单透镜成象系统的分数维傅立叶变换分析

Analysis of Single Lens Imaging System Using Fractional Fourier Transforms

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 。

The relation between Fresnel diffraction and fractional Fourier transforms has been established. Another description of this relation is expressed in this paper, and by using this relation and the properties of fractional Fourier transform of lens, a single lens imaging system of which the magnification is greater or litter than one is analyzed. The results indicate that the Fresnel diffraction as fractional Fourier transform can be combined with the fractional Fourier transform of lens forming a group of fractional Fourier transforms, and the imaging is implemented through tow fractional Fourier transforms.