Page 144 - Introduction to Information Optics

2.7. Processing with Photorefractive Optics 1 29

determined by setting W = X and S = 0, for which we have

2h =
Xd '

When the readout beam is shifted closer to the input object by a distance S,
the distance between the zeroth-order and the first-order diffraction will be
2h — S. To avoid overlapping between the two diffraction orders, the separ-
ation between them should be greater than twice the target X; that is,

2h-S^2X, (2.121)

for which the maximum permissible target translation is

s =
max
Xd

The shift-tolerance FOM for the JTC can be written as

2n
FOM, TC = XS mM = 4^ ~ 2X\ (2.123)

which is inversely proportional to the thickness of the PR crystal and decreases
rapidly as the width of the target X increases.
Similarly, for the RC correlation shown in Fig. 2.43, the Bragg diffraction
wave vectors can be written as

i ,
'

- a
k ~ X3 n \

where k 0 and k x are the writing vectors, and k 2 and k 3 are the reading and the
diffracted wave vectors, respectively. With reference to momentum conserva-