WIP: Beam Phase Space Reconstruction - MENT Algorithm

[otavio-silveira]

Description

This pull request adds a script to perform tomographic reconstructions of the transverse phase space of electron beam using the maximum entropy method (MENT) described in:
J. J. Scheins. Tomographic Reconstruction of Transverse and Longitudinal Phase Space Distributions using the Maximum Entropy Algorithm. DESY, May 10, 2004.

Objective

The goal is to reconstruct the beam's phase space at the end of the LINAC, using quadrupole scans and the emittance measurement screen.

Implementation

Script ment_reconstruction.py
The script reconstructs two-dimensional distributions from their one-dimensional projections. It includes the following main classes:

1. ScreenProcess
   Responsible for processing screen images. It provides functionalities such as scaling, cropping, and extracting projections from images.
2. ConvexPolygon
   Defines a grid of convex polygons constructed from the intersection of lines derived from the projections bins and transformed by transformation matrices
3. DistribReconstruction
   It performs the reconstruction of the beam distribution using the provided projections and applying MENT algorithm.

Additionally, the script includes auxiliary functions to facilitate visualization such as plot_lines, plot_convex, paint_convex.

Script trans_matrices.py
This script implements typical two-dimensional matrices used in ConvexPolygon to transform projection bins.

Notebook reconstruction_from_grid.ipynb
It demonstrates the method's implementation, using a simulated two-dimensional gaussian distribution

Testing, Validation and Next Steps

Initial tests were performed with simulated data in the notebook. The results indicate that the method successfully reconstructs gaussian distributions. The method are being used to reconstruct images from LINAC's screens.

[fernandohds564]

Very nice @otavio-silveira. Please, put the notebook in the examples folder, in the root directory.