静电拉伸薄膜反射镜的面形分析

Analysis on the shape of electrostatic stretching membrane mirror

静电拉伸薄膜反射镜属于一种空间新概念超轻反射镜。成形控制是其关键技术,而面形分析是成形控制的基础。基于Karman方程分析了薄膜反射镜在均匀载荷作用下的面形,并推导了抛物面面形所需的非均匀载荷;对Ф300 mm口径薄膜反射镜进行了有限元建模,针对不同载荷作用下的薄膜拉伸面形进行了光机集成分析,反射镜中心挠度与理论计算吻合,反射镜在非均匀连续载荷作用下的波前差相对于均匀载荷作用降低了一个数量级,非均匀离散载荷下的面形也得到了改善。结果表明:薄膜反射镜在非均匀载荷下可以有效抑制像差并能控制薄膜成形。基于仿真结果设计了半解析薄膜反射镜成形控制的方法,为薄膜反射镜的成形控制提供了技术基础。

Electrostatic stretching membrane mirror is a new-concept ultra lightweight mirror for space application. Shape control is the key technology, and surface shape analysis is the basis of shaping control. The shapes of membrane mirror applied under uniform load were studied. Non-uniform loads were solved by Karman equations. Then shapes of ~300 mm diameter membrane mirror under different loads were simulated by structural/optical integrated analysis. The central sags are consistent with the theoretical values. Wave front errors of the membrane mirror under non-uniform load can be decreased by one order of magnitude compared with that of the membrane mirror under uniform load, and shapes under non-uniform discrete load also improved. The results of simulation show that aberrations can be reduced effectively and the surface shape under non-uniform loads can be controlled. A semi-analytical control method of electrostatic stretching membrane mirror is designed according to the results of simulation. The research results provide a foundation for the shape control of membrane mirrors.