Evaluation of the mirror surface figure error based on the SlopeRMS

The slope of the root mean square (SlopeRMS) can be applied to evaluate mid-spatial frequency mirror surface errors for larger aperture mirrors. In this paper, the SlopeRMS is analyzed from three different perspectives. First, the relationship between the SlopeRMS and the basis polynomials is discussed, and the mathematic relationship between the SlopeRMS and the standard orthogonal basis was obtained. Second, the SlopeRMS is analyzed by applying the Wiener process, with the results indicating that the ideal mirror surface error obeys the Gauss distribution law. Then, a power spectrum analysis method based on the SlopeRMS is proposed. The discrete random variables for describing the coma, astigmatism and quatrefoil were analyzed and the spectral energy distribution for the Zernike polynomials is discussed. Finally, by processing the error data of the Thirty Meter Telescope tertiary mirror surface figure, the frequency domain energy distribution of the actual mirror surface figure was obtained.