.. include:: /substitutions.rst

.. _rfactoranalysis:

Rfactor_analysis
================

The Rfactor_analysis files (Rfactor_analysis_refcalc.pdf and
Rfactor_analysis_superpos.pdf) plot the results of the |R-factor|
calculations, as well as rudimentary analysis.

The topmost plot on each page is the same as given in the
:ref:`Rfactor_plots.pdf<Rfactorplots>` files, i.e., the theoretical and 
experimental |IV| curves for a given beam, as well as the |R factor|.

The second plot shows the Y functions (see, e.g.,
:cite:t:`pendryReliabilityFactorsLEED1980`) of the |IV| curves, and the
difference between the two. Since the |R factor| is determined  by integrating
the squared difference between the Y functions, this plot gives a  rough
idea where the main contributions to the |R factor| come from.

Finally, the third plot on each page makes this more explicit by  plotting
the cumulative sum of the squared difference between the Y functions
:math:`\frac{(Y_1 - Y_2)^2}{(Y_1^2 + Y_2^2)}`, which is the term used 
in the Pendry |R factor|. This allows quick identification of the areas 
contributing most to the |R factor|.


.. figure:: /_static/output_examples/Rfactor_analysis_refcalc_example.svg
   :width: 60%
   :align: center

   An |R-factor| analysis plots for a single beam calculated in the example
   on the Hematite :math:`(012)-(1 \times 1)` surface discussed
   :ref:`here<example_Fe2O3>`.