Multi-variable H-β optimization approach for the lateral support design of a wide field survey telescope

We have proposed a multi-variable H-β optimization approach (MHOA). Compared with the conventional push-pull-shear lateral support optimization (CPLSO), which has only one design variable, β, MHOA adds another design variable, H, which is the support position height. By contrast, the support position height of CPLSO is usually fixed at mid-thickness, H_m (or at H₀, the height of the center of gravity for the mirror), on the outer rim of the mirror blank. In addition, hybrid optimization with the sub-problem approximation method and first order method is also applied in MHOA. To verify the feasibility and the advancement, the optimization of the lateral support of the 2.5 m-wide field survey telescope (WFST) is performed with MHOA in this paper. Three designs with different supporting points, including 18 supporting points, 24 supporting points, and 36 supporting points, are obtained, and the residual half path length errors are 23.71 nm, 19.60 nm, and 17.79 nm, respectively. Furthermore, other things being equal, CPLSO with H=H₀ as well as CPLSO with H=H_m are used separately to validate the H-β design idea quantitatively. The results have suggested that limiting the value of the residual half path length error, obtained by MHOA, has improved almost 20 nm compared to that of CPLSO with H=H₀, and almost 10 nm compared with that of CPLSO with H=H_m.