Optical processing using outer-product concepts

Abstract

A row vector when left-multiplied by a column vector produces a two-dimensional rank-one matrix in an operation commonly called an outer product between the two vectors. The outer product operation can form the basis for a large variety of higher order algorithms in linear algebra, signal processing, and image processing. This operation can be best implemented in a processor having two-dimensional (2-D) parallelism and a global interaction among the elements of the input vectors. Since optics is endowed with exactly these features, an optical processor can perform the outer product operation in a natural fashion using orthogonally oriented one-dimensional (1-D) input devices such as acoustooptic cells. Algorithms that can be implemented optically using outer-product concepts include matrix multiplication, convolution/correlation, binary arithmetic operations for higher accuracy, matrix decompositions, and similarity transformations of images. Implementation is shown to be frequently tied to time-integrating detection techniques. These and other hardware issues in the implementation of some of these algorithms are discussed.