Representation of complex optical surfaces with adaptive radial basis functions

摘要

For state-of-the-art optical elements in laser fusion applications, optical surfaces, especially those with residual fabrication error, are generally complex in symmetry, shape of aperture, and spatial frequency distribution. It is critical to represent the optical surface with high accuracy, efficiency, and flexibility during the stages of design, fabrication, and testing. For this purpose, in this paper, we propose that adaptive radial basis functions (ARBF) can be applied to represent the complex optical surface. As more degrees of freedom are harnessed by an adaptive algorithm, the proposed approach presents better accuracy and needs fewer basis functions than that of the classical radial basis functions. Both surfaces, with global and local variation, can be well represented by the proposed method. Furthermore, the fitting ability of ARBF is verified with the measured data from an element polished by magnetorheological finishing technology. Optimization frameworks of the shape parameters for practical use are also discussed. For good measure, spatial relevance between surface height and nodes location shows that ARBF is fairly flexible in representing complex optical surfaces. (C) 2019 Optical Society of America