Geometrical misalignment-induced nonlinear error in homodyne interferometers

This paper discusses the generation of a novel periodic nonlinear error in homodyne interferometers due to geometric misalignments. These misalignments arise from cumulative assembly errors among the sensor head interior, target mirror, test platform, and detector, leading to dynamic misplacement of the measurement beam on the detector's surface. A physical model was developed to explain this error, focusing on the interference field produced by Gaussian beams under conditions of beam separation and inclined interference. Observations from misaligned setups revealed a strong correlation between the modulation of the interference signal by an envelope curve and the distorted, complex patterns of Lissajous figures, with the movement of the target mirror. Numerical simulations and experimental results demonstrated that segmented elliptical fitting effectively calibrates vortex trajectories and substantially reduces periodic nonlinear errors. However, numerical simulations also uncovered previously undetected picometer-scale second-order nonlinear errors due to the geometric misalignments. This research highlights the physical mechanisms behind new nonlinear errors, emphasizing their importance in advancing homodyne interferometers toward picometer-level accuracy.