Optimum Source Size for the Mach-Zehnder Interferometer

Abstract

A vector analytic treatment is given of the formation of undisturbed fringes by an ideal Mach‐Zehnder interferometer with an extended source. The path difference of two interfering rays at an arbitrary point in the field is found to depend, in a simple way, upon the source point from which the rays originate, the field point examined, and a dyadic which is a function of the unit normals to the last mirror and divider plate of the interferometer. The fringe clarity condition, that all pairs of interfering rays reaching the field point have path differences within a specified range, is developed in the form of an inequality. Analysis of this fundamental inequality shows that all admissible area sources must be areas enclosed between two conics in the source plane. For fringes perpendicular to the plane of centers of the interferometer elements, the optimum source is a circle with radius inversely proportional to the square root of the number of clear fringes desired. This result holds for all interferometers of parallelogram planform. For fringes parallel to the plane of centers, each interferometer orientation presents a special case. The optimum source area is obtained for two of these, viz., the 45° and 30° interferometers.