Add initial documentation

Add synthetic data tutorial
Add read the docs setup

source/index.rst

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+.. AMBER documentation master file, created by
+   sphinx-quickstart on Fri Apr 11 10:48:14 2025.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+AMBER documentation
+===================
+
+This is the documentation for the **A** lgorithm for **M** ultiplexing spectrometer
+**B** ackground **E** stimation with **R** otation-independence **AMBER** which is a method to estimate and background within 3D data sets. 
+
+This software is the result of the collaboration between the instrument responsible at the `CAMEA <https://www.psi.ch/en/sinq/camea>`_ beamline at SINQ, at the 
+`Paul Scherrer Institut <https://psi.ch/>`_ with the `Swiss Data Science Center <https://www.datascience.ch/>`_ through the "Data Science for Multiplexing Spectrometers" (DS4MS) project supported by 
+the fifth call for Collaborative Research Data Science Projects. 
+
+
+Badges
+------
+
+.. image:: https://gitea.psi.ch/lass_j/AMBER/actions/workflows/test.yaml/badge.svg
+  :width: 200
+  :alt: Test Status
+
+
+
+
+
+
+Installation
+------------
+Installation can be done through PyPI using
+
+.. code-block::
+
+   python -m pip install AMBER
+
+Alternatively, the newest version can be installed directly from the source repository through
+
+.. code-block::
+
+   python -m pip install git https://gitea.psi.ch/lass_j/AMBER.git@master
+
+
+General Introduction
+--------------------
+
+
+**AMBER** has been developed with multiplexing neutron spectrometers in mind, i.e. a novel version of the triple axis instrument which acquires multiple data points simultaneously. 
+However, the algorithm is more general and can be utilized on data with other origins. 
+
+The main requirements of the data are
+
+#. Rotation independence of the background in two out of three directions.
+#. Smooth change of background along all directions 
+#. The signal is sparse but continuous in all directions
+
+**AMBER** minimizes the following cost function for the signal and background given the set of parameters :math:`\lambda`, :math:`\beta`, and :math:`\mu` on a voxelated data set:
+
+.. math::
+    \min_{X,b} \frac{1}{2}\lVert Y-X-\mathcal{R}b\rVert_{2}^2+\lambda\vert| X |\vert_{1} +\frac{\beta}{2} \mathrm{Tr} \left( b^T L_{b} b \right) +\frac{\mu}{2} \boldsymbol{1}_{n_x}^TX^T L_{\omega} X\boldsymbol{1}_{n_y}
+
+where :math:`Y`, :math:`X`, and :math:`b` are the measured signal, the subtracted signal and the rotation independent background, respectively. :math:`\mathcal{R}` is a rotation operator taking
+the radial :math:`b` to the full space. These three parameters constitute the fitting term while the rest are denoted penalty terms. :math:`\lambda` controls the weighing of sparcity of the subtracted signal gauge through the L-1 norm
+:math:`\vert| X |\vert_{1}`, :math:`\beta` controls the smoothness of the background while :math:`\mu` the smoothness of the subtracted signal. 
+
+For further details, see the the paper. 
+
+
+
+
+
+Documentation & Tutorials
+-------------------------
+
+For **AMBER** the following tutorials have been created
+
+
+.. toctree::
+   :maxdepth: 2
+   :caption: Contents:
+
+
+   tutorials/index.rst
+
+
+Contribute
+----------
+
+
+
+Contact
+-------
+
+