TABLE OF CONTENTS Two of the most basic concepts of signal processing are spectrum analysis and correlation. In this chapter we will describe in detail how these two concepts are implemented in optical signal processing architectures. We will introduce these mathematical concepts in the context of a more general framework appropriate for categorizing different types of optical signal processing architectures. We will distinguish spectrum analyzers and correlators as time- and space-integrating, and we will distinguish correlators as incoherent (e.g., shadow casting) and coherent (e.g., interferometric). Specific examples of each type of processor will be analyzed in detail.
If we confine our attention to two-dimensional functions (or images), which can vary in time, then the input image to an optical system is defined by f( x, y, t) and the output image is defined by g( x, y, t). For linear systems the relationship between input and output is given by the superposition integral
where h(0, 0, 0, x ?, y ?, t ?) is the system impulse response (or kernel). This is a quite general result, which is not as interesting as the more specific cases that we will consider.
Many optical processors are implemented with one-dimensional acousto-optic Bragg cells, in which case we usually limit the optical processor to two-dimensional (2-D) linear operations that can be performed with one-dimensional (1-D) processors. Two types of kernels can then be considered: shift-invariant and separable. Shift-invariant kernels are of the...
