Partial compensation interferometry for measurement of surface parameter error of high-order aspheric surfaces

Surface parameters are the properties to describe the shape characters of aspheric surface, which mainly include vertex radius of curvature (VROC) and conic constant (CC). The VROC affects the basic properties, such as focal length of an aspheric surface, while the CC is the basis of classification for aspheric surface. The deviations of the two parameters are defined as surface parameter error (SPE). Precisely measuring SPE is critical for manufacturing and aligning aspheric surface. Generally, SPE of aspheric surface is measured directly by curvature fitting on the absolute profile measurement data from contact or non-contact testing. And most interferometry-based methods adopt null compensators or null computer-generated holograms to measure SPE. To our knowledge, there is no effective way to measure SPE of highorder aspheric surface with non-null interferometry. In this paper, based on the theory of slope asphericity and the best compensation distance (BCD) established in our previous work, we propose a SPE measurement method for high-order aspheric surface in partial compensation interferometry (PCI) system. In the procedure, firstly, we establish the system of two element equations by utilizing the SPE-caused BCD change and surface shape change. Then, we can simultaneously obtain the VROC error and CC error in PCI system by solving the equations. Simulations are made to verify the method, and the results show a high relative accuracy.