Optimization design for edge-lateral support of a medium-aperture lightweight primary mirror

Lightweight primary mirrors are increasingly applied both in ground-based and space-based telescopes. Because the absolute stiffness of the lightweight mirror is much lower than that of the solid one, the design of lateral support becomes more difficult. Based on parallel push-pull support, we have proposed a multi-class variable F-θ optimization approach (MVFOA), where F denotes the magnitude of the support force and θ denotes the support position. Compared with conventional optimization approaches, which only have one class of design variables, F or θ, MVFOA considers the impact of F and θ simultaneously. In addition, we also study push-pull-shear lateral support and propose an unequal-angle push-pull-shear support optimization approach (UPSOA). To verify the advancement of above approaches, by means of finite element calculation, the lateral support optimization of a 2.5 m ultra-low expansion honeycomb sandwich mirror is performed in this paper. For parallel push-pull support with 24 forces, three optimization approaches with different variables, including single-class variable F, single-class variable θ, and multi-class variable F-θ, are compared, and the RMSs of surface deformations are 17.60 nm, 15.93 nm, and 14.81 nm, respectively. For push-pull-shear support with 24 forces, the optimal result by UPSOA occurs when β equals to 0.84 and the RMS of surface deformations is 10.83 nm. UPSOA also solves the problem that the forces in the region x≈±R are much larger than the ones in the region x≈0 in the equal-angle push-pull-shear support optimization approach (EPSOA). Through the analysis of results, we find that optimal β of the honeycomb sandwich mirror is greater than that of the meniscus mirror in push-pull-shear support. In addition, both in parallel push-pull support and push-pull-shear support, it also can be concluded that the position and the magnitude of optimal lateral support forces depend on the stiffness distribution of the mirror along the altitude axis rather than the mass distribution.