A simple technique for observing periodic nonlinearities in Michelson interferometers

We describe a simple, convenient method for measuring nonlinearities in displacement-measuring Michelson interferometers. Nonlinearities with a spatial periodicity of one optical fringe are a well-known source of error in precision interferometry. Our experimental technique for observing these errors is most immediately applicable to commercial interferometer systems for which the cube-corner retroreflectors can be attached directly to the faces of a beamsplitter cube, creating a monolithic interferometer optic with excellent noise immunity. The optical path difference in this bolted-together interferometer can be changed slightly by rotating the interferometer relative to an external laser. It should be noted that the basic principle described here-generating small path differences through a rotation of the optics relative to the laser-may itself be a source of significant errors in certain length measurements. The validity of our method has been demonstrated by measuring optical mixing errors of calculable magnitude. We describe a matrix method suitable for modeling optical mixing errors in both single-pass and double-pass (plane mirror) interferometers. Also, we report experimental measurements of periodic nonlinearities for two representative interferometers and conclude that, in the majority of engineering metrology applications, these errors are of only minor importance. Published by Elsevier Science Inc.