Separation and compensation of nonlinear errors in sub-nanometer grating interferometers

Abstract

In this paper, to separate and compensate the nonlinear error in the grating interferometer, we analyze the source and generation mechanism of this error, deduce the nonlinear error model of the measured signal and the calculated phase signal, and study the characteristics of the established nonlinear error model. The reason why the frequency multiples of ideal phase signals and higher-order nonlinear errors caused by ghost reflections and angular errors of the laser’s z-axis are not integers is explained. Then, a nonlinear error separation and compensation method based on cross-correlation coefficient is proposed. Experiments show that the frequency multiplier relationship between the high-order nonlinear error and the ideal interference signal is close to but not equal to 3-fold. The peak-to-peak value of the compensated nonlinear error is reduced from 17.40 nm to 7.05 nm.