Compensation of astigmatism in coordinate measurement for optical aspheric elements

When a three Coordinate Measurement Machine is used to test the surface shape of an aspheric element in grinding and polishing, obtained result often shows astigmatism errors due to an imperfect compensation programming. This paper analyzes these measurement data, and points out that the astigmatism errors comes from the imprecise compensation programming for the radius of three-dimensional probe in the CMM. Then, It presents an off-line data processing method to compensate the measurement data and to eliminate the astigmatism. By calculation of the tangent vectors of row and column at the meshed central point, the normal vector of each point on the surface is obtained. By calculation of the offsets between the centers of probe and the contact points, the radius of the tree-dimensional probe in the CMM is compensated. The experiment of a standard sphere show that this method decreases the astigmatism PV(Peak-to-Valley) of the measurement result from 4.921 9 μm to 0.065 2 μm, eliminating basically the astigmatism errors and improving the accuracy of the coordinate measurement. Obtained results verify the effectiveness of the proposed compensation programming for the radius of tree-dimensional probe in the CMM. ? 2016, Science Press. All right reserved.