Algorithm for calculating geometric parameter of axial symmetry conic surface

Modern space telescopes use conic surfaces rather than sphere surfaces in optical systems to avoid the unnecessary aberration brought by sphere surfaces. Geometric parameters of conic surfaces include the vertex radius and aspheric coefficient (e2), they are significant to the performance of the telescopes. As the coordinate measuring machine (CMM) is widely used, the measurement for the geometric parameters of conic surface is much more convenient. We introduced a new algorithm for calculating vertex radius and e2 based on the data measured by the CMM through a few steps: measuring the coordinates, finding the axis and calculating the normal aberration theory. According to the simulation and experiment, the error of vertex radius is less than 0.01%, the error of e2 is less than 0.0002,which can meet the demands for most measurements.