Page 152 - Introduction to Information Optics

2.8. Processing with Incoherent Light

(a) (b)

Fig. 2.47. Restoration of blurred image, (a) A black-and-white blurred (color) image, (b) Deblurre
(color) image.

Figure 2.47a shows a blurred color image due to linear motion. By inserting
this blurred transparency in the processor of Fig. 2.44 a deblurred color image
is obtained, as shown in Fig. 2.47b. Thus, we see that by properly exploiting
the coherence contents, complex amplitude processing can be obtained from an
incoherent source. Since the deblurred image is obtained by incoherent
integration (or superposition) of the broadband source, the coherent artifact
can be suppressed. In addition, by using white light illumination, the polychro-
matic content of the image can also be exploited, as shown in this example.
Let us provide another example: an image subtraction with white light
processing. Since the spatial coherence depends on the corresponding point
pair of the images to be subtracted, a strictly broad spatial coherence function
is not required. Instead, a point-pair spatial coherence function is actually
needed. To ensure the physical reliability of the source-encoding function, we
let the point-pair spatial coherence function be

sin[N(7i//i)(x 2-.x' 2)] nw
- x' 2) = sine
lul
where 2h is the main separation of the two input image transparencies, N » 1
and w « d, F converge to a sequence of narrow pulses located at (x 2 — x' 2) =
nh, as shown in Fig. 2.48a. Thus, a high degree of coherence among the
corresponding point pair can be obtained. By Fourier transforming the
preceding equation the source-encoding function can be shown as

nd
rect
= 2^
n = 1
where w is the slit width, and d = (lf)/h is the separation between the slits. The