Page 138 - Introduction to Information Optics

2.7. Processing with Photorefractive Optics

a

(a) (b)

Fig. 2.39. (a) Construction of a transmission-type filter, (b) Construction of a reflection-type filter.

thickness of the crystal, and 6 and A0 are the internal construction angle and
its variation. Under the assumption of weak coupling; i.e., |v| « |c|, the nor-
malized diffraction efficiency ^ can be approximated as

2
2
v sinc c,, r\ r (2.109)
Based on preceding equations, the angular selectivity for the transmission-type
and the reflection-type holographic filters can be shown to be

1 sin a cos a d sin a cos a d
(2.110)
2
AaL v/« — sin a cos'a
2
where 2a is the external construction angle, as shown in Fig. 2.39. The variation
of the angular selectivities is plotted in Fig. 2.40a.
Similarly, the wavelength selectivity for the transmission-type and the
reflection-type holographic filters can be shown as

(2.111)
sin a/n

sin sin
n j d sin a
2
2
(n - cos a) 1/2
(2.112)