Multi-probe method for straightness profile measurement based on least uncertainty propagation (2nd report)—Two-point method considering cross-axis translational motion, pitch motion and sensor's random error

For straightness profile measurements, the traditional standard for hardware datums has been the straightedge, level and optical beam. Currently, the proliferation of computers has brought about development of the software datum. Conventional software datums are error separation techniques that separate a surface profile from parasitic motions by using multiple sensors and/or multiple arrangements (multiple orientations or multiple alignments). The multiple sensor method can separate the surface profile with just one scanning. Therefore, the multiple sensor method is useful, even if the parasitic motion includes non-repeatable components. However, random error propagation of the multiple sensor method has been reported in the case of large sampling numbers.In this paper, a novel two-point method for straightness profile measurement is proposed. The proposed method can reduce the propagation of uncertainty caused by the cross-axis motion, pitch motion and random error of the estimated surface profile. The proposed method consists of a weighted addition and inverse filtering. The suitable weight of the weighted addition that gives the least uncertainty propagation is derived by a simple equation using the standard deviation of the cross-axis motion, pitch motion and random error.