Design and implementation of a real-time compensation algorithm for nonlinear error based on ellipse fitting.

To improve the measurement accuracy of interferometer displacement measurement systems, this study analyzes the characteristics of the interference signal to identify sources of nonlinear errors and develops compensation strategies. Specifically, a model is established for the nonlinear errors of the interferometer, which can be attributed to a laser and polarizing beam splitter (PBS). Following that, the dual orthogonal lock-in amplification algorithm is used to separate and compensate for the frequency uncertainty and amplitude errors. Additionally, a real-time compensation algorithm based on ellipse fitting is proposed to compensate for errors caused by the PBS and the uncertainty of amplitude caused by the light source. Experimental results demonstrate that the peak-to-peak value of the compensated nonlinear error is reduced from 11.62 nm to 5.37 nm.