A New Algorithm for Solving the Best-Fit Sphere of Optical Aspherical Surface
To solve the best-fit sphere (BFS) accurately is one of the technological keys for the generating and testing of optical aspherical surfaces. This paper presents a new algorithm for solving the BFS of aspherical surfaces to suppress some deficiencies in the existing BFS algorithms. In the proposed approach, a BFS is constructed, which passes through both sides of endpoints in the section of the aspherical surfaces, the center of the BFS is shifted along the x-axis, and its radius of curvature is automatically computed. The variable step size method is proposed to speed up the convergence of the iteration. Through numerically solving the BFS of conic and cubic surface, the advantages of the proposed approach are verified. The results show that the proposed approach is of rapid convergence, and high accuracy; it is not only suitable for the conic surface, but also for higher order aspheres. The obtained asphericity and material removal function is more suitable for the machining and test.
Xianghua Liu, Zhengyi Jiang and Jingtao Han
J. Q. Lin et al., "A New Algorithm for Solving the Best-Fit Sphere of Optical Aspherical Surface", Advanced Materials Research, Vols. 418-420, pp. 1472-1477, 2012