Page 90 - Introduction to Information Optics

2.2. Processing under Coherent and Incoherent Illumination 75

which describes a completely coherent illumination, where K 2 is a propor-
tionality constant. In other words, a monochromatic point source describes a
strictly coherent processing regime, while an extended source describes a
strictly incoherent system. Furthermore, an extended monochromatic source is
also known as a spatially incoherent source.
By referring to the completely incoherent illumination, we have

r(.v, .y; x'y') = Kj(S(.x'

and the intensity distribution at the output plane can be shown as

2
2
/(a, ft = IT |/!(a - x, /? - y)! /(.x, >')| dxdy, (2,14)

in which we see that the output intensity distribution is the convolution of the
input signal intensity with respect to the intensity impulse response. In other
words, for the completely incoherent illumination, the optical signal processing
system is linear in intensity, that is,

(2.15)

where the asterisk denotes the convolution operation. On the other hand, for
the completely coherent illumination; i.e., F(x. y;x'y') = K 2, the output inten-
sity distribution can be shown as

/(a, 0) = 0(a, /%*(a, P) = \\ h(a - x, fi - y)/(x, y) dxdy
JJ (2.1.6)

h*(a - x', fi - y')f*(x', y') dxdy'

when

0(a, P)=\\ h(a - x, p - >-)/(x, y) dxdy, (2.17)

for which we can see that the optical signal processing system is linear in
complex amplitude. In other words, a coherent optical processor is capable of
processing the information in complex amplitudes.