Page 150 - Introduction to Information Optics

2.8. Processing with Incoherent Light I 35

On the other hand, if the signal processing is a 1-D operation, the
information processing can be carried out with a 1-D fan-shaped broadband
filter. The output intensity distribution can be shown as

7(x, y) - \f(x, y; A) * h(x, y; AH) * dA, (2, 1 34)
A -I
where the integral is over the entire spectral band of the light source. Again,
we see that the output irradiance is essentially obtained by incoherent super-
position of the entire spectral-band-image irradiances, by which the coherent
artifact noise can be avoided. Since one can utilize a conventional white light
source, the processor can indeed be used to process polychromatic images. The
advantages of exploiting the incoherent source for coherent processing are that
it enables the information to be processed in complex amplitude as a coherent
processor, and it is capable of suppressing the coherent artifact noise as an
incoherent processor.

2.8.2. SIGNAL PROCESSING WITH WHITE LIGHT

One interesting application of coherent optical processing is the restoration
of blurred images, as described in Sec. 2.5.2, by means of inverse filtering.
Deblurring can also be obtained by a white light processor, as described in the
preceding section.
Since smeared image deblurring is a 1-D processing operation, inverse filtering
takes place with respect to the smeared length of the blurred object. Thus, the
required spatial coherence depends on the smeared length instead of the entire
input object. If we assume that a spatial coherence function is given by

F(x 2 - x' 2) = sinc< T —-
(Ax 2
as shown in Fig. 2.46a, the source-encoding function can be shown as

/x N
y(x,) = rect M

where Ax 2 is the smeared length, w = (//)/(Ax 2) is the slit width of the
encoding aperture (as shown in Fig. 2.46b, and

fl, -"<*,-
rect I — I = \
^ ' (0, otherwise