Implementation of the extended Nijboer-Zernike (ENZ) theory for Python. This toolbox can be used to compute the point-spread function (PSF) using the scalar ENZ theory, see [1], [2], and [3]. It contains code to fit the phase and the generalised pupil function using real- and complex-valued Zernike polynomials, see [4].

• real- and complex-valued Zernike polynomials
• complex point-spread function computation
• multi-threaded computation of the :math:V_n^m terms (Eq.(2.48) in [3])
• routines to fit and evaluate the phase and the generalised pupil function
• load/save functions for each object
• numerous examples & documentation
• ENZPL algorithm example for phase retrieval

• Python 3
• pthreads (tested on Linux and Mac OS X Yosemite)
• Numpy
• h5py
• [optional] matplotlib
• [optional] PyQt5
• [optional] CVXOPT

Make sure you have installed the packages in requirements.

git clone https://github.com/jacopoantonello/enzpy.git
cd enzpy

# static local installation
python setup.py install --user

# or install in development mode
# python setup.py develop --user

The easiest way to use this toolbox is to install Anaconda for Python 3, which includes all the necessary packages in requirements, except for PyQt5 and CVXOPT. Once you have installed Anaconda, create an environment:

conda create -n py3 python=3 anaconda
source activate py3

and install enzpy:

git clone https://github.com/jacopoantonello/enzpy.git
cd enzpy
python setup.py install

PyQt5 is necessary to run the examples with a graphical interface: alpha_abs.py and alpha_abs_qt.py.

This toolbox does not support Windows.

After installing enzpy, you can run the examples located in examples/:

• through_focus_intensity.py is taken from [1], and computes the intensity as a function of the radial coordinate and the defocus parameter.
• psf_plot.py plots a diffraction-limited PSF at different defocus planes.
• phase_plot.py plots the first 10 real-valued Zernike polynomials.
• fit_phase.py estimates a vector of real-valued Zernike coefficients from a phase grid by taking inner products numerically.
• fit_gpf estimates a vector of real-valued Zernike coefficients from a phase grid by taking inner products numerically. The coefficients can be used to approximate the generalised pupil function.
• beta_abs.py and beta_abs_qt.py plot the point-spread function that corresponds to a given complex-valued Zernike analysis of the generalised pupil function. The coefficients can be adjusted using the command line (beta_abs.py) or a Qt widget (beta_abs_qt.py).
• alpha_abs.py and alpha_abs_qt.py plot the point-spread function that corresponds to a given real-valued Zernike analysis of the phase aberration function. The coefficients can be adjusted using the command line (alpha_abs.py) or a Qt widget (alpha_abs_qt.py).
• enzpl/run contains an example of the ENZPL algorithm, which uses PhaseLift (see [5]) and the ENZ theory to correct a random aberration.

Alternatively, you can execute the consistency tests:

cd tests
nosetests -v -x --pdb *.py

[1] nijboerzernike.nl

[2] A. J. E. M. Janssen, "Extended Nijboer–Zernike approach for the computation of optical point-spread functions," J. Opt. Soc. Am. A 19, 849–857 (2002)

[3] J. Braat, S. van Haver, A. Janssen, P. Dirksen, Chapter 6 Assessment of optical systems by means of point-spread functions, In: E. Wolf, Editor(s), Progress in Optics, Elsevier, 2008, Volume 51, Pages 349-468, ISSN 0079-6638, ISBN 9780444532114

[4] J. Antonello and M. Verhaegen, "Modal-based phase retrieval for adaptive optics," J. Opt. Soc. Am. A 32, 1160-1170 (2015)

[5] E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, "Phase retrieval via matrix completion," SIAM J. Imaging Sci. 6, 199–225 (2013)