球面折射系统和复合厚透镜的分数傅里叶变换

Fractional Fourier transform of spherical refracting system and compound thick lens

提出单球面折射系统可以作为光学分数傅里叶变换的最基本单元。在此基础上可以构造多种厚透镜或复合厚透镜分数傅里叶变换系统。推导了系统结构参数与分数傅里叶变换的级次的关系。指出单球面折射系统及其构造的透镜系统对输入物函数的分数傅里叶变换输出可以位于自由空间,也可在球面折射材料内部或折射材料端面。输出平面位置的灵活性及其构造复杂系统的多样性,对于分数傅里叶变换的应用和光学信息处理必定具有潜在的实用价值。

Single spherical refracting system as the most basic unit for performing fractional Fourier transform was proposed. Based on this, many thick lens fractional Fourier transform systems were constructed. The relation between the system parameters and the order of fractional Fourier transform implemented were derived. The output function of single spherical refracting system or its combination could be located at free space, end plane or within the refracting material. The location flexibility of output plane and the multiplicity of complicated system composed of single spherical refracting system must have potential practical value in fractional Fourier transform application and optical information processing.