Add Supermirror Polarizer Efficiency Algorithm

Re-release as I can't push directly to @jclarkeSTFC's fork

37180

New algorithm to calculate the supermirror polarizer efficiency using a group workspace containing spin states, plus the efficiency of the analyser cell, calculated previously. This is part of the polarized SANS epic.

Output can either be to a workspace, a file, or both.

Fixes #36139

Summary of work

Added algorithm
Added tests
Added doc page

Further detail of work

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, e_cell, is given by AnalyserEfficiency.

The polarization of the polarizer, $P_{SM}$, is given by

$$ \huge P{SM} = \frac{T{00} - T{01}}{2P{cell}(T{00} + T{01})} = \frac{T{00} - T{01}}{2(2\epsilon{cell} - 1)(T{00} + T_{01})} $$

Since the efficiency, $\epsilon{SM}$ , is given by $\frac{1 + P{SM}}{2}$, we have that

$$ \huge \epsilon{SM} = \frac{1}{2} + \frac{T{00} - T{01}}{4(2\epsilon{cell} - 1)(T{00} + T{01})} $$

Error correction:

$$ \huge \sigma{\epsilon{SM}} = \sqrt{|\frac{\delta \epsilon{SM}}{\delta T{00}}|^2 \sigma^2{T{00}} + |\frac{\delta \epsilon{SM}}{\delta T{01}}|^2 \sigma^2{T{01}} + |\frac{\delta \epsilon{SM}}{\delta \epsilon{cell}}|^2 * \sigma^2{\epsilon{cell}}} $$

where:

$$ \huge \frac{\delta \epsilon{SM}}{\delta T{00}} = \frac{T{01}}{2(2\epsilon{cell} - 1)(T{00} + T{01})^2} $$

$$ \huge \frac{\delta \epsilon{SM}}{\delta T{01}} = \frac{-T{00}}{2(2\epsilon{cell} - 1)(T{00} + T{01})^2} $$

$$ \huge \frac{\delta \epsilon{SM}}{\delta \epsilon{cell}} = \frac{T{01} - T{00}}{2(2\epsilon{cell} - 1)^2(T{00} + T_{01})} $$

To test:

This will generate a simple example:

wsPara = CreateSampleWorkspace('Histogram', Function='User Defined', UserDefinedFunction='name=UserFunction,Formula=0.5*exp(-0.0733*12*x*(1-0.9))',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+0.9))',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='16', 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]))

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