signal-to-noise ratio is large, the energy reaching the correlation

plane may be too small to measure. The efficiency of the hologram,

the ratio of the power in the correlation to the power in the input

test image, is an important criterion in evaluating a practical CGH-

matched filter. Mathematically, it is given as

 ff Ig(x,y) f*(x,y) 2dx dy
 = _____________________ (4.1)
 H
 ff Ig(x,y)I2dxdy

where H has been coined the Horner efficiency,28 f is the reference

scene, g is the test scene, and denotes an ideal correlation. The

correlation derived from a Vander Lugt-matched filter is not ideal.

To determine the Horner efficiency for a CGH-matched filter, equation

4.1 must include an accurate model of the encoding scheme. This

efficiency can be measured experimentally using a known input source

and calibrated detectors. Caulfield28 estimated that efficiencies for

certain matched filters could be as low as 10-6. Butler and Riggins29

used models of CGH filters to verify Caulfield's prediction and went

on to recommend techniques for improving the efficiency.

 The matched filter is used to determine the presence of a target

in a large scene. A test scene is correlated with a reference, and

the correlation plane is thresholded to indicate the target location.

Occasionally, the Vander Lugt filter will generate correlation values

above the threshold in areas where no target exists. Accordingly, the

correlation of an actual target corrupted by noise may be lower than

the threshold. Due to the presence of noise, random and otherwise,

the performance of the filter must be measured in terms of the

probability of detection and the probability of false alarm. The

probability of detection, Pd, is defined as the probability that a