Abstract

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) [CrossRef]  ] 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.

© 2021 Optical Society of America

Quasi-discrete Hankel transform

Li Yu, Meichun Huang, Mouzhi Chen, Wenzhong Chen, Wenda Huang, and Zhizhong Zhu
Opt. Lett. 23(6) 409-411 (1998)

Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields

Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega
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Reconstruction of optical fields with the Quasi-discrete Hankel transform

Andrew W. Norfolk and Edward J. Grace
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Theory and operational rules for the discrete Hankel transform

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Quasi fast Hankel transform

A. E. Siegman
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