CHAPTER II

 BACKGROUND

 The background technology is reviewed here to understand the

operation of an optical processor more fully. A number of different

types of optical processors are in use today. These include one-

dimensional signal processors, two-dimensional image processors and

multi-dimensional digital processors. Only two-dimensional image

processors used for matched filtering are described here. A matched

filter optimizes the signal-to-noise ratio at a specific point when

the characteristics of the input are known.16 Typically, the desired

pattern and the nature of the background or noise in the input image

are known. Specifically, the input consists of a known signal s(x,y)

and an additive noise n(x,y). The system is linear and space

invariant with impulse response h(x,y). The criterion of optimization

will be that the output signal-to-noise power ratio be a maximum.

This optimum system will be called a matched filter for reasons that

will become clear as the derivation proceeds.

 Communication Theory

 A system is any unit that converts an input function I(x,y) into

an output function O(x,y). The system is described by its impulse

response--its output when the input is an impulse or delta function.

A linear system is one in which the output depends linearly on the

input and superposition holds. That is, if the input doubles, so does

the output. More precisely stated, let 01 be the output when I1 is