Page 142 - Introduction to Information Optics

2.7. Processing with Photorefractive Optics

By substituting Eq. (2.115) into Eq. (2.116), the output correlation peak
intensity as a function of the shift distance can be shown to be

R(S)

Thus, we see that the intensity is modulated by a broad sine factor with a width
equal to

In order to keep the target object within this width, the sine factor has to be
sufficiently broad compared with the width of the target and the location of
the input reference point source; that is,

W X

where X is the width of the input target. In order to avoid an overlapping
situation, the location of this point source should be X 0 ^ X5/2, by which we
have W ^ 6X. It follows that the object shift constraint is

which is inversely proportional to the thickness of the PR filter. In other
words, the thinner the PR filter, the higher the shift tolerance will be. How-
ever, the thinner the PR filter, the lower will be the storage capacity. If
the product of the target width and the maximum permissible shift is defined
as the figure of merit (FOM) for the shift tolerance, the FOM for the VL-C can
be shown to be

(2.119)

which is inversely proportional to the thickness of the PR filter, and propor-
tional to A. and the square of the focal length.
Let us now consider a PR-crystal-based JTC as shown in Fig. 2.42, where
q Q and cj l are the reference and input targets. The corresponding Bragg