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About pyvisgen
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`pyvisgen` is a python implementation of the VISGEN tool developed at `Haystack Observatory <https://www.haystack.mit.edu/astronomy/>`__.
It uses the Radio Interferometer Measurement Equation (RIME) to simulate the measurement process
of a radio interferometer. A gridder is also implemented to process the resulting visibilities and
convert them to images suitable as input for the neural networks developed in the
`radionets project <https://github.com/radionets-project/pyvisgen>`__.

Input Images
============

As input images for the RIME formalism, we use GAN-generated radio galaxies created by `Rustige et. al. <https://doi.org/10.1093/rasti/rzad016>`_
and `Kummer et. al. <https://doi.org/10.18420/inf2022_38>`_ Below, you can see four example images consisting of FRI and FRII sources.


.. image:: https://github.com/radionets-project/pyvisgen/assets/23259659/285e36f6-74e7-45f1-9976-896a38217880
   :align: center
   :width: 90%
   :alt: Sources generated with a GAN.

Any image can be used as input for the formalism, as long as they are stored in the h5 format, generated with |h5py|_.

.. |h5py| replace:: ``h5py``
.. _h5py: https://www.h5py.org/


RIME
====

Currently, we use the following expression for the simulation process:

.. math::

   \mathbf{V}_{\mathrm{pq}}(l, m) = \sum_{l, m} \mathbf{E}_{\mathrm{p}}(l, m) \mathbf{K}_{\mathrm{p}}(l, m) \mathbf{B}(l, m) \mathbf{K}^{H}_{\mathrm{q}}(l, m) \mathbf{E}^{H}_{\mathrm{q}}(l, m)

Here, :math:`\mathbf{B}(l, m)` corresponds to the source distribution, :math:`\mathbf{K}(l, m) = \exp(-2\pi\cdot i\cdot (ul + vm))` represents
the phase delay, and :math:`\mathbf{E}(l, m) = \mathrm{jinc}\left(\frac{2\pi}{\lambda}d\cdot \theta_{lm}\right)` the telescope properties,
with :math:`\mathrm{jinc(x)} = \frac{J_1(x)}{x}` and :math:`J_1(x)` as the first Bessel function. An exemplary result can be found below.

.. image:: https://github.com/radionets-project/pyvisgen/assets/23259659/858a5d4b-893a-4216-8d33-41d33981354c
   :alt: visibilities


Visualization of Jones matrices
===============================

In this section, you can see visualizations of the matrices :math:`\mathbf{E}(l, m)`  and :math:`\mathbf{K}(l, m)`.

Visualization of the :math:`\mathbf{E}` matrix
----------------------------------------------
.. image:: https://github.com/radionets-project/pyvisgen/assets/23259659/194a321b-77cd-423b-9d01-c18c0741d6c5
   :alt: visualize_E

Visualization of the :math:`\mathbf{K}` matrix
----------------------------------------------
.. image:: https://github.com/radionets-project/pyvisgen/assets/23259659/501f487a-498b-4143-b54a-eb0e2f28e417
   :alt: visualize_K