菲涅耳衍射及柯林斯公式的快速傅里叶变换计算

在衍射的快速傅里叶变换（FFT）计算中，为减小频谱混叠对计算结果的影响，应尽可能缩小取样间隔对函数进行离散。然而，大数目的取样对于容量有限的FFT程序通常会形成困难。本文通过对频谱混叠能量及菲涅耳衍射积分的研究，提出误差跟踪计算方法。利用这种方法，只要用小容量FFT程序，便能完成任意给定取样间隔或计算精度的菲涅耳衍射及柯林斯公式的计算。

The Accurate Calculation of Fresnel Diffraction and Collins' Formula by Using the Fast Fourier Transform

In order to reduce the influence of th e mixing and overlap of frequency spectrum on the calculated result in the calcu lation of the fast Fourier transform (FFT) of diffraction,the interval of sampli ng should be taken to be as small as possible.However,a many number of sampling leads to great difficult in general to FFT program with finite computer memory.I n this paper,a error trace calculation methd is proposed based on the study of t he mixing and overlap energy of frequency spectrum and the Fresnel diffraction i ntegral.Using our method,the FFT program needs a little of computer memory to fi nish the calculation of Fresnel diffraction with the arbitrary interval of sampl ing and the demanded precision.This method can be extended conveniently to Colli ns formula.