Planar 3-DOF Pose Measurement for Macromotion Stages via 1-D Phase-Guided Image Correlation

Abstract

Real-time and high-precision measurement with multi-degree-of-freedom (multi-DOF) sensing capability is critical for ensuring the positioning performance of macromotion stages. This article proposes a planar 3-DOF pose measurement method based on 1-D image correlation. By employing a dual-axis digital image grating (DIG) configuration, this approach achieves axial absolute positioning and in-plane angle estimation over a large travel range using exclusively 1-D image information, fundamentally avoiding the cumulative errors inherent in incremental strategies. To address the 1-D image scaling induced by stage rotation, a coarse-to-fine registration framework incorporating a phase-correlation-guided two-parameter inverse compositional Gauss–Newton (2P-ICGN) algorithm is developed to guarantee rapid and high-precision matching. Furthermore, an Abbe-offset-based kinematic compensation model is established to mitigate rotation-to-translation measurement coupling. Experimental results demonstrate that over a 30-mm travel range, the method yields mean absolute errors (MAEs) of 0.65 and <inline-formula> <tex-math notation="LaTeX">$0.69~\mu $ </tex-math></inline-formula>m in the <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula>- and <inline-formula> <tex-math notation="LaTeX">$Y$ </tex-math></inline-formula>-directions, respectively, alongside an angular MAE of 0.12° within the effective working range. The system delivers an actual update frequency of 259.7 Hz, providing an efficient and reliable solution for macromotion positioning.