Page 146 - Introduction to Information Optics

2.8. Processing with Incoherent Light 1 5 I

which is inversely proportional to the thickness of the PR filter and decreases
as the maximum permissible shift distance increases.
In view of the preceding results, for moderate width of the input target, we
see that RC performs better in terms of shift tolerance than both VLC and JTC.

2.8. PROCESSING WITH INCOHERENT LIGHT

The use of a coherent light enables the use of optical processing to carry out
complex amplitude processing, which offers a myriad of applications. However,
coherent processing also suffers from coherent artifact noise, which limits its
processing capabilities. To alleviate these limitations, we discuss methods to
exploit the coherence contents from an incoherent source for complex ampli-
tude processing. Since all physical sources are neither strictly coherent nor
strictly incoherent, it is possible to extract their inherent coherence contents for
coherent processing.

2.8.1. EXPLOITATION OF COHERENCE

Let us begin with the exploitation of spatial coherence from an extended
incoherent source. By referring to the conventional optical processor shown in
Fig. 2.44, the spatial coherence function at the input plane can be written as

F(.x 2 - x' 2) = y(x 1 )exp - x' 2) (2.127)

which is the well-known Van Citter-Zernike theorem, where y(x-^) is the
extended source, / is the focal length of the collimated lens, and /I is the wave-

Fig. 2.44. Incoherent source optical processor: /,, Incoherent source; Lj, collimating lens; L 2 and
L 3, achromatic transformation lenses; P l, source encoding mask; P 2, input plane; P 3, Fourier
plane; and P 4, output plane.