Page 172 - Introduction to Information Optics

Exercises i 5 7
(b) Evaluate the intensity distribution of the subtracted image at the
output plane.
2.25 Refer to the broadband spectrum analyzer of Sec. 2.5.4.
(a) Determine the frequency resolution of the analyzer.
(b) For a large number of scan lines, compute the number of resolution
elements at the output plane.
(c) Compute the space bandwidth product of the wide-band spectrum
analyzer.
2.26 The spatial resolution of a CRT scanner is 2 lines/mm and the raster-scan
aperture is assumed 10 x 13 cm. If the CRT is used for wide-band intensity
modulation,
(a) Compute the space-bandwidth product of the CRT.
(b) If the time duration of the processing signal is 2 sec and we assume
that the separation among the scanned lines is equal to the resolution
of the CRT, determine the highest temporal frequency limit of the
CRT.
2.27 Consider a two-dimensional rectangular impulse function as given by

fx\ fx\
f(x,y ) = rect(-Jrectl-1

(a) Evaluate the Mellin transform of /(x, y).
(b) Sketch the result of part (a).
(c) Show that the Mellin transform is indeed a scale invariant transform-
ation.
(d) By preprocessing /(x, y), draw a coherent optical system that is
capable of performing the Mellin transformation.
2.28 Given a circularly symmetric function, such as

1 r
R
f(r) ={ ' ^ °
[0, otherwise.
2
2
where r = ^/x + y ,
(a) Expand the circular harmonic series at the origin of the (x, y} co-
ordinate system.
(b) Assuming that the center of the circular disk of part (a) is located at
x = 0, y = R 0, expand the circular harmonic series of this disk at
x = 0, y = 0.
2.29 Given the spokelike function shown in Fig. 2.71; that is,

r ft 11 N
f(r, 0) = rect — + - * £ d(9 - nO s),
\ U n 2 ., ^ ,