奇异值方法在大口径反射镜面形分析中的应用

Large Aperture Reflection Mirror Figure Analysis with Singular Value

为了更好地分析大口径反射镜的面形,引入奇异值方法来分析系统的重力印透造成的大尺度起伏以及由磨削加工、测量噪声等因素造成的中高频误差。首先对奇异值分解的基本方法以及在反射镜表面评价中的具体应用方法进行了研究;之后利用数值仿真,验证了奇异值分解应用在反射镜表面分析中的可行性;最后,将提出的方法应用在实际的反射镜镜面评价之中,得到系统去除高频误差后的结果。所提出的方法对于低信噪比的大口径反射系统面形评价有较好的指导作用。

We introduce a singular value method to evaluate the mid-and high-frequency error in the large aperture reflecting mirror figure due to gravity print through and noise from processing and measurement. Firstly, we study the singular value method applied to mirror figure evaluaton. Then, the feasibility that the singular value method can be applied to the reflecting mirror figure is verified by numerical simulation. Finally, the proposed method is applied to autual evaluation of the reflecting mirror figure, and the results with highfrequency error in the system eliminated are obtained. The proposed method may help evaluate the large aperture reflecting mirror figure with lower signal to noise ratio.