A new high-precision sphere-fitting method with small segment angles

Measuring a spherical surface with small segment angle (e.g. 1°) precisely is a big challenge in scientific research and engineering applications. To fit sphere surfaces with small segment angles with high precision, a five-parameter constrained nonlinear least square fitting (CNLSF) method is presented in this work, where an Adam optimization algorithm with a prominent anti-interference ability is employed. We discuss various factors which influence the final uncertainty evaluation of the sphere's radius. A Monte Carlo simulation is conducted by superimposing Gaussian noise on the ideal spherical data to simulate practical instrument errors, then the relationship between the fitting bias of the sphere's radius and noise the level, the number of sampling points and the segment angle is investigated by comparing the performance of the linear least square fitting algorithm, the nonlinear least square fitting algorithm and the CNLSF algorithm. Finally, the simulated and experimental results show that the CNLSF method performs more precisely and robustly than the other algorithms, even when the corresponding segment angle approaches 1°, which illustrates that it is a promising and practical method in the real measurement world. (paper)