Ultraprecision Real-Time Displacements Calculation Algorithm for the Grating Interferometer System

Sensors

Ming Zhang¹  Xin Li¹  Leijie Wang¹  Yu Zhu¹  Weinan Ye¹  Jinchun Hu¹  Chuxiong Hu¹ 

[1] State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China;

关键词: grating interferometer;    ultraprecision;    real-time;    algorithm;    rotation–translation coupling;    geometric error;   

DOI  :  10.3390/s19102409

来源: DOAJ

【 摘 要 】

Grating interferometry is an environmentally stable displacement measurement technique that has significant potential for identifying the position of the wafer stage. A fast and precise algorithm is required for real-time calculation of six degrees-of-freedom (DOF) displacement using phase shifts of interference signals. Based on affine transformation, we analyze diffraction spot displacement and changes in the internal and external effective optical paths of the grating interferometer caused by the displacement of the wafer stage (DOWS); then, we establish a phase shift-DOWS model. To solve the DOWS in real time, we present a polynomial approximation algorithm that uses the frequency domain characteristics of nonlinearities to achieve model reduction. The presented algorithm is verified by experiment and ZEMAX simulation.

【 授权许可】

Unknown