The Optimization Design of a Lightweight 2 m SiC Mirror for Ground-Based Telescopes

Abstract

The weight of the primary mirror increases as the aperture of ground-based telescopes increases, making it more challenging to maintain the positional stability and surface accuracy of the solid primary mirror. Consequently, a 2 m lightweight silicon carbide (SiC) mirror and an optimization method were proposed in this study. The relationship between the gravitational deformation of the mirror and its thickness and number of supports was derived based on force analysis of the mirror; the thickness of the mirror and the appropriate number of supports were obtained as initial parameters for optimization. The back structure of the mirror was designed in a lotus pattern to improve its rigidity. Numerous structural parameters were classified into major and non-major parameters based on the results of a sensitivity analysis. The non-major and major structural parameters were optimized using a Latin hypercube design method and a non-dominated sorting genetic algorithm, respectively. The optimized 2 m lightweight SiC mirror had a mass of 119 kg and an areal density of 38.7 kg/m2. The surface figure error root-mean-square (RMS) in the vertical state of the optical axis and the first modal resonance of the mirror assembly calculated using finite element analysis were 11.3 nm and 76.5 Hz, respectively. Modal tests of the mirror assembly were conducted using the hammering method, achieving a maximum relative frequency error of 7.4% compared with the simulation results. The optimized 2 m SiC mirror was over 50% lighter than traditional passive Zerodur mirrors of the same size.