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