Integer order Hankel transform

This routine implements Hankel transforms of integer order based on a Fourier-Bessel series.

Description

This routine implements Hankel transforms of integer order based on a Fourier-Bessel series expansion. The algorithm is based on a recently published research work:

M. Guizar-Sicairos and J. C. Gutierrez-Vega, Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,
J. Opt. Soc. Am. A 21, 53-58 (2004).

The numerical method features great accuracy and is energy preserving by construction, it is especially suitable for iterative transformation
processes.

With the c.mat array, that contains Bessel functions zeros, Hankel transforms of order 0-4 may be computed, with up to 3000 sampling points. A trasformation, and inverse transformation example is given.

This routine was tested under MATLAB 6.5 R13

• Acknowledgements: This submission has inspired the following:; Hankel Transform
• MATLAB release: MATLAB 6.5 (R13)
• Other Files: c.mat, ; Hankel_transform.m

[Paul A. Sean]

Excellent algorithm implementation, fast and accurate. The source code is readable. I strongly recommend its use for propagation problems involving circular simmetries.

[Alejo Threepwood]

Me parece un programa diferente y buenísimo, es ideal para descontracturarse.

[Zoitucha Cha]

Cuando vi este programa dije ORALE!!!!!

[Nemrac Bolma]

It's a simple expansion to high orders of "Li Yu, M. Huang, M. Chen, W. Chen, W. Huang, and Z. Zhu,??Quasi-discrete Hankel transform,?? Opt. Lett. 23, 409?411 (1998).

[Ajeo Threepwood]

-Ehh me parece q la pelicula estuvo muy buena....
-Yo nunca la habia visto...
-Yo la vi 2 veces!
-Si,yo la vi 3 veces viteh,pero la tercera no la entendi viteh!

[Pradyu A]

dosent work. Gives error

[Rajesh Pandey]

The proposed algorithm is fast and accurate.