通过用光学传输矩阵的方法分析用球面镜实现分数阶傅里叶变换，指出球面谐振腔中的谐振过程也是分数阶傅里叶变换过程，进而推导出腔的几何尺寸与变换阶数对应的分析方程，给出了谐振腔稳定性的判据。最后分析了几个谐振腔，并指出引入此方法的意义。 By using the method of optical transmission matrix to analyze the fractional Fourier transform with the spherical mirror, it is pointed out that the resonance process in the spherical resonator is also a fractional Fourier transform process, and the analytical equation corresponding to the geometry of the cavity and the transform order , Gives the criterion of resonator stability. Finally, several resonant cavities are analyzed, and the significance of introducing this method is pointed out.