest in r eal time information processing. The large majority of publications on this topic deals with space-invariant transforms whilst space-variant transforms are mainly discussed in the context of a few specific exam ples. In this paper we use matrix algebra to design paraxial diffracti ve elements which can be used in a simple optical setup to perform arb itrary specified space-variant transforms. The applicability of our me thod is demonstrated in two design examples. First, the transmission f unction of a diffractive element which performs a focusing operation i s computed. Secondly, the same procedure is used to obtain an element that implements a Hough transform. The correct optical functions of bo th elements are shown in computer simulation experiments. (C) 1998 Els evier Science B.V.