Uncertainty analysis of sphere parameter estimation from NMM-1 point cloud measurements

The reliable estimation of sphere parameters is important for precision metrology, calibration, and uncertainty evaluation. This study investigates the effects of the number of measurement points and the sampled region on the uncertainty of sphere parameter fitting using the least-squares (LS) method. Contact surface topography data of a high-precision bearing ball were acquired on the NMM-1 platform using two scanning strategies. Repeated subsampling was applied to evaluate the uncertainty of the fitted parameters under different sampling conditions. The results show that the fitting uncertainty depends not only on the number of measurement points, but also on the geometric coverage of the sampled region. Although increasing the number of points generally improves fitting stability, the gain becomes progressively smaller beyond a certain range. This study therefore provides an experimental basis for the design and selection of sampling strategies for reliable sphere parameter estimation under non-ideal measurement conditions.