First-order periodic error correction: validation for constant and non-constant velocities with variable error magnitudes

Abstract

This paper provides experimental validation of the real-time, digital first-order periodic error reduction scheme described by Chu and Ray. Measurements are completed using a single-pass, heterodyne Michelson interferometer designed to minimize common error contributors such as dead path, Abbe and environment. Motion generation over a range of velocities is achieved using an air bearing stage. Periodic error magnitude and type is varied through independent rotations of a half wave plate and polarizer located in the measurement path; experimental magnitudes for constant velocity conditions are compared to the analytical model described by Cosijns et al. It is shown that the correction algorithm can successfully attenuate first-order error, and identify other error orders, to sub-nm levels for a wide range of frequency mixing conditions and constant/non-constant velocity profiles.