根据菲涅耳衍射公式，导出了含介质的单透镜与双透镜系统输出面的光场复振幅分布，并与分数傅里叶变换定义式比较，得到了实现分数傅里叶变换的系统结构参量.运用矩阵光学方法，导出上述系统的ABCD矩阵，并与分数傅里叶变换矩阵比较，研究发现两种方法所得结果一致.

Based on Fresnel diffraction formula,the complex amplitude distribution of output plane was derived for the one-lens system and two-lens system with the different media.Compared with the definition of Fractional fourier transform,the structure parameters were obtained. The ABCD matrix of the optical systems was also obtained by using matrix method.Compared with the matrix of Fractional Fourier transform,the matrix methods is coincident with that of the diffraction integral.