B-spline adaptive sampling method for freeform surface measurement using laser differential confocal technology

Abstract A B-spline adaptive sampling (B-SAS) method is proposed for three-dimensional freeform surface measurements using a laser differential confocal sensor (LDCS). High-precision focusing on optical freeform surfaces was achieved by axial scanning using the LDCS. The B-SAS method, based on the arc length and curvature uniformity, was introduced to enable the adaptive distribution of sampling points on freeform surfaces. Experiments show that the B-SAS method improves the repeatability accuracy of the peak-to-valley (PV) (3 σ ) for freeform surfaces by 27% compared to the uniform sampling method, and the corresponding measurement efficiency is improved by 41%. The repeatability accuracy of the PV (3 σ ) and root-mean-square (3 σ ) of the measured surfaces, using the B-SAS method, are lower than 27 and 8.5 nm, respectively. This method realizes highly accurate and efficient freeform surface measurements and provides a solution for measuring freeform surfaces with large angles.