A macroscopic theory of interference and diffraction of light from finite sources, I. Fields with a narrow spectral range

Abstract

A macroscopic theory of interference and diffraction of light in stationary fields produced by finite sources which emit light within a finite spectral range is formulated. It is shown that a generalized Huygens principle may be obtained for such fields, which involves only observable quantities. The generalized Huygens principle expresses the intensity at a typical point of the field in terms of an integral taken twice independently over an arbitrary surface, the integral involving the intensity distribution over the surface and the values of a certain correlation factor, which is found to be the ‘degree of coherence’ previously introduced by Zemike. Next it is shown that under fairly general conditions, this correlation factor is essentially the normalized integral over the source of the Fourier (frequency) transform of the spectral intensity function of the source, and that it may be determined from simple interference experiments. Further, it is shown that in regions where geometrical optics is a valid approximation, the coherence factor itself then obeys a simple geometrical law of propagation. Several results on partially coherent fields, established previously by Van Cittert, Zernike, Hopkins and Rogers, follow as special cases from these theorems. The results have a bearing on many optical problems and can also be applied in in ­ vestigations concerned with other types of radiation.