Page 84 - Introduction to Information Optics

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2.1. Coherence Theory of Light
Needless to say, the degree of coherent is bounded by 0 ^ |r 12(t)| < 1, in
which |r 12| = 1 represents strictly coherent, and |r 12| = 0 represents strictly
noncoherent. We note that, in high-frequency regime, it is not easy or
impossible to directly evaluate the degree of coherence. However, there exists
a practical fringe visibility relationship for which the degree of coherence \r l2\
can be directly measured, by referring to the Young's experiment in Fig. 2.2, in
which £ represents a monochromatic extended source. A diffraction screen is
located at a distance f 10 from the source, with two small pinholes in this screen,
Q, and Q 2, separated at a distance d. On the observing screen located r 20 away
from the diffracting screen, we observe an interference pattern in which the
maximum and minimum intensities / max and / min of the fringes are measured.
The Michelson visibility can then be defined as

I/ A max min (2.3)
max ' min
We shall now show that under the equal intensity condition (i.e., /j = J 2)» the
visibility measure is equal to the degree of coherence. The electromagnetic
wave disturbances u^t) and u 2(t] at Q 1 and Q 2 can be determined by the wave
equation, such as

where c is the velocity of light. The disturbance at point P, on the observing
screen, can be written as

=cut

Fig. 2.2. Young's experiment.