根据球面的几何特征,分析了单球面折射光学系统折射面倾斜和偏心时的失调特征;由失调元件矩阵和共轴元件矩阵的依次相乘,得到了完备的描述失调单球面折射光学系统的矩阵;从系统衍射积分与失调矩阵元的关系导出了该系统的失调衍射积分,并利用单球面折射光学系统的分数傅里叶变换结构参数得到了系统失调时的分数傅里叶变换结果.这些结果可用于数值计算和模拟该系统失调时对输入复振幅的衍射和分数傅里叶变换.

According to geometric feature of spherical surface,the misalignment characteristics of single spherical refracting system when the refracting surface was tilted and decentered were analyzed.From the principle of ordered multiplication of matrix of on-axis element and matrix of decentered element,the strict matrix which described the misaligned single spherical refracting system were presented.With the relation between system diffraction integral and the misaligned matrix element,the diffraction integral of the misaligned system was derived.Based on the structure parameters of fractional Fourier transform of single spherical refracting system,the misaligned fractional Fourier transform was also obtained.The result can be used in numerical calculation and simulation of diffraction and fractional Fourier transform of input complex amplitude of misaligned single spherical refracting system.