Improved algorithm for the quasi-discrete Hankel transform.

An improved algorithm for numerical evaluation of the Hankel transform is developed. The algorithm originally proposed by Yu et al. [Opt. Lett.23, 409 (1998)OPLEDP0146-959210.1364/OL.23.000409] uses the quadrature in which the nodes are zeros of the Bessel function. In this work, it is shown that the accuracy of the algorithm can be significantly improved, with virtually no increase in computation time, via two steps. One is to halve the weight of the last node, and the other is to extrapolate a function tail using the modified Bessel function of the second kind, which gives the analytical estimation of the integral remainder.