应用量纲归一化方法改进的分数傅里叶变换快速算法

An Improved Fast Algorithm for the Fractional Fourier Transform Based on the Method of the Dimensional Normalization

提出了一种实现分数傅里叶变换快速计算的改进算法,该算法将量纲归一化的方法应用到分数傅里叶变换光学系统中,严格导出了空域、分数傅里叶变换域和傅里叶变换域的采样间隔,并根据该采样间隔模拟分数傅里叶变换光学系统实现了分数傅里叶变换快速算法.相应的数值模拟实验表明:该算法计算的强度值结果与Kutay的算法相应的计算结果一致;以Kutay算法的计算结果为参考,该算法计算的准确性要优于Bultheel的算法的计算结果;与Kutay的算法和Bultheel的算法相比较,该算法的计算速度较快.实验还表明,该算法的计算结果不会随人为确定的2个参数(波长和透镜焦距)的变化而变化,具有良好的稳定性.

An improved algorithm,based on the method of the dimensional normalization,for the fast calculation of the fractional Fourier transform is proposed. In the algorithm,the sampling intervals of the transform domains,such as spatial domain,Fourier domain and fractional Fourier domain,are strictly deduced out in the condition of dimensional normalization. Based on these sampling intervals,the fast algorithm for the fractional Fourier transform is implemented by simulating the optical fractional Fourier transform system. Numerical simulation experiments demonstrate that the calculated intensity results of this algorithm are consistent with that of Kutay＇s algorithm（ in the Ozaktas group）. Referring to the computed results of the Kutay＇s algorithm,the calculation accuracy of the algorithm proposed in this paper is better than that of Bultheel＇s algorithm. Compared with the Kutay＇s algorithm and the Bultheel＇s algorithm,the algorithm proposed in this paper calculates faster. Experiments also show that the computed results of the algorithm proposed in this paper do not vary with the variation of the two artificially determined parameters（ such as wavelength and the focal length of the lens）,which proves the robust of the algorithm.