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2.7. Processing with Photorefractive Optics 1 15

where n represents the nth iteration, ran [•] represents a uniformly distributed
random function within the range [0,1], sign represents a sign function,
and /)(A£) is the Boltzmann distribution function.
9. Repeat step 8 for each pixel until the system energy E is stable. Then
assign a reduced temperature T to the system and repeat step 8 again.
10. Repeat steps 8 to 9 back and forth until a global minimum E is found;
the final h(x, y) will be the desired BCF. In practice, the system will
reach a stable state if the number of iterations is larger than 4/V, where
/V is the total number of pixel elements within the BCF.

2.7. PROCESSING WITH PHOTOREFRACTIVE OPTICS

Besides electronically addressable SLMs, photorefractive (PR) optics also
plays an important role in real-time optical processing. Because of their volume
storage capability, PR materials have been used to synthesize large capacity
composite filters. This section briefly discusses the PR effect and some of its
processing capabilities.

2.7.1. PHOTOREFRACTIVE EFFECT AND MATERIALS

Photorefractive effect is a phenomenon in which the local refractive index of
a medium is changed by a spatial variation of light intensity. In other words,
PR materials generally contain donors and acceptors that arise from certain
types of impurities of imperfections. The acceptors usually do not directly
participate in the photorefractive effect, whereas the donor impurities can be
ionized by absorbing photons. Upon light illumination, donors are ionized, by
which electrons are generated in the conduction band. By drift and diffusion
transport mechanisms, these charge carriers are swept into the dark regions in
the medium to be trapped. As a consequence, a space charge field is built up
which induces a change in the refractive index.
We now consider how two coherent plane waves with equal amplitude
interfere within the photorefractive medium, as illustrated in Fig. 2.35. The
intensity of the interference fringes is given by

//••* ^
! 1 + cos (-^ ) I, (2.99)

where / 0 is a constant intensity, A = A/sin 0 is the period of the fringes, and A
is the wavelength of the light beams. In the bright regions close to the