二阶矩过程在大口径反射镜面形质量分析中的应用

为了更好地评价大口径反射镜反射面面形,本文首先通过理论计算,得出了二阶矩过程的数字特征与结构函数(SF)、表面均方根(RMS)、斜率均方根(Slope RMS)之间的关系,得出以上3种常见的评价函数,皆为二阶矩过程数字特征的组合,以及后面两种评价函数都可以用结构函数表示的结论。然后对于结构函数的具体求解方法进行了讨论并对Zernike多项式中的彗差、像散项的结构函数进行了分析;之后利用离散随机变量功率谱分析,讨论了二阶矩过程评价方法对于噪声的敏感程度以及Zernike多项式频谱能量分布;最后基于二阶矩过程的自回归性提出了一种评价反射镜面形的子孔径非相关拼接方法。

Application of the second order process in large aperture reflect mirror surface evaluation

In order to evaluate the mirror surface figure, the metrology of second order process is discussed in this paper. Firstly, we could obtain the conclusion by theoretical calculation that there are some relationship among the digital characteristics of the second order moment process and the three evaluation functions： structure function （SF）, surface root mean square （RMS）, slope root mean square （slope RMS）. That is all the three evaluations are combinations of the digital characteristics of the second order process, especially for the latter two evaluation functions （RMS and slope RMS） can be represented by the former （SF）. And then, how to acquire the structure function is described, and the Zernike polynomial coma and astigmatism with structure function are analyzed. The sensitivity of the second order process evaluation to noise and Zernike polynomial spectrum energy distribution are discussed by using discrete random variable power spectrum density analysis subsequently. Finally, a novel method of non-relevant sub-aperture stitching is proposed to evaluate the reflect mirror surface accuracy based on the feature of second order process autoregressive.