Page 109 - Introduction to Information Optics

94 2. Signal Processing with Optics
retrieve the information loss due to blurring there is a price to pay in terms of
entropy, which is usually very costly. Aside from the physical realizability, if we
force ourselves to synthesize an approximate inverse filter which satisfies the
physical realizable condition, then a practical, although not optimum, inverse
filter can be synthesized, as given by

H(p) (2.58)

where A(p) and (f)(p) are the corresponding amplitude and phase filters.
In view of the Fourier spectral distribution of the distorted point image
shown in Fig. 2.21, the restored Fourier spectra that we would like to achieve
is the rectangular spectral distribution bounded by T m and Ap. If we allow the
distribution of the amplitude and the phase filters to vary within the physical
realizable constraints as shown in Figs. 2.22a and 2.22b, the restored spectral
distribution is the shaded areas. It is evident that the blurred image can be
restored for some degrees of restoration error. By defining the degree of
restoration as given by

1 F(p)H(p)
(percent) dp x 100, (2.59)

where Ap is the spatial bandwidth of interest, a plot can be drawn, as shown

-P

Fig. 2.21. The solid curve represents the Fourier spectrum of a linear smeared point image. The
shaded area represents the corresponding restored Fourier spectrum.