Page 145 - Introduction to Information Optics

130 2. Signal Processing with Optics

x, u
A transform lens A
A
PR crystal
BS BS M R-k o
kl
I fir^~— ->z
^7
< v> '• \
Vk3

Fig, 2.43. A PR-based reflection-type wavelength-multiplexed correlator (RC).

lion, the transversal and longitudinal dephasing wave vectors can be written as

HA j

Similarly, the correlation peak intensity as a function of the shift distance S can
be shown to be

nd S(x 1-S)
(2.124)

Again, to maintain the target within the sine factor, we have

W X

for which we have

2
2
SX < f - 2S . (2.125)
a '
Since the shift variable S can be positive or negative, S should be maintained
within half the maximum permissible translation S max. Thus, by substituting
S = 5 max/2, we obtain

4nA
(2.126)