In the testing of optical surfaces with large aperture or large aperture angle, sub-aperture stitching technology has been developed for a long time, while most testing analysis is for the rotationally symmetrical surface. In view of a cylindrical surface sub-aperture stitching algorithm based on discrete phase data, by using Legendre polynomials to fit the wave surface, numerical simulation and analysis for several main influencing factors have been carried out. For instance, a bicubic interpolation method has been used for non-numerical point in a discrete phase and fuzzy points in overlapping areas during the process of stitching sub-apertures, on account of its accuracy and calculation time. By considering alignment error, random noise, position error, especially rotation error in non-rotationally symmetrical cylindrical surface testing, we stimulate 9 sub-aperture phase data from a measured phase data to analyze the correction coefficient which determines the percentage of error correction in stitching algorithm. While the correction coefficient is approaching 1, the stitching result is most likely overcorrected. In order to achieve the best error correction, the correction coefficient should be set at around 0.6. Furthermore, combined with chaos particle swarm optimization, we reduce the possibility of the algorithm falling into the local optimum, and improve the accuracy of stitching.
Aspheric surfaces are widely used in modern optical systems. At present, five-axis machine tools are widely used for aspheric surfaces grinding and shaping. The technology of milling aspheric surface with five-axis machine tool is studied. According to the B-C double turntable five-axis machine tool, its kinematics model is analyzed. The tool path algorithm of rotating symmetrical aspheric cup grinding wheel is studied. A five-axis machine tool processing model of cup grinding wheel is established. By calculating contact points, planning tool axis vector and surface vector. The mathematic mapping between tool axis vector and rotation angles of B and C axes is obtained, and the algorithm model of tool path based on vector method is established. Finally, the aspheric surface with diameter 100mm, quadric surface coefficient k=-1 and curvature radius 300mm is machined by five-axis machine tool through simulation and example analysis with MATLAB. The result is measured by three-coordinate measuring instrument, and the PV value of the surface is 5.25um. The RMS value is 0.88um, which verifies the correctness of the tool path algorithm for cup grinding wheel.
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