Radius of curvature R and conic constant k are important parameters of aspheres.Null testing or CGH are usually used to evaluate the processing quality of aspheric mirrors in fabricating process . When the null compensator emerges a problem, additional method to ensure the accuracy of paraxial radius of curvature and conic constant is required. Based on the equation of conic aspheric, the computing model from which the paraxial radius of curvature R and conic constant k can be obtained was established, and a set of solving algorithm using singular value decomposition (SVD) method was derived. The simulating result of a 1800mm aspheric mirror is presented and the solving precision reaches R=6120±0.026mm, k=-1.0194±0.0008, thus the supplement to null testing of aspheric mirror is achieved effectively .
We present a method to measure the radius of curvature of a concave conic asphere. By analysis the central area of the asphere, we can measure the radius of an arbitrary point in the central area instead of the vertex of asphere. In the procedure, we firstly adjust the interferometer until the interferogram of the central area approach nulls, then put the laser tracker ball at the beam focus of the interferometer and move the tracker ball to touch the central area of the aspherical surface to get the two positions. With these measurement data, we can calculate the radius of curvature of the aspherical vertex and its uncertainty.