An investigation of two unexplored periodic error sources in differential-path interferometry

This paper describes two sources of periodic error in differential-path interferometry that have remained largely unexplored: dynamic periodic error that is exhibited by heterodyne interferometer systems under high-speed displacements and intermodulation periodic error caused by amplifier nonlinearity. Dynamic periodic error occurs when the measurement signal, or intended ac interference term, and unwanted dc interference terms, that exist due to frequency leakage in physical implementations of heterodyne interferometers, are both present within the phase measuring electronics’ modulation bandwidth. The situation is similar to the well-documented pseudo-static periodic error observed at low slide speeds, where the intended ac interference, leakage-induced ac interference, and ac reference terms all lie within the modulation bandwidth. equency–Path (F–P) model of the propagation of light from the source to detector for differential-path interferometers is also presented. This model identifies each possible path for each light frequency from the source to detector and predicts the number of interference terms that may be expected at the detector output. We show that, regardless of the interferometer configuration, the behavior of each interference term with respect to optical path changes may be grouped into one of four categories: optical power, ac interference, ac reference, and dc interference. The application of the F–P model to the generic description of periodic error in a single pass, Michelson-type heterodyne interferometer is provided.