Six Degrees of Freedom Displacement Measurement System for Wafer Stage Composed of Hall Sensors

Bo Zhao; Weijia Shi; Jiawei Zhang; Ming Zhang; Xue Qi; Jiaxin Li; Feng Li; Jiubin Tan

doi:10.3390/s18072030

Six Degrees of Freedom Displacement Measurement System for Wafer Stage Composed of Hall Sensors

Sensors (Basel). 2018 Jun 25;18(7):2030. doi: 10.3390/s18072030.

Authors

Bo Zhao¹, Weijia Shi², Jiawei Zhang³, Ming Zhang⁴, Xue Qi⁵, Jiaxin Li⁶, Feng Li⁷, Jiubin Tan⁸

Affiliations

¹ School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China. hitzhaobo@hit.edu.cn.
² School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China. shiweijia@hit.edu.cn.
³ School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China. hit_zhangjiawei@163.com.
⁴ School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China. 17S001042@stu.hit.edu.cn.
⁵ School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China. 17S001051@stu.hit.edu.cn.
⁶ School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China. 1140110416@hit.edu.cn.
⁷ School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China. 1140110428@hit.edu.cn.
⁸ School of Electrical Engineering and Automation, Harbin Institute of Technology, D-403 Science Park, 2 Yikuang Street, Harbin 150080, China. jbtan@hit.edu.cn.

Abstract

This paper proposes a decoupled six degrees of freedom (DOF) displacement measurement methodology, which is accomplished by utilizing six pairs of permanent magnets and six Hall sensors. Firstly, the coordinate transformation was mathematically derived, which represented the relationships between the main coordinate system of the motion system and each body coordinate system of the Hall sensors. With the aid of an ellipsoid function and the least squares method, only the output voltages of the six Hall sensors were required to decouple the six-DOF displacement and inclination of the motion platform with high accuracy. Finally, the experimental measurements demonstrate the effectiveness of the six DOF displacement measurement methodology, based on which the maximum errors of displacements can reach 0.23 mm and the maximum errors of inclinations can reach 0.07°.

Keywords: Hall sensor; displacement measurement; ellipsoid function; the least squares method.