30m望远镜三镜镜面面形误差的斜率均方根评价

Evaluation of mirror surface figures for TMT based on SlopeRms

由于传统的均方根方法在评价大口径反射镜时难以精确表达光学表面的中空间频率误差,本文提出了基于斜率均方根(SlopeRms)的误差评价方法来评价光学表面面形。该方法先以Zernike多项式拟合光学表面面形,在此基础上求解不同空间间隔上的斜率均方根。这种评价方法可以很好地区分小尺寸磨削工具造成的误差和大口径反射镜在多点支撑下造成的面形误差。文中建立了SlopeRms的数学模型,推导了SlopeRms的计算方法,并以此方法为基础对30m望远镜(TMT)三镜面形进行了评价。结果显示,采用斜率均方根的评价方法得到的光学表面面形值达到0.9μrad,优于传统的RMS评价方法(RMS=115nm),满足设计要求。结果显示,基于斜率均方根的误差评价方法能更加全面和客观地评价大口径反射镜面形,具有实际意义。

As the traditional method based on Root Mean Square（RMS）is hard to accurately express middle spatial frequency errors of an optical surface in evaluation of a large aperture telescope,this paper proposes a new method based on SlopeRms to evaluate the optical surface.The method solves the SlopeRms in different space intervals after fitting the optical surface figure by Zernike polynomial.It can better quantify the small scale irregularities and the surface figure error from a smaller size grinding tool or from an aperture mirror surface figure error in multi-point support.The mathematical model of SlopeRms is established,how to calculate the SlopeRms is deduced and then the surface figure for TMT（Thirty Meter Telescope）tertiary mirror is evaluated by the proposed method.The obtained results show that the mirror surface figure error is 0.9μrad,which is better than that of traditional method（RMS=115nm）and meets the design requirement.It means that the method based on SlopeRms can objectively evaluate the mirror surface figure error for a large aperture telescope.