Abstract

Matrix operations, such as vector-matrix and matrix-matrix multiplication, are of great interest since a large variety of problems in signal processing, image processing and computing can be cast in terms of linear vector space operations. Optical systems, with their ability to multiply and add a two-dimensional arrays of numbers and to provide an arbitrary interconnection between them, have been investigated intensively in the recent past for performing matrix operations. Most of these optical systems were linear in their characteristics and hence operated in an analog mode. This restricted the accuracy achievable to 6-8 bits. One way of overcoming this limitation is to resort to nonlinear optical devices which can implement the basic operations involved in binary arithmatic, such as AND, OR, NOT, logic operations. The other approach involves using linear operation of convolution in performing pseudo-binary multiplication (the bits are allowed to assume values >1) as first suggested to optics community by Whitehouse and Speiser¹. Psaltis, etal applied this concept to a two-dimensional optical correlator and demonstrated high accuracy correlation of one-dimensional binary encoded sequences.² In the last two years several researchers proposed schemes for merging this and related concepts with different architectures for optical matrix processing.^3-6 It is the aim of this paper to systematically study the different architectures that result; compare their requirements of: a) input devices, b) output devices, c) optical systems and d) post processing electronics; and try to draw some general conclusions.

© 1985 Optical Society of America