Modeling analysis and error correction of dynamic angle measurement based on grating shear interferometry

Abstract

This paper analyzes the principle of dynamic angle measurement using grating shearing interferometry (GSI), and derives a mathematical model for angle measurement and its maximum angular velocity limit. The study identifies that the increase in measurement error with the measurement angle in GSI systems is due to aberrations, which distort the period, position, and shape of the interference fringes. The source of measurement error is thus attributed to these aberrations. To address this issue, the paper proposes a method that uses the one-dimensional square-wave phase grating as diffractive beamsplitters and optimizes the system’s parameters. Simulation results demonstrated that this method corrects aberrations within a ± 20 mrad field of view (FOV) to the diffraction limit, thereby eliminating the aberration-induced measurement error. Experimental validation was performed using a fast steering mirror (FSM). When the angle of FSM is within ±10 mrad and its angular velocity is below 4.72 rad/s, the angular error of the optimized GSI measurement system can be within ±6µrad, and the measurement uncertainty is only 0.14 µrad. This method effectively addresses the problem of increasing GSI measurement error with angle, enabling high-precision dynamic angle measurement.