Application of Wolf’s theory of coherence

A theory of optical coherence in terms of modal fields and the ensemble average of their amplitudes was recently placed on a firm footing by Wolf [ J. Opt. Soc. Am.72, 343 ( 1982)]. We discuss the physical consequences of this formulation for coherence definition and illustrate some special features of its use. The presence of an aperture and partial reflection at a boundary demonstrate the effects on the degree of coherence of mode number reduction and selective modal attenuation. The propagation of fields from nonuniform sources is used to illustrate the advantage of using modes suited to propagation problems even though the modal correlations may be more involved than those introduced by Wolf.