Evaluation of mirror surface figures for TMT based on SlopeRms

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.