针对分数傅里叶变换衍射光学光束整形器件,比较了按离散点与按菲涅耳积分计算得到的变换矩阵间的差距,从中分析得出按离散点计算的变换矩阵引入的离散化误差与分数傅里叶变换系统参数的关系.模拟计算结果表明,该离散化误差不能忽略.为了在输出面上得到真实的光强分布,应采用菲涅耳积分计算其变换矩阵.鉴于该变换矩阵非幺正,本文利用YG算法进行了光束整形器件的设计.

For the diffractive optical element (DOE) realizing beam shaping in the fractional Fourier transform domain,the transform matrix calculated by the discrete sampling points was compared with that calculated by the Fresnel integral,and the discretization error of the intensity distribution on the output plane was qualitatively obtained.Simulated results show this discretization error cannot be neglected.Therefore the Fresnel integral should be used to obtain the true intensity distribution on the output plane.Because the transform matrix calculated with the Fresnel integral was non-unitary,YG algorithm was used to design the DOE realizing beam shaping in the fractional Fourier transform domain in this paper.