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。

To specify the large aperture flat mirror, the discrete Fourier transform (DFT) is discussed in the processing for the slope data achieved from the pentaprism. The basic mathematic principle is processed to analysis the advance of DFT in processing the slope data. Then, the Zernike polynomials and power spectral density method are involved to evaluate the spatial domain and spatial frequency domain property of the method involved in this paper. For the large reflecting mirror, the algorithm is verified to make sure that it is enough to specify the low order mirror figure.