By. Gu et al., ALGEBRAIC DESIGN OF PARAXIAL DIFFRACTIVE ELEMENTS FOR GENERAL SPACE-VARIANT TRANSFORMS, Optics communications, 149(4-6), 1998, pp. 245-251
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.