Page 168 - Introduction to Information Optics

Exercises

q
coherent
plane
wave a H(p.q)

L 2

'-H
+— f

Fig. 2.65.

assumed to be spatial-frequency limited. If this object transparency is
inserted at the input plane of the FDP,
(a) Determine the spectral distribution at the Fourier plane.
(b) Design a stop-band filter for which the light distribution at the output
plane will be f(x, y).
2.13 Consider the coherent optical processor shown in Fig. 2.65. The spatial
filter is a one-dimensional sinusoidal grating.

H(p) = i

where a 0 is an arbitrary constant that is equal to the separation of the input
object functions f^x, y) and f 2(x, y). Compute the complex light field at
the output plane P 3.
2.14 A method for synthesizing a complex spatial filter is shown in Fig. 2.66a.
If a signal transparency s(x, y) is inserted at a distance d behind the
transform lens, and the amplitude transmittance of the recorded filter is
linearly proportional to the signal transparency,
(a) What is the spatial carrier frequency of the spatial filter?
(b) If the spatial filter is used for signal detection, determine the appro-
priate location of the input plane, as shown in Fig. 2.66b.
2.15 Suppose that the input object functions on an FDP is a rectangular
grating of spatial frequency p 0, as shown in Fig. 2.67.
(a) Evaluate and sketch the spectral content of the input object at the
Fourier domain.
(b) If we insert a small half-wave plate at the origin of the Fourier
domain, sketch the light distribution at the output plane and com-
ment on your observation.