An unfolding-based model for analysis of rotation and translation coupling in grating interferometers

Menghan Yang; Can Cui; Lifu Liu; Pengbo Zhao; Lvye Gao; Xinghui Li

doi:10.1117/12.3036410

20 November 2024 An unfolding-based model for analysis of rotation and translation coupling in grating interferometers

Menghan Yang, Can Cui, Lifu Liu, Pengbo Zhao, Lvye Gao, Xinghui Li

Proceedings Volume 13243, Advanced Sensor Systems and Applications XIV; 132430G (2024) https://doi.org/10.1117/12.3036410
Event: SPIE/COS Photonics Asia, 2024, Nantong, Jiangsu, China

Abstract

Grating interferometers with high accuracy, strong robustness and multi-dimensional measurement ability have become a main approach in ultra-precision positioning. However, the installation errors, especially the nonideal rotation and translation of the grating, will affect the phase of diffraction beam, resulting in displacement calculation errors. In this paper, a common phase variation model of grating interferometer regarding to the mechanical errors is proposed. A simplified geometric model of general grating interferometers base on the principle of optical-path-unfolding is first established for convenience and universality. Optical path tracing algorithm and the ray vector analysis method are adopted to analyze the phase variations due to optical-path length change and Doppler effect. The experiment results indicate that when the grating moves 100 mm in X-direction with a rotation of 100 arcseconds around Y-axis, a non-linear error of 11.4 nm is generated. For deflection angles of 300 arcseconds around three axes, cross-talk errors between translation axes will reach 45.6 μm in a range of 30 mm for the measurement system illustrated. The Unfolding-Based model proposed in this paper can be applied to most of the grating interferometers. Calculation errors can be effectively quantified through the model and algorithm, which provide a reference for the optimization of optical path as well as the design of calibration algorithm. The results further improve the necessity of six degree-of-freedom measurement ability in ultra-precision positioning.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Menghan Yang, Can Cui, Lifu Liu, Pengbo Zhao, Lvye Gao, and Xinghui Li "An unfolding-based model for analysis of rotation and translation coupling in grating interferometers", Proc. SPIE 13243, Advanced Sensor Systems and Applications XIV, 132430G (20 November 2024); https://doi.org/10.1117/12.3036410

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