Coherence Properties of Radiation Fields

The radiation emitted by an extended source S generates a total field amplitude A at the point P that is a superposition of an infinite number of partial waves with the amplitudes An and the phases emitted from the different surface elements dS (Fig. 2.22), i.e., 

If a constant time-independent phase difference A0 = 0(Pi) —(piPi) exists for the total amplitudes A = Aqq at two different points Pi, P2, the radiation field is spatially coherent. All points Pm, Pn that fulfill the condition that for all times t, 0(P/, t) — (j) Pn,t) 7T have nearly the same optical path difference from the source. They form the coherence volume. 

The superposition of coherent waves results in interference phenomena that, however, can be observed directly only within the coherence volume. The dimensions of this coherence volume depend on the size of the radiation source, on the spectral width of the radiation, and on the distance between the source and observation point P. 

The following examples illustrate these different expressions for the coherence properties of radiation fields. 

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In the previous subsections we have described the coherence properties of radiation fields in a more general way. We now briefly discuss a more quantitative description which allows us to define partial coherence and to measure the degree of coherence. 

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