On the Propagation of Mutual Coherence

Abstract

Section 1 presents a brief history of the development of coherence theory and discusses some of the advantages of Wolf’s general formulation of the theory in terms of Gabor’s analytic signals.Section 2 contains an analysis of the limiting cases of coherence and incoherence, showing for these extremes the form of the mutual coherence function in a quasi-monochromatic field. In particular it is shown that in such a field coherence is characterized by a mutual coherence function which, apart from a simple periodic factor, is expressible as the product of a wave function with its complex conjugate, each factor depending on the coordinates of one point only. It is also shown that an incoherent field cannot exist in free space.The mutual coherence function obeys rigorously two wave equations, and in Sec. 3 these equations are solved with the help of appropriate Green’s functions to find the field produced by a general plane polychromatic source. The solution is simplified by the quasi-monochromatic approximation; and the limiting cases are discussed in detail showing that a coherent source always gives rise to a coherent field, and that a well known theorem of Van Cittert and Zernike represents an approximation to the incoherent limit of the quasi-monochromatic solution.