在菲涅耳衍射与分数维傅立叶变换关系的理论基础上 ,给出了这一关系的另一表示方式 ,以此理论和透镜的分数维傅立叶变换特性分析了放大率大于 1和小于 1的单透镜成象系统。结果表明 ,作为菲涅耳衍射的分数维傅立叶变换可以与透镜的分数维傅立叶变换组成分数维傅立叶变换群 ,两次分数维傅立叶变换完成了一次成象过程 Based on the theory of Fresnel diffraction and fractional Fourier transform, another representation of this relationship is given. Based on this theory and the fractional Fourier transform of the lens, the magnitudes greater than 1 and less than 1 are analyzed Lens imaging system. The results show that the Fresnel diffraction Fractional Fourier Transform can form a Fractional Fourier Transform group with the Fractional Fourier Transform of the lens. The Fractional Fourier Transform completes the imaging process