.. _irena-reflectivity:
.. _model.reflectivity:

.. index::
    model; Reflectivity

Reflectivity
============

.. Figure:: media/Reflectivity1.png
   :align: left
   :width: 300px
   :figwidth: 320px

This tool models and fits X-ray and neutron reflectivity for up to 8 layers
using the recursive Parratt algorithm (L. G. Parratt, *Phys. Rev.*, **95**(2),
359–369, 1954). The underlying code was provided by Andrew Nelson
(Andrew_Nelson@users.sourceforge.net). The GUI follows the conventions of the
rest of the Irena package.

For more complex fitting than this tool supports, use Andy Nelson's more capable
package *Motofit*, available at http://motofit.sourceforge.net/ under the GNU
license. When publishing results from this tool, cite:

   A. Nelson, "Co-refinement of multiple-contrast neutron/X-ray reflectivity
   data using MOTOFIT," *J. Appl. Cryst.* (2006), 39, 273–276.

**Optional XOPs for speed**

The code supports the optional ``abeles.xop`` and ``GenCurveFit.xop``.
Both are optional, but ``abeles.xop`` provides a 5–10× speedup. Both can be
downloaded from Andrew Nelson's website (see above).

Use
---

A sample 3-column reflectivity dataset is included in the Irena folder
(``…Wavemetrics/Igor Pro/User Procedures/Irena/reflectivity.txt``). Load it
through the Data loading tool as QRS data.

Select "*Reflectivity*" from the SAS menu.

**Panel sections:**

1. :ref:`Standard data selection tools <DataSelection>` at the top. Select
   data type, folder, and wave names for Q, reflectivity, and error. Click
   "*Graph*" to generate the graphs. For a single-value Q-resolution, uncheck
   the "*Resolution?*" checkbox and enter the value; for a Q-resolution wave,
   select its wave name here. The resolution wave must be in the same folder
   as the data and must have the same number of points.

2. Additional options:

   - "*Oversample model?*" — calculates the model at 5× the number of input
     data points. Useful for sparse data (e.g., neutron reflectivity).
   - "*0 at the substrate*" — counts thickness starting from the substrate
     rather than from the top (default is from the top).
   - "*L1 at the substrate*" — counts layers from the substrate rather than
     from the top.

3. Select the number of layers. Enter the SLD of the top environment (typically
   air, so 0; for measurements under water, adjust accordingly). Each tab
   contains controls for one layer: thickness (Å), real and imaginary SLD,
   and roughness.

4. Substrate roughness and SLD.

5. Flat (measurement) background.

6. Fit control buttons.

After selecting data, three graphs appear:

.. Figure:: media/Reflectivity2.png
   :align: left
   :width: 100%

The top graph is a log-log plot of reflectivity vs Q. The middle graph shows
reflectivity × Q\ :sup:`n` (n = 0 to 4, selectable in the panel). The bottom
graph shows the SLD profile. Fitting is performed in reflectivity × Q\ :sup:`n`
space to improve numerical stability. Data range selection with cursors must be
done in the **top** (log-log) graph.

Example with known parameters (two-layer system):

.. Figure:: media/Reflectivity3.png
   :width: 45%
.. Figure:: media/Reflectivity4.png
   :width: 45%

Enter these layer values and a substrate SLD of 2.073 (real part) and 2.37×10\ :sup:`-6`
(imaginary part). Set resolution to 1% (uncheck the resolution wave checkbox and
enter 1%). Click "*Graph model*" to compare the model to data:

.. Figure:: media/Reflectivity5.png
   :align: left
   :width: 100%

Adjust parameters to explore sensitivity.

Control details
~~~~~~~~~~~~~~~

**Resolution wave** — Q-resolution input options: fixed percentage (e.g., 1%
of Q), a wave containing percentage values per point, a wave containing ΔQ
per point, or a wave containing (ΔQ)\ :sup:`2` per point.

**Auto update** — recalculates the model after each parameter change. Required
for slider use. Disable on slow computers.

**Scale data** — apply a scaling factor to match reflectivity to 1 at Q = 0.

**Use errors** — includes uncertainty values in the fit. Fitting without
uncertainties may be unreliable.

**Fitting** — Select the data range with cursors in the top graph and click
"*Fit model*". Fitting is performed in reflectivity × Q\ :sup:`n` space;
using n = 4 is recommended to avoid neglecting high-Q data. If the fit
fails but reaches a partial solution, "*Reverse fit*" restores the pre-fit
parameters.

For best results, use :ref:`Genetic optimization <important.GeneticOptimization>`.
Genetic optimization requires realistic low and high parameter limits.

**Insert/remove layer** — adds or removes a layer from the current model.

**Parameter linking** — links two parameters together (e.g., if one is known
to be N × another), allowing them to be fit simultaneously.

**Save data** — copies model data into the data folder for future use. When
reloading data from a folder that already contains reflectivity results, the
option to restore the previous solution is offered.

**Export data** — saves an ASCII file for external use. This option is
deprecated; the preferred approach is to use "*Save data*" and then the ASCII
data export tool.

.. note::

   For fitting requirements beyond what this tool supports, use Motofit
   (http://motofit.sourceforge.net/wiki/index.php/Main_Page).