Analytical description of interference between two misaligned and mismatched complete Gaussian beams

A typical application for laser interferometers is a precision measurement of length changes that result in interferometric phase shifts. Such phase changes are typically predicted numerically, due to the com- plexity of the overlap integral that needs to be solved. In this paper we will derive analytical representations of the interferometric phase and contrast (aka. fringe visibility) for two beam interferometers, both homodyne and heterodyne. The fundamental Gaussian beams can be arbitrarily misaligned and mismatched to each other. A limitation of the analytical result is that both beams must be detected completely, which can experimentally be realized by a sufficiently large single-element photodetector.