PyHank - Quasi-Discrete Hankel Transforms for Python

Edward Rogers

PyHank is a python implementation of the quasi-discrete Hankel transform as developed by Manuel Guizar-Sicairos and Julio C. Guitierrez-Vega

"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)

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. 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 a more advanced approach that 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

Installation

Installation can simply be done from pip. PyHank requires numpy and scipy, but these will be installed by pip if necessary.

pip install pyhank

For building the docs, the following are required:

• sphinx-gallery >= 0.7
• matplotlib >= 3.2

For development, and running the tests, the following are recommended:

• pytest ~= 5.4.3
• flake8 ~= 3.8.3
• pytest-flake8 ~= 1.0.6
• pytest-cov ~= 2.10.0

Bugs & Contribution

Please use Github to report bugs, feature requests and submit your code: http://github.com/etfrogers/pyhank

Documentation

The documentation for PyHank can be found at Read the docs

Usage

See the Usage examples at ReadTheDocs