Software Datum Design for Cross-Axis Motion Measurement of X-Stage Based on Least Uncertainty Criterion

Cross-axis translational motion of a table on a machine tool is important in ultraprecision processes. Currently, conventional software datums that separate the cross-axismotion fromthe straightness profile of the straightedge by using multiple sensors and/or multiple arrangements are well-known. However, in large sampling numbers, the multiple sensor method tends to propagate random error. In this paper, a novel software datum for cross-axis motion measurement that can reduce the uncertainty due to the datum profile, pitch motion and random error is proposed. The proposed method consists of a weighted addition and inverse filtering. The suitable weight for the weighted addition yielding the least uncertainty is derived by an equation using standard deviations of the datum profile, pitch motion and random error of the sensors.