Concept of Cross-Spectral Purity in Coherence Theory

An examination of the conditions under which the normalized coherence function γ(x1,x2,τ), at two points x1 and x2 in an optical field, is reducible to the product of a function of x1, x2 and a function of τ leads to the concept of cross spectral purity. Spectrally pure beams of light are characterized by the property that their coherence function is so reducible and, operationally, by the fact that superposition does not affect the spectral distribution. Light beams that do not have this property are called spectrally impure, and it is shown to be characteristic of such beams that the interference fringes exhibit a detailed periodic coloring. A measure of the departure from cross-spectral purity is introduced and evaluated in some special cases. It is shown by an example that spectrally pure and spectrally impure beams of light may be derived from the same source with similar optical components. Moreover, these beams may be identical as regards their intensity, their spectral distribution, and their degree of coherence, and differ only as regards their state of spectral purity.