为了更好地检测与评价大口径平面镜,引入了离散傅里叶级数作为处理五棱镜扫描结果的数学工具。从基本理论出发,分析了离散傅里叶方法本身性质以及在处理斜率信息上的优势;之后借助功率谱以及Zernike多项式,分析了经过傅里叶方法处理得到结果的空间域以及频域的特性。针对米级口径的反射镜面形数据,进行模拟数据采集,之后对于该数据进行处理,得到可以用于检测装调的低阶面形。 In order to better detect and evaluate large-aperture plane mirrors, a discrete Fourier series was introduced as a mathematical tool to process the pentaprism scan results. Based on the basic theory, the properties of the discrete Fourier method and its advantages in dealing with the slope information are analyzed. After that, the spatial and the frequency domain properties of the results obtained by the Fourier method are analyzed by power spectrum and Zernike polynomials. For the meter-level mirror-shaped data, analog data acquisition, and then for the data processing, can be used to detect the installation of low-level shape.