Fringe shifts in multiple-beam Fizeau interferometry

A computer program was developed to compute the profile of multiple-beam Fizeau fringes and was tested against laboratory observations. By using the program as a tool for studying the behavior of the fringes, a simplified model of the fringe formation process was developed. The shifts of the fringes from their expected locations are caused primarily by a reduction in spatial frequency that is due to the oblique projection of the fringes onto the detector. The angle at which the fringes are inclined to the input beam of the interferometer may be calculated by using a phase law developed by Brossel [Proc. Phys. Soc. 59, 224 (1947)] and is independent of the reflectivity of the cavity. Once the orientations of the fringe planes and the detector are known, the fringe shifts may be calculated by using simple trigonometry. Although the absolute shift of a particular fringe may be an appreciable fraction of a fringe spacing, neighboring fringes have nearly identical shifts, making the relative fringe shift inconsequential. The finesse of the fringes may be increased by either tilting the Fizeau cavity or defocusing the detector optics. Unlike the tilt angle required to minimize the fringe shift, the tilt angle that maximizes the finesse is a strong function of the cavity reflectivity.