Page 123 - Introduction to Information Optics

108 2. Signal Processing with Optics

Inverse-
f(x,y) Nonlinear - Linear '•• Nonlinear
Processing Processing Processing

Fig. 2.31. A homomorphic processing system.

In order for a linear optical processor to perform the correlation operation, a
Fourier domain filter or a spatial domain filter for the JTC should be made
available, such as

for FDP,

and

h( x, y) = log f(x, y), for JTC.

If the logarithmic transform input signal is displayed at the input plane of the
optical correlator (either FDP or JTC), output correlation terms can be written
as

0(x, y) = [log n(x, y)] * [log f(-x + b, -3;)]*
+ [log/(x, y)] * [log/(-x + b, -y)]*,

in which the first term represents the cross-correlation between the logn and
signal log/, and the second term denotes the autocorrelation of log / Thus we
see that high correlation peak detection can be obtained at the output plane.
In order to make the processing more optimum, an additional step of
converting the logarithmic noise into white noise is necessary. This step is
generally known as the prewhitening process. Figure 2.32 shows a block box
representation for the signal detection under multiplication regime, in which a
linear optical processor (either FDP or JTC) is used within the system for the
homomorphic processing.

2.6.4. SYNTHETIC DISCRIMINANT ALGORITHM
There are, however, techniques available to alleviate the rotational and
scale-variant constraints in an optical processor. Aside from the distortion
variant constraint, the spatial filters (Fourier and spatial domain) we have
described are basically two-dimensional filters of the storage capacities of