$$\renewcommand\AA{\unicode{x212B}}$$

# CarpenterSampleCorrection v1¶

CarpenterSampleCorrection dialog.

## Summary¶

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

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

## 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



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