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It is one of several possible optical configurations that permit signal processing. An input transparency of complex amplitude transmittance gi{xl9 y j is placed in the front focal plane of lens Lx and illuminated by a plane-parallel beam of uniform intensity and zero phase. 3 of Chapter 1 (see also Goodman [83]), represented by the Fourier transform G^w, v) of the input. 2-1) J — oo J — oo where λ is the wavelength and (u, v) are the rectangular spatial frequencies 2. y2) FIG. 2-1. Coherent-optical processor.

5l· z = 2 wp c FIG. 6-1. The minimum-bias spectral window W0(p) of Eq. 6-14). ) 20 HENRY STARK where J 0 ( ) is the Bessel function of the first kind of order zero, and ζ1 is the first zero of J0(x). The function W0(-) is shown in Fig. 6-1. It is pro­ portional to the square of the spread function associated with the optimum apodizer for imaging smooth objects [11, Eq. (39)]. The apodizing properties of this function are discussed in the literature [12]. The window is strongly concentrated about the origin and its envelope for large values of p goes as p~5.

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