\(\renewcommand\AA{\unicode{x212B}}\)

PolarizationCorrectionWildes v1¶

Summary ¶

Corrects a group of polarization analysis workspaces for polarizer and analyzer efficiencies.

Properties ¶

Name	Direction	Type	Default	Description
InputWorkspaces	Input	str list	Mandatory	A list of workspaces to be corrected corresponding to the flipper configurations.
OutputWorkspace	Output	WorkspaceGroup	Mandatory	A group of polarization efficiency corrected workspaces.
Flippers	Input	string	00, 01, 10, 11	Flipper configurations of the input workspaces. Allowed values: [‘00, 01, 10, 11’, ‘00, 10, 11’, ‘00, 01, 11’, ‘00, 11’, ‘0, 1’, ‘0’]
Efficiencies	Input	MatrixWorkspace	Mandatory	A workspace containing the efficiency factors P1, P2, F1 and F2 as histograms

This algorithm corrects for non-ideal instrument component efficiencies in a polarization analysis experiment by following the procedure and conventions introduced by Wildes [1]. In the full polarization analysis case it solves the corrected count rates \(\Sigma^{++}\), \(\Sigma^{+-}\), \(\Sigma^{-+}\) and \(\Sigma^{--}\) from the equation

\[\begin{split}\begin{bmatrix} \Sigma^{++} \\ \Sigma^{+-} \\ \Sigma^{-+} \\ \Sigma^{--} \end{bmatrix} = \bm{M} \begin{bmatrix} I^{00} \\ I^{01} \\ I^{10} \\ I^{11} \end{bmatrix},\end{split}\]

where \(I^{jk}\) are the experimental count rates for flipper configuration \(jk\) and \(\bm{M}\) is the four-by-four correction matrix as defined by equations (4) in [1].

Flipper configurations ¶

InputWorkspaces is a list containing one to four workspace names (X unit: wavelength) corresponding to the instrument configurations given as Flippers. Supported configurations are:

'00, 01, 10, 11': Full polarization corrections. Four input workspaces are required. They should be in the input group in the following order: both flippers off, analyzer flipper on, polarizer flipper on, both flippers on.
'00, 01, 11' and '00, 10, 11': Polarization corrections with the assumption that the corrected count rates \(\Sigma^{+-} = \Sigma^{-+}\). In this case the intensity of the missing flipper configuration (01 or 10) can be solved from the other intensities. Workspaces in the input group should be in the following order: both flippers off, one flipper on, both flippers on.
'00, 11': Polarization corrections with the assumption that the corrected count rates \(\Sigma^{+-} = \Sigma^{-+} = 0\). In this case the intensities of the missing flipper configurations (01 and 10) can be solved from the other intensities. Workspaces in the input group should be in the following order: both flippers off, both flippers on.
'0, 1': Polarization corrections when no analyzer has been used. Workspaces in the input group should be in the following order: polarizer flipper off, polarizer flipper on.
'0': Polarization corrections for a direct beam measurement in a reflectometry experiment.

Output ¶

The algorithm’s output is a group workspace containing the corrected workspaces. The names of each corrected workspace is prefixed by _++, _+-, _-+ or _-- depending on which \(\Sigma^{mn}\) they correspond to.

Efficiency factors ¶

The Efficiencies input property expects to get a workspace with the following properties:

Contains four histograms, each labeled by their vertical axis as P1, P2, F1, F2. Other histograms (if present) are ignored.
The Y values of each histogram should be the corresponding efficiencies as functions of wavelength as defined in [1].
The wavelength values (X values) should be the same is in the input workspaces.

Note

Users at ILL can load a conforming efficiency workspace from disk by LoadILLPolarizationFactors v1.

Error propagation ¶

Note

Errors are calculated as per Wildes [1], except for the numerically solved intensity in '00, 01, 11' and '00, 10, 11' flipper configurations in which case the uncertainties of \(\Sigma^{+-}\) or \(\Sigma^{-+}\) are set to zero.

Usage ¶

Note

To run these usage examples please first download the usage data, and add these to your path. In Mantid this is done using Manage User Directories.

Example - PolarizationEfficiencyCor

LoadILLReflectometry(
    Filename='ILL/D17/317370.nxs',
    OutputWorkspace='direct_beam',
    XUnit='TimeOfFlight')
LoadILLReflectometry(
    Filename='ILL/D17/317370.nxs',
    OutputWorkspace='reflected_beam',
    Measurement='ReflectedBeam',
    BraggAngle=0.8,
    XUnit='TimeOfFlight')
# Sum pixels containing the reflected intensity
GroupDetectors(
    InputWorkspace='reflected_beam',
    OutputWorkspace='reflected_beam',
    WorkspaceIndexList=[199, 200, 201, 202, 203, 204, 205])
ConvertUnits(
    InputWorkspace='reflected_beam',
    OutputWorkspace='reflected_beam',
    Target='Wavelength',
    EMode='Elastic')
# There are some unphysical wavelengths
CropWorkspace(
    InputWorkspace='reflected_beam',
    OutputWorkspace='reflected_beam',
    XMin=0.)
# Fake two flipper configurations
RenameWorkspace(
    InputWorkspace='reflected_beam',
    OutputWorkspace='up'
)
CloneWorkspace(
    InputWorkspace='up',
    OutputWorkspace='down'
)
Scale(
    InputWorkspace='down',
    OutputWorkspace='down',
    Factor=0.1
)
LoadILLPolarizationFactors(
    Filename='ILL/D17/PolarizationFactors.txt',
    OutputWorkspace='efficiencies',
    WavelengthReference='up')
PolarizationEfficiencyCor(
    InputWorkspaces='up, down',
    OutputWorkspace='corrected',
    Efficiencies='efficiencies',
    Flippers='00, 11')

orig = mtd['up']
corr = mtd['corrected_++']
index = orig.yIndexOfX(15.)
ratio_up = corr.readY(0)[index] / orig.readY(0)[index]
print("Ratio of corrected and original 'up' intensity at 15A: {:.4}".format(ratio_up))
orig = mtd['down']
corr = mtd['corrected_--']
index = orig.yIndexOfX(15.)
ratio_down = corr.readY(0)[index] / orig.readY(0)[index]
print("Ratio of corrected and original 'down' intensity at 15A: {:.4}".format(ratio_down))

Output:

Ratio of corrected and original 'up' intensity at 15A: 0.1062
Ratio of corrected and original 'down' intensity at 15A: 10.38

References ¶

Categories: AlgorithmIndex | Reflectometry

Source ¶

C++ header: PolarizationCorrectionWildes.h

C++ source: PolarizationCorrectionWildes.cpp