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PolarizationEfficienciesWildes v1

Summary

Calculates the efficiencies of the polarizer, flippers and the analyser for a two-flipper instrument setup.

See Also

PolarizationCorrectionWildes

Properties

Name	Direction	Type	Default	Description
InputNonMagWorkspace	Input	WorkspaceGroup	Mandatory	Group workspace containing the transmission measurements for the non-magnetic sample
InputMagWorkspace	Input	WorkspaceGroup		Group workspace containing the transmission measurements for the magnetic sample.
Flippers	Input	string	00,01,10,11	Flipper configurations of the input group workspace(s).
InputPolarizerEfficiency	Input	MatrixWorkspace		Workspace containing the known wavelength-dependent efficiency for the polarizer.
InputAnalyserEfficiency	Input	MatrixWorkspace		Workspace containing the known wavelength-dependent efficiency for the analyser.
OutputFpEfficiency	Output	MatrixWorkspace	Mandatory	Output workspace containing the polarizing flipper efficiencies
OutputFaEfficiency	Output	MatrixWorkspace	Mandatory	Output workspace containing the analysing flipper efficiencies
OutputPolarizerEfficiency	Output	MatrixWorkspace		Output workspace containing the polarizer efficiencies.
OutputAnalyserEfficiency	Output	MatrixWorkspace		Output workspace containing the analyser efficiencies.
IncludeDiagnosticOutputs	Input	boolean	False	Whether to include additional diagnostic outputs.
OutputPhi	Output	MatrixWorkspace	phi	Output workspace containing the values for Phi.
OutputRho	Output	MatrixWorkspace	rho	Output workspace containing the values for Rho.
OutputAlpha	Output	MatrixWorkspace	alpha	Output workspace containing the values for Alpha.
OutputTwoPMinusOne	Output	MatrixWorkspace	two_p_minus_one	Output workspace containing the values for the term (2p-1).
OutputTwoAMinusOne	Output	MatrixWorkspace	two_a_minus_one	Output workspace containing the values for the term (2a-1).

Description

This algorithm calculates the instrument component efficiencies in a polarized analysis experiment by implementing the Wildes [1] approach for calibrating an instrument with two flippers.

A non-magnetic transmission run should be provided via the InputNonMagWorkspace property. This can be used to calculate both flipper efficiencies and phi, as follows:

\[\phi = \frac{(I^{00}_{1} - I^{01}_{1})(I^{00}_{1} - I^{10}_{1})}{I^{00}_{1}I^{11}_{1} - I^{01}_{1}I^{10}_{1}}\]

\[f_p = \frac{I^{00}_{1} - I^{01}_{1} - I^{10}_{1} + I^{11}_{1}}{2(I^{00}_{1} - I^{01}_{1})}\]

\[f_a = \frac{I^{00}_{1} - I^{01}_{1} - I^{10}_{1} + I^{11}_{1}}{2(I^{00}_{1} - I^{10}_{1})}\]

The algorithm will only be able to calculate polarizer and/or analyser efficiencies if you also provide a magnetic transmission run via the InputMagWorkspace property. This can used to calculate the polarizer and analyser efficiencies as follows:

\[(2p-1)^2 = \phi\Bigg(\frac{(1-2f_a)I^{00}_{2} + (2f_a-1)I^{10}_{2} - I^{01}_{2} + I^{11}_{2}}{(1-2f_p)I^{00}_{2} + (2f_p-1)I^{01}_{2} - I^{10}_{2} + I^{11}_{2}}\Bigg)\]

From which you can solve for the polarizer efficiency (\(p\)) and then solve for the analyser efficiency (\(a\)) from the following relationship:

\[\phi = (2p-1)(2a-1)\]

Alternatively, previously calculated polarizer and/or analyser efficiency workspaces can be passed to the InputPolarizerEfficiency and InputAnalyserEfficiency properties respectively. If workspaces are provided for both then they are used directly as the output polarizer and analyser efficiencies. If only one is provided then it is used to solve for the other efficiency.

Both types of input workspace group should contain four child workspaces. A flipper configuration must be passed to the Flippers property to identify which child workspaces in the input group(s) correspond to which instrument configurations. The Flippers property takes a string in the form '00, 01, 10, 11', which would indicate both flippers off, analyzer flipper on, polarizer flipper on, both flippers on. The flipper configuration can be provided in any order that matches the child workspaces in the input group(s).

Outputs

As a minimum, the algorithm calculates the polarizing and analysing flipper efficiencies, producing two output workspaces that give these values as a function of wavelength.

If the OutputPolarizerEfficiency property is set then an output workspace will be produced giving the polarizer efficiency as a function of wavelength.

If the OutputAnalyserEfficiency property is set then an output workspace will be produced giving the analyser efficiency as a function of wavelength.

If property IncludeDiagnosticOutputs is set to True then the following diagnostic output workspace properties will be set, again with values calculated as a function of wavelength:

• OutputPhi - outputs the value that was calculated for \(\phi\).

• OutputRho - calculates \(2f_p - 1\).

• OutputAlpha - calculates \(2f_a - 1\).

• OutputTwoPMinusOne - calculates \(2p-1\). This will only be included in the diagnostic output if the OutputPolarizerEfficiency property has also been set.

• OutputTwoAMinusOne - calculates \(2a-1\). This will only be included in the diagnostic output if the OutputAnalyserEfficiency property has also been set.

Workspace names are automatically provided for each of the diagnostic outputs (see the property default values), but can be overwritten if desired.

Usage

Example - PolarizationEfficienciesWildes

ws00 = CreateSampleWorkspace(XUnit="Wavelength", NumBanks=1, BankPixelWidth=1, Function="User Defined", UserDefinedFunction="name=UserFunction, Formula=x*0+12")
ws01 = CreateSampleWorkspace(XUnit="Wavelength", NumBanks=1, BankPixelWidth=1, Function="User Defined", UserDefinedFunction="name=UserFunction, Formula=x*0+1")
ws10 = CreateSampleWorkspace(XUnit="Wavelength", NumBanks=1, BankPixelWidth=1, Function="User Defined", UserDefinedFunction="name=UserFunction, Formula=x*0+2")
ws11 = CreateSampleWorkspace(XUnit="Wavelength", NumBanks=1, BankPixelWidth=1, Function="User Defined", UserDefinedFunction="name=UserFunction, Formula=x*0+10")

nonMag = GroupWorkspaces([ws00, ws01, ws10, ws11])

wsM00 = CreateSampleWorkspace(XUnit="Wavelength", NumBanks=1, BankPixelWidth=1, Function="User Defined", UserDefinedFunction="name=UserFunction, Formula=x*0+6")
wsM01 = CreateSampleWorkspace(XUnit="Wavelength", NumBanks=1, BankPixelWidth=1, Function="User Defined", UserDefinedFunction="name=UserFunction, Formula=x*0+0.2")
wsM10 = CreateSampleWorkspace(XUnit="Wavelength", NumBanks=1, BankPixelWidth=1, Function="User Defined", UserDefinedFunction="name=UserFunction, Formula=x*0+0.3")
wsM11 = CreateSampleWorkspace(XUnit="Wavelength", NumBanks=1, BankPixelWidth=1, Function="User Defined", UserDefinedFunction="name=UserFunction, Formula=x*0+1")

mag = GroupWorkspaces([wsM00, wsM01, wsM10, wsM11])

PolarizationEfficienciesWildes('nonMag', 'mag', Flippers='00,01,10,11', IncludeDiagnosticOutputs=False, OutputFpEfficiency="fp", OutputFaEfficiency="fa", OutputPolarizerEfficiency="p", OutputAnalyserEfficiency="a")
fp = AnalysisDataService.retrieve("fp")
print("Polarizing flipper efficiency is: {:.4}".format(fp.readY(0)[0]))

Output:

Polarizing flipper efficiency is: 0.8636

References

[1]

A. R. Wildes, Neutron News, 17 17 (2006) doi: 10.1080/10448630600668738

Categories: AlgorithmIndex | Reflectometry\PolarizationCorrections

Source

C++ header: PolarizationEfficienciesWildes.h

C++ source: PolarizationEfficienciesWildes.cpp