Page 420 - Introduction to Information Optics

7.7. Pattern Recognition with Photorefractive Optics 405

8o(x) -> x
output plane
Fig. 7.42. A PR-based RC. g 0(x), reference target; g t(x), input scene; /c (), reference beam.

where v\ is the refractive index of the PR crystal, and /' is the apparent (or
actual) focal length, which is given by

(7.54)

Thus, the allowable thickness of the PR crystal filter is limited by

t = 25' (7,55)

in which we assume that the thick-crystal filter is centered at the apparent focal
length /'. By using the coupled-wave theory, the output correlation peak
intensity can be shown as

nt S(x 0 — S)
2
\g 0(x)\ sine dx (7.56)
-b/2
The width of the sine factor is given by

„, 2 ^/' 2 (7.57)
st

To maintain a high correlation peak intensity, the target width should be
adequately small, such as