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# CalculateCarpenterSampleCorrection v1¶

## Summary¶

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

## 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

Input

number

0.3175

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



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")

# 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)



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,

# 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)



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]