反射镜的面形精度是保证空间望远镜成像质量的关键因素, 随着空间遥感器口径的增大以及光机结构的轻量化使得反射镜结构刚度越来越低, 从而使得反射镜的面形非常容易受到环境微振动的影响。然而, 遥感器在轨工作状态下, 星上具有多种振动源, 如步进电机、动量轮、机械制冷机等。为了研究扰动源对反射镜面形动态误差的影响, 提出了一种基于模态叠加和泽尼克多项式拟合的面形动力学响应分析方法。对于每一阶模态, 其光学表面的振型均可以表示为一组泽尼克多项式的线性组合, 并得到一组泽尼克系数。然后, 通过模态叠加法可以求出反射镜表面整体的动态面形误差, 该误差是由泽尼克系数所表示。由于每一项泽尼克系数对应明确的物理像差含义, 所以通过该方法可以方便地分析微振动引起的光学面形响应以及系统像差。

The optical surface error is one of the key factors to guarantee the image quality for space telescopes. Increasing aperture and minimizing structural mass result in a relatively lightweight and flexible telescope mirror, whose surface figure is vulnerable to micro-vibration disturbances. Unfortunately, there are a variety of disturbances in space, such as stepper motors, momentum wheels, and cryocoolers. In order to investigate the effect of dynamic optical surface errors on disturbances, a method based on modal superposition and Zernike polynomials(ZPs) fitting was proposed. On the basis of normal mode, the response of an opto-mechanical structure under force excitations could be approximated by the sum of normal modes of the system. For each mode shape, the optical surface could be fitted as a linear combination of ZPs, which were typically used to describe optical surface errors and represent the aberrations of optical systems. Then, modal superposition technique was applied to compute the combined response of surface error. Finally, the dynamic response of optical surface error to disturbances was given in terms of ZPs. So, the influence of disturbances on the aberrations of optical system can be predicted straightforwardly.