implement the CMF optically, two techniques can be used: (1) transform

the digital image to optical image via a high resolution CRT or

digitally addressed camera and produce a Vander Lugt Filter in the

conventional holographic manner, or (2) retain the image in a digital

format and produce the filter through computer-generated hologram

techniques. This latter technique has the advantage of using the

dynamic range of the digital computer until the final product is

produced. That is, if the CMF function is displayed and transformed

optically, the display will limit the dynamic range. By producing a

computer-generated holographic filter, the dynamic range is retained

till a later stage. In addition, complex filter functions and

frequency pre-emphasis can be easily incorporated.

 However the CMF is implemented, the weights must be chosen for

optimal performance in a specific application. Hester and

Casasent56,57 developed what is called the Synthetic Discriminant

Function (SDF) which is a CMF that gives the same correlation output

intensity for each pattern in the training set. The weights required

to provide a constant correlation output for each pattern are not

unique. Additional constraints can be placed upon the SDF to reduce

the response to specific unwanted targets, to reduce dynamic range, or

to incorporate other desirable features. Starting with a training set

(Figure 5.1) which adequately describes the conditions in which the

desired target could be found, the SDF is formed as a linear

combination of all of the training images (Figure 5.2). The weights

are determined using matrix techniques which typically requires

considerable time on a large computer.58-63 The weights are adjusted

to provide a correlation with each member of the training set as close