Design of a Segmented Mirror with a Global Radius of Curvature Actuation System: Contributions of Multiple Surrogates

Abstract

Due to fabrication difficulties, separately-polished segmented mirrors cannot meet the co-phasing surface shape error requirements in the segmented telescope system. Applying the global radius of curvature (GRoC) actuation system for the individual segments has become an effective solution in space-based telescopes. In this paper, we designed a segmented mirror with a GRoC actuation system. The direct optimization by numerical simulations has low computational efficiency and is not easy to converge for optimizing the actuation point’s position on the segmented mirror. For this problem, three common surrogates, including polynomial response surface (PRS), radial basis function neural network (RBFNN), and kriging (KRG), were summed to propose the multiple surrogates (MS) which have the higher approximate ability. The surrogates were then optimized through the multi-island genetic algorithm (MIGA), and the segmented mirror met the design requirement. Compared with direct optimization through numerical simulations, the results show that the proposed multiple-surrogate-based optimization (MSBO) methodology saves computational cost significantly. Besides, it can be deployed to solve other complex optimization problems.

Keywords

• multiple-surrogate-based optimization
• multi-island genetic algorithm
• Latin hypercube sampling
• segmented mirror with a GRoC actuation system