Study on the Limit ability of shaping aspheric surfaces by FEM

摘要

To shape aspheric surfaces on ultra-thin spherical mirrors can avoid problems of manufacture and measurement for large-aperture aspherical mirrors. In order to study the ability of shaping aspheric surfaces and find out some aspherical parameters that can describe the ability, the limit ability of shaping aspheric surfaces is investigated. Firstly, the relation between asphericity gradient and stress of shaping aspheric surfaces on ultra-thin mirrors is analyzed, and the asphericity gradient of spheres is determined to represent the limit ability. Secondly, based on an example of off-axis large-aperture ultra-thin mirrors, the spheres with the different asphericity gradient are worked out, and the figure errors and the maximal stresses for shaping aspheric surfaces are gotten by Finite Element Method (FEM). Thirdly, according to analysis results, the relation between maximal asphericity gradient of sphere and maximal stresses is created, and the relation between initial figure errors of spheres and maximal asphericity gradient is presented on ZERODUR material. Finally, the maximal stresses of other materials after deformation are solved by using Hook law and FEM. Above analysis results show that the material ZERODUR applied shaping aspherical surfaces is not broken under conditions of the asphericity gradient threshold 1.62e-5, the corresponding initial figure errors RMS threshold 0.49mm, and the P-V threshold 1.74mm, when the aspherical accuracy is 21.09nm. In addition, according to the maximal stresses of ZERODUR, the maximal stresses of other materials are estimated, and their limit ability of shaping aspheric surfaces also can be defined.