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For balloon-borne telescopes, the primary mirror is the most important optical element, but designing a primary mirror with an excellent overall performance is a challenge. To comprehensively consider the contradictory objectives of the root mean square (RMS) surface error under gravity in the X and Z directions, the mass and fundamental frequency of the primary mirror, a parametric primary mirror design using the compromise programming method based on topology optimization is proposed. The parametric design of the compromise programming method based on topology optimization is used to find the optimal solution for X-direction RMS (RMSx), Z-direction RMS (RMSz), mass, and fundamental frequency. Compared with the initial primary mirror structure designed according to traditional experience, the overall performance is improved. Results show that the respective mass of the primary mirror, the RMSx and the RMSz decreased by 8.5%, 14.3% and 10.5% compared to those before optimization. Comprehensive consideration can prove the effectiveness of parametric design based on the topology optimization of the primary mirror. This method provides a reference for the design of other primary mirrors for balloon-borne telescope and space cameras.

Topology Optimization Based Parametric Design of Balloon Borne Telescope’s Primary Mirror