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中文摘要：
为降低支撑控制难度和节约制造成本，同时又保证在线光学加工检测所需的支撑精度，提出超大口径反射镜的支撑布局优化方法。研究支撑状态下的反射镜面形精度，解决面形拟合和优化目标提取的问题；以斜率均方根（SlopeRMS）为目标建立非圆形口径的超薄反射镜加工支点布局优化模型，使其具备自适应有限元分析的功能；针对工程中大量使用的轻量化反射镜，设计出适应其几何变化的支撑转换结构，并展开以面形均方根（RMS）误差为目标的支点位置的优化设计；通过30 m口径望远镜（TMT）第三镜和某2 m口径反射镜的支撑布局优化，验证了所采用方法的效果。算例结果表明，所提方法具有较好的几何适应性，布局优化后支撑系统的精度满足超大口径反射镜的光学制造要求。
英文摘要：
When fabricating ultra-large aperture mirrors, it′s always very crucial to reduce the control difficulty and to lower the cost of the support system while providing the support accuracy required for on-line fabrication and testing. For this purpose, layout optimization method of supporting points for the equal-force support system is proposed. Firstly through surface fitting, surface figure accuracy of supported mirror is analyzed, and the objectives for layout optimization are auto-updated. Afterward support layout optimization, whose model has the capability of adaptive finite element analysis, of arbitrary-shaped thin flat mirrors is carried out. Sequentially load transfer structure for lightweight mirrors, which are widely used, is designed and the support location within each transfer is optimized. Finally the optimization method is applied to 30 m telescope （TMT） tertiary mirror and a 2-m aperture mirror. Results show that the proposed method has the required accuracy for the optical fabrication of ultra-large mirrors.
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