Six degrees of freedom displacement measurement system for wafer stage composed of hall sensors

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°.