Method for measuring the radius of mean curvature of a sphericalsurface based on phase measuring deflectometry

In this paper, a method for measuring the radius of mean curvature (Rm) of the spherical surface based on phase measuring deflectometry is proposed. With our method, the average of the Rm in a small region is constrained by a preknown radius of curvature (Rp), and the height of an anchor point in this region can be calculated with iterative and optimization methods. Then both the height and slope data of the spherical surface can be obtained, and the Rm of each point of the spherical surface can be calculated by a differential geometric method. The feasibility of the proposed method is verified by simulation. In the experiment, a spherical surface with 88.652 mm radius of curvature is measured to demonstrate the effectiveness of this method, which can be used to accurately measure the Rm of each point on the spherical surface by online or in situ measurement.