基于Dini展开的高阶Hankel变换及其在光束传输中的应用

High order Hankel transform based on Dini expansion and its applications in beam propagation

基于Dini级数展开,导出了p(>0)阶准离散Hankel变换(the pth-order quasi-discrete Hankel transform based on Dini series expansion,pDQDHT)算法,并给出了该算法在光束传输中的应用.通过不同输入函数分别对pDQDHT算法进行测试及光束通过透镜传输的应用实例,结果表明:pDQDHT算法不仅精度高于现有的Hankel变换算法,可以进行多次正、逆变换,能广泛应用于光束分步传输问题,而且执行速度也与一般的快速Hankel变换算法相当.

Based on Dini series expansion, p（ 0） order quasi discrete Hankel transform （pDQDHT） algorithm is deduced. The application of this algorithm in beam propagation is presented. pDQDHT algorithm is tested with various input functions and used in beam propagation through lens. Experimental results show that the pDQDHT algorithm possesses a high accuracy compared with existing Hankel transformation algorithms. The pDQDHT algorithm can be transformed forwardly and inversely and widely used in beam distribution of transmission. The implementing speed is comparable to that of general fast Hankel transform algorithm.