带透镜球差的分数傅立叶变换

Fractional Fourier Transform with Spherically Aberrated Lens

从Lohmann提出的两类分数傅立叶变换系统出发,引入了透镜球差并分析了球差对分数傅立叶变换系统的影响。以平面波入射为例,进行了数值计算。研究表明,球差对分数傅立叶变换面上光强分布的影响是显著的;在相同球差的情况下,两类系统相同分数傅立叶变换面上的光强分布明显不同;正、负球差和不同大小的球差,它们的作用是不同的。因而,在透镜有球差的情况下,Lohmann提出的两类实现分数傅立叶变换的光学装置不再等价。

Starting from the two types of fractional Fourier transforming systems suggested by Lohmann, the effect of lens with spherical aberration on the fractional Fourier transform was introduced and analyzed. Assuming a plane wave as an input function, the output intensity distributions in the different fractional Fourier transform planes were obtained by numerical calculation. It is shown that the same spherical aberration contributing to the output intensity distribution in different fractional Fourier transforming systems is different even for the same fractional order, and also shown that the positive or negative spherical aberration and different values of spherical aberration contributing to the output intensity distribution is in great difference. The Lohmann's two types of optical setups with spherically aberrated lens for implementing the fractional Fourier transform are no longer equivalent.