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CalculateCarpenterSampleCorrection v1

Summary

Calculates both absorption and multiple scattering corrections, originally used to correct vanadium spectrum at IPNS.

See Also

CarpenterSampleCorrection, CylinderAbsorption, MonteCarloAbsorption, MayersSampleCorrection, PearlMCAbsorption, VesuvioCalculateMS

Properties

Name	Direction	Type	Default	Description
InputWorkspace	Input	MatrixWorkspace	Mandatory	The name of the input workspace.
OutputWorkspaceBaseName	Output	WorkspaceGroup	Mandatory	Basename of the output workspace group for corrections.Absorption suffix = ‘_abs’. Multiple Scattering suffix = ‘_ms’.
AttenuationXSection	Input	number	2.8	Coefficient 1, absorption cross section / 1.81 if not set with SetSampleMaterial
ScatteringXSection	Input	number	5.1	Coefficient 3, total scattering cross section if not set with SetSampleMaterial
SampleNumberDensity	Input	number	0.0721	Coefficient 2, density if not set with SetSampleMaterial
CylinderSampleRadius	Input	number	0.3175	Sample radius, in cm
Absorption	Input	boolean	True	If True then calculates the absorption correction.
MultipleScattering	Input	boolean	True	If True then calculates the multiple scattering correction.

Description

This algorithm is a port to C++ of a multiple scattering absorption correction, used to correct the vanadium spectrum for the GPPD instrument at the IPNS. The correction calculation was originally worked out by Jack Carpenter and Asfia Huq and implemented in Java by Alok Chatterjee. The java code was translated to C++ in Mantid by Dennis Mikkelson.

• Elastic scattering is assumed

In [1] we see that the calculation of the attenuation factor F involves an integral over the sample cylinder. By expanding the integrands as a power series, we can factor out any dependence on scattering cross section and radius. These integral terms are denoted by \(Z_{mn}\) and so we may write:

\[\frac{1}{F} = \sum_{m=0}^\infty\sum_{n=0}^\infty\frac{(-1)^{m+n}}{m!n!}(\mu R)^{m+n} Z_{mn}(\theta)\]

where \(\mu\) is the inverse scattering length.

The functions \(Z_{mn}(\theta)\) are written in terms of Chebyshev expansion coefficients:

\[Z_{mn}(\theta) = \sum_{s=0}^\infty c_{s}(m,n)cos(s\theta)\]

where the Chebyshev coefficients \(c_{s}(m,n)\) up to m + n \(\leqslant\) 5 have been tabulated and are stored as an array by the algorithm.

This version of the correction follows the implementation in [1] in that it only calculates for the correction in-plane, unlike [2], [3] that generalizes the correction to out-of-plane.

This algorithm calculates and outputs the absorption and/or multiple scattering correction workspaces to be applied to the InputWorkspace. Thus, there are, at most, two workspaces in the OutputWorkspaceBaseName group workspace. This allows for flexibility of applying either correction to a workspace without having to apply both (as is the case with CarpenterSampleCorrection v1). For the case where both corrections are calculated, the output will be the following:

1. The absorption correction workspace will be OutputWorkspaceBaseName + _abs and will be in .getItem(0).

2. The multiple scattering correction workspace will be OutputWorkspaceBaseName + _ms and will be in .getItem(1).

This is the child algorithm that CarpenterSampleCorrection v1 (previously known as MultipleScatteringCylinderAbsorption) uses to calculate and apply the correction to a sample workspace.

Usage

Example: Calculate corrections for a simple cylindrical sample

ws = CreateSampleWorkspace("Histogram",NumBanks=1,BankPixelWidth=1)
ws = ConvertUnits(ws,"Wavelength")
ws = Rebin(ws,Params=[1])
SetSampleMaterial(ws,ChemicalFormula="V")

#restrict the number of wavelength points to speed up the example
wsOut = CalculateCarpenterSampleCorrection(ws,CylinderSampleRadius=0.2)

print("Absorption Correction Output:  {}".format(wsOut.getItem(0).readY(0)))
print("Multiply Scattering Correction Output:  {}".format(wsOut.getItem(1).readY(0)))

Output:

Absorption Correction Output:  [0.85283805 0.79620318 0.74348494 0.69440412 0.64870017 0.62121997]
Multiply Scattering Correction Output:  [0.09633662 0.09991619 0.1034959  0.10705826 0.11058382 0.11280196]

To reproduce what CarpenterSampleCorrection v1 does, you can calculate and apply the correction as follows

Example: Apply correction for a simple cylindrical sample using getItem

ws = CreateSampleWorkspace("Histogram",NumBanks=1,BankPixelWidth=1)
ws = ConvertUnits(ws,"Wavelength")
ws = Rebin(ws,Params=[1])
SetSampleMaterial(ws,ChemicalFormula="V")

corrections = CalculateCarpenterSampleCorrection(ws,CylinderSampleRadius=0.2)

# Get absorption correction
absCorr = corrections.getItem(0)

# Get multiple scattering correction
msFactor  = corrections.getItem(1)
msCorr = Multiply(ws, msFactor)

# Apply absorption correction to workspace
ws_abs_corrected = Divide(ws, absCorr)

# Apply multiple scattering correction to workspace
ws_ms_corrected = Minus(ws, msCorr)

# Apply both corrections
wsOut = Minus(ws_abs_corrected, msCorr)

print("Absorption Corrected Output:  {}".format(ws_abs_corrected.readY(0)))
print("Multiple Scattering Corrected Output:  {}".format(ws_ms_corrected.readY(0)))
print("Combined Corrected Output:  {}".format(wsOut.readY(0)))

Output:

Absorption Corrected Output:  [ 6.66892661  7.14329517 21.0999759   8.1904963   8.76755487  2.51509668]
Multiple Scattering Corrected Output:  [ 5.13959844  5.11923959 14.06392099  5.07861898  5.05856725  1.38618331]
Combined Corrected Output:  [ 6.1210107   6.57502041 19.47638255  7.58160094  8.13860778  2.33885171]

Example: Apply correction for a simple cylindrical sample using getItem

ws = CreateSampleWorkspace("Histogram",NumBanks=1,BankPixelWidth=1)
ws = ConvertUnits(ws,"Wavelength")
ws = Rebin(ws,Params=[1])
SetSampleMaterial(ws,ChemicalFormula="V")

#restrict the number of wavelength points to speed up the example
basename = "corrections"
CalculateCarpenterSampleCorrection(ws,OutputWorkspaceBaseName=basename,
                                   CylinderSampleRadius=0.2)

# Get absorption correction
absCorr = mtd[basename+"_abs"]

# Get multiple scattering correction
msFactor = mtd[basename+"_ms"]
msCorr = Multiply(ws, msFactor)

# Apply absorption correction to workspace
ws_abs_corrected = Divide(ws, absCorr)

# Apply multiple scattering correction to workspace
ws_ms_corrected = Minus(ws, msCorr)

# Apply both corrections
wsOut = Minus(ws_abs_corrected, msCorr)

print("Absorption Corrected Output:  {}".format(ws_abs_corrected.readY(0)))
print("Multiple Scattering Corrected Output:  {}".format(ws_ms_corrected.readY(0)))
print("Combined Corrected Output:  {}".format(wsOut.readY(0)))

Output:

Absorption Corrected Output:  [ 6.66892661  7.14329517 21.0999759   8.1904963   8.76755487  2.51509668]
Multiple Scattering Corrected Output:  [ 5.13959844  5.11923959 14.06392099  5.07861898  5.05856725  1.38618331]
Combined Corrected Output:  [ 6.1210107   6.57502041 19.47638255  7.58160094  8.13860778  2.33885171]

References

[1] (1,2)

J.M. Carpenter Attenuation Correction Factor for Scattering from Cylindrical Targets Review of Scientific Instruments 40.4 (1969): 555. doi: 10.1063/1.1684003

[2]

D.F.R. Mildner, J.M. Carpenter, and C.A. Pelizzari Generalized Attenuation Correction Factor for Scattering from Cylindrical Targets Review of Scientific Instruments 45.4 (1974): 572. doi: 10.1063/1.1686687

[3]

D.F.R. Mildner and J.M.Carpenter Improvements to the Chebyshev Expansion of Attenuation Correction Factors for Cylindrical Samples. J Appl Crystallogr 23.5 (1990): 378–386 doi: 10.1107/S0021889890005258

Categories: AlgorithmIndex | CorrectionFunctions\AbsorptionCorrections

Source

C++ header: CalculateCarpenterSampleCorrection.h

C++ source: CalculateCarpenterSampleCorrection.cpp