Healy John J, Sheridan John T
UCD Communications and Optoelectronic Research Centre, College of Engineering, Mathematical and Physical Sciences, University College Dublin, Belfield, Dublin 4, Ireland.
J Opt Soc Am A Opt Image Sci Vis. 2010 Jan;27(1):21-30. doi: 10.1364/JOSAA.27.000021.
The linear canonical transform provides a mathematical model of paraxial propagation though quadratic phase systems. We review the literature on numerical approximation of this transform, including discretization, sampling, and fast algorithms, and identify key results. We then propose a frequency-division fast linear canonical transform algorithm comparable to the Sande-Tukey fast Fourier transform. Results calculated with an implementation of this algorithm are presented and compared with the corresponding analytic functions.
线性规范变换提供了一种通过二次相位系统进行傍轴传播的数学模型。我们回顾了关于该变换数值逼近的文献，包括离散化、采样和快速算法，并确定了关键结果。然后，我们提出了一种与桑德 - 图基快速傅里叶变换相当的频分快速线性规范变换算法。给出了用该算法的实现计算出的结果，并与相应的解析函数进行了比较。
