定义0阶Hankel变换:
则在特定采样点上可以用FFT计算
其中特定采样点取值如下
那么,如果积分区间在[0, a],而变量y的范围为[0, b],对应的Hankel变换为
Less points to evaluate Hankel transform3
1. Zhang, D., Yuan, X., Ngo, N., & Shum, P. (2002). Fast Hankel transform and its application for studying the propagation of cylindrical electromagnetic fields. Optics Express, 10(12), 521. https://doi.org/10.1364/OE.10.000521
2. Magni, V., Cerullo, G., & De Silvestri, S. (1992). High-accuracy fast Hankel transform for optical beam propagation. Journal of the Optical Society of America A, 9(11), 2031. https://doi.org/10.1364/JOSAA.9.002031
3. Levin, D. (1996). Fast integration of rapidly oscillatory functions. Journal of Computational and Applied Mathematics, 67(1), 95–101. https://doi.org/10.1016/0377-0427(94)00118-9