PyHank: Quasi-Discrete Hankel Transforms for Python¶
Introduction¶
PyHank is a Python implementation of the quasi-discrete Hankel transform as developed by Manuel Guizar-Sicairos and Julio C. Guitierrez-Vega [1].
It was designed for use primarily in cases where a discrete Hankel transform is required, similar to the FFT for a Fourier transform. It operates on functions stored in NumPy arrays. If you want an Hankel transform that operates on a callable function, you may be interested in hankel by Steven Murray.
I have used this code extensively for beam-propagation-method calculations of radially-symmetric beams (see Typical usage for an example of this). In the radially symmetric case, the 2D FFT over \(x\) and \(y\) that would be used in a non-symmetric system is replaced by a 1D QDHT over \(r\), making the computational load much lighter and allowing bigger simulations.
PyHank was inspired by Adam Wyatt’s Matlab version which I used for many years, before moving to Python and needing my own implementation. It aims to simplify the interface (using Python’s object-oriented approach) and utilise existing NumPy/SciPy functions wherever possible.
It has both a simple single-shot interface, and also supplies a transformer object which speeds up computation significantly if making multiple transforms on the same grid.
Contributions and comments are welcome using Github at: http://github.com/etfrogers/pyhank
| [1] | “Computation of quasi-discrete Hankel transforms of the integer order for propagating optical wave fields” Manuel Guizar-Sicairos and Julio C. Guitierrez-Vega J. Opt. Soc. Am. A 21 (1) 53-58 (2004) |
Usage examples
Bugs & Contribution¶
Please use Github to report bugs, feature requests and submit your code: http://github.com/etfrogers/pyhank