Localized fringes from identical twin image sources

Abstract

Twin coherent monochromatic point sources of light produce Young's optical interference fringes throughout space. Often in interferometry, there are effectively identical twin sources (partially reflected images of a single source by plane surfaces). They are small, but are far from being point sources. The consequence is long known: the fringes are ‘localized’, being visible in a certain region only. Here the isometry between the image sources (their identical shape and size) is exploited to deduce the three-dimensional shape of this region and the form of the fringes within it by means of wave optics. In the short wavelength limit the fringes are localized in a definite tube about a certain curve in space, given in cylindrical polar coordinates (r, φ, z) by z = Z tan φ/ tan φ, r = R, where (R, ± φ, ±, Z) locate the sources (and describe their mutual orientation). Also the fringe sheets within this tube differ from the hyperboloids of Young's fringes, being instead nested pieces of concentric cylindrical surfaces.