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PolarizerEfficiency v1

Summary

Calculates the efficiency of a polarizer.

Properties

Name	Direction	Type	Default	Description
InputWorkspace	Input	WorkspaceGroup	Mandatory	Input group workspace to use for polarization calculation
AnalyserEfficiency	Input	MatrixWorkspace	Mandatory	Analyser efficiency as a function of wavelength
OutputWorkspace	Output	MatrixWorkspace		Polarizer efficiency as a function of wavelength
SpinStates	Input	string	11,10,01,00	Order of individual spin states in the input group workspace, e.g. “01,11,00,10”
OutputFilePath	Input	string		File name or path for the output to be saved to.

Description

Calculates how the efficiency of a polarizer varies with wavelength. The ordering of the workspaces in InputWorkspace is taken from the SpinStates parameter, and the analyser efficiency, \(\epsilon_{cell}\), is given by AnalyserEfficiency.

The polarization of the polarizer, \(P_{SM}\), is given by [1]

\[P_{SM} = \frac{T_{00} - T_{01}}{2P_{cell}(T_{00} + T_{01})}\]

Since the efficiency, \(\epsilon_{SM}\), is given by \(\frac{1 + P_{SM}}{2}\), we have that

\[\epsilon_{SM} = \frac{1}{2} + \frac{T_{00} - T_{01}}{2(2\epsilon_{cell} - 1)(T_{00} + T_{01})}\]

The error in the calculation can then be determined thus:

\[\sigma_{\epsilon_{SM}} = \sqrt{|\frac{\partial \epsilon_{SM}}{\partial T_{00}}|^2 * \sigma^2_{T_{00}} + |\frac{\partial \epsilon_{SM}}{\partial T_{01}}|^2 * \sigma^2_{T_{01}} + |\frac{\partial \epsilon_{SM}}{\partial \epsilon_{cell}}|^2 * \sigma^2_{\epsilon_{cell}}}\]

where:

\[\frac{\partial \epsilon_{SM}}{\partial T_{00}} = \frac{T_{01}}{(2\epsilon_{cell} - 1)(T_{00} + T_{01})^2}\]

\[\frac{\partial \epsilon_{SM}}{\partial T_{01}} = \frac{-T_{00}}{(2\epsilon_{cell} - 1)(T_{00} + T_{01})^2}\]

\[\frac{\partial \epsilon_{SM}}{\partial \epsilon_{cell}} = \frac{T_{01} - T_{00}}{(2\epsilon_{cell} - 1)^2(T_{00} + T_{01})}\]

Usage

Example - Calculate Polarizer Efficiency

wsPara = CreateSampleWorkspace('Histogram', Function='User Defined', UserDefinedFunction='name=UserFunction,Formula=0.5*exp(-0.0733*12*x*(1-0.1))',XUnit='Wavelength', xMin='1',XMax='8', BinWidth='1', NumBanks='1', BankPixelWidth='1')
wsPara1 = CloneWorkspace(wsPara)
wsAnti = CreateSampleWorkspace('Histogram', Function='User Defined', UserDefinedFunction='name=UserFunction,Formula=0.5*exp(-0.0733*12*x*(1+0.1))',XUnit='Wavelength', xMin='1',XMax='8', BinWidth='1', NumBanks='1', BankPixelWidth='1')
wsAnti1 = CloneWorkspace(wsAnti)

grp = GroupWorkspaces([wsPara,wsAnti,wsPara1,wsAnti1])
eCell = CreateSampleWorkspace('Histogram', Function='User Defined', UserDefinedFunction='name=UserFunction,Formula=(1 + tanh(0.0733 * 12 * x * 0.2))/2',XUnit='Wavelength', xMin='1',XMax='8', BinWidth='1', NumBanks='1', BankPixelWidth='1')

psm = PolarizerEfficiency(grp, eCell)
print("Polarizer efficiency at a wavelength of " + str(mtd['psm'].dataX(0)[3]) + " Å is " + str(mtd['psm'].dataY(0)[3]))

Output:

Polarizer efficiency at a wavelength of 4.0 Å is ...

References

[1]

Polarization-analyzed small-angle neutron scattering. I. Polarized data reduction using Pol-Corr, Kathryn Krycka et al, Journal of Applied Crystallography, 45 (2012), 546-553 doi: 10.1107/S0021889812003445

Categories: AlgorithmIndex | SANS\PolarizationCorrections

Source

C++ header: PolarizerEfficiency.h

C++ source: PolarizerEfficiency.cpp