Fringe localization.

The technique for locating the region of fringe localization for an interferometer used with a spatially incoherent source is well known. For each light ray going into an interferometer, two or more rays will emerge. The fringes are localized in the region where these emerging rays derived from a single input ray intersect. The proof most often given for the above result involves a large amount of geometry and algebra. 1,2 The purpose of this short Letter is to point out that the proof follows directly from the van Cittert-Zernike theorem. The van Cittert-Zernike theorem states that for a quasimonochromatic spatially incoherent source, the magnitude of the degree of spatial coherence |μs| between two points P(x1,y1) and P(x2,y2) is given by the magnitude of the normalized Fourier transform of the intensity distribution of the source. That is,