Page 86 - Introduction to Information Optics

2.1. Coherence Theory of Light

1 2 3 4
Separation d
Fig. 2.3. Vibility as a function of separation.

on how nearly monochromatic the source is. The visibility as affected by the
path difference can be written as

c
Ar (2.5)
Au'

where c is the velocity of light and Ay is the spectral bandwidth of the source.
The preceding equation is also used to define the coherence length (or temporal
coherence) of the source, which is the distance at which the light beam is
longitudinally coherent.
In view of the preceding discussion, one sees that spatial coherence is
primarily governed by the source size and temporal coherence is governed by
the spectral bandwidth of the source. In other words, a monochromatic point
source is a strictly coherent source, while a monochromatic source is a temporal
coherent source and a point source is a spatial coherence source. Nevertheless,
it is not necessary to have a completely coherent light to produce an
interference pattern. Under certain conditions, an interference pattern may be
produced from an incoherent source. This effect is called partial coherence. It
is worthwhile to point out that the degree of temporal coherence from a source
can be obtained by using the Michelson interferometer, as shown in Fig. 2.4. In
short, by varying one of the minors, an interference fringe pattern can be
viewed at the observation plane. The path difference, after the light beam is