Creating a Model

The main component of an experiment in EasyReflectometry is the Model. This is a description of the Sample and the environment in which the experiment is performed. The Model is used to calculate the reflectivity of the Sample at a given set of angles (Q-points). The resolution functions are used to quantify the experimental uncertainties in wavelength and angle, allowing the Model to accurately describe the data.

Model

A Model instance contains a Sample and variables describing experimental settings. To be able to compute reflectivities it is also necessary to have a Calculator (interface).

from easyreflectometry.calculators import CalculatorFactory
from easyreflectometry.model import Model
from easyreflectometry.sample import Sample

default_sample = Sample()
model = Model(sample=default_sample, scale=1.0, background=1e-6)

interface = CalculatorFactory()
model.interface = interface

This will create a Model instance with the default_sample and the environment variables scale factor set to 1.0 and a background of 1e-6. Following the interface is set to the default calculator that is Refnx.

Resolution Functions

A resolution function enables the EasyReflectometry model to incorporate the experimental uncertainties in wavelength and incident angle into the model. In its essence the resolution function controls the smearing to apply when determining the reflectivity at a given Q-point. For a given Q-point the smearing to apply is given as a weighted average of the neighboring Q-point, which weights are by a normal distribution. This normal distribution is then defined by a Q-point dependent Full Width at the Half Maximum (FWHM) that is given by the resolution function.

PercentageFwhm

Often we rely on a resolution function that has a simple functional dependency of the Q-point. By this is understood that the applied smearing in a Q-point has a FWHM that is simply a percentage of the value of the Q-point.

from easyreflectometry.model import Model
from easyreflectometry.model import PercentageFwhm

resolution_function = PercentageFwhm(1.1)

m = Model(resolution_function=resolution_function)

This will create a Model instance where the resolution function is defined as 1.1% of the Q-point value, which again is the FWHM for the smearing.

LinearSpline

Alternatively the FWHM value might be determined and declared directly for each measured Q-point. When this is the case the provided Q-points and the corresponding FWHM values can be used to declare a linear spline function and thereby enable a determination of the reflectivity at an arbitrary point within the provided range of discrete Q-points.

from easyreflectometry.model import Model
from easyreflectometry.model import LinearSpline

m = Model()

resolution_function = LinearSpline(q_data_points=[0.01, 0.2, 0.31], fwhm_values=[0.001, 0.043, 0.026])

m.resolution_function = resolution_function

This will create a Model instance where the resolution function defining the FWHM is determined from a linear interpolation. In the present case the provided data Q-points are ([0.01, 0.2, 0.31]) and the corresponding FWHM function values are ([0.001, 0.043, 0.026]).