Page 143 - Introduction to Information Optics

128 2. Signal Processing with Optics

xl
ko transform lens

•x3

output plane
Fig. 2.42. A PR-based JTC,

diffraction wave vectors can be written as

2
Y X 0

Y 2 \
X
l \ *
z,
X
_ |i I
r 2 - , n
u
4 — i/- ^ T
Z.

Similarly, one can show that the output correlation peak intensity is given by

2
R(S) = ^Xo - /z)| sine (x 0 - S) (2.120)

Again, we see that the peak intensity is modulated by a broad sine factor due
to the Bragg diffraction limitation. To keep the target within the width of the
sine factor, W must be broader than the width of the input targets, i.e.,

For JTC the maximum distance 2h between the two input objects can be