\(\renewcommand\AA{\unicode{x212B}}\)

CarpenterSampleCorrection v1

CarpenterSampleCorrection dialog.

Summary

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

See Also

CalculateCarpenterSampleCorrection, CylinderAbsorption, MonteCarloAbsorption, MayersSampleCorrection, PearlMCAbsorption, VesuvioCalculateMS

This algorithm is also known as: MultipleScatteringCylinderAbsorption

Properties

Name	Direction	Type	Default	Description
InputWorkspace	Input	MatrixWorkspace	Mandatory	The name of the input workspace.
OutputWorkspace	Output	MatrixWorkspace	Mandatory	The name of the output workspace.
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

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 calls CalculateCarpenterSampleCorrection v1 to calculate both absorption and multiple scattering corrections and then applies both to the sample workspace.

Usage

Example: 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 = CarpenterSampleCorrection(ws,CylinderSampleRadius=0.2)

print("Output:  {}".format(wsOut.readY(0)))

Output:

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: CarpenterSampleCorrection.h

C++ source: CarpenterSampleCorrection.cpp