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ApplyPaalmanPingsCorrection v1

Summary

Applies a calculated absorption correction in the Paalman and Pings factor style.

Properties

Name	Direction	Type	Default	Description
SampleWorkspace	Input	MatrixWorkspace	Mandatory	Name for the input Sample workspace.
CorrectionsWorkspace	Input	WorkspaceGroup		Name for the input Corrections workspace.
CanWorkspace	Input	MatrixWorkspace		Name for the input Can workspace.
CanScaleFactor	Input	number	1	Factor to scale the can data
CanShiftFactor	Input	number	0	Amount by which to shift the container data
OutputWorkspace	Output	MatrixWorkspace	Mandatory	The output corrections workspace.
RebinCanToSample	Input	boolean	True	Enable or disable RebinToWorkspace on CanWorkspace.

Description

Applies absorption corrections calculated in the Paalman and Pings absorption factor format. The various partial absorption factors are denoted as \(A_{a,b}\) where the subscript \(a\) denotes the component the neutron is scattered from and \(b\) denotes the component where the neutron is absorbed. The various partial absorption factors, and what their names must contain in the CorrectionsWorkspace group are detailed in the table below. If any of the partial absorption factors are not supplied, they are assumed to be one.

Symbol	Scatter From	Absorbed By	Workspace Name
\(A_{s,s}\)	sample	sample	ass
\(A_{s,sc}\)	sample	sample and container	assc
\(A_{c,c}\)	container	container	acc
\(A_{c,sc}\)	container	sample and container	acsc

This algorithm can be used to apply absorption corrections calculated with PaalmanPingsMonteCarloAbsorption. It can also be used to apply absorption corrections calculated with either the CylinderPaalmanPingsCorrection or FlatPlatePaalmanPingsCorrection algorithms as well as the legacy indirect calculate corrections routine, providing that the sample and container are first converted to wavelength and the corrections are interpolated to match the sample as demonstrated in the example below.

All workspaces are converted into wavelength using the appropriate mode of ConvertUnits. Then CanShiftFactor is added to wavelength of the CanWorkspace. Then one of the two following equations is performed (dependent on the number of correction factors provided):

\[I_s = \frac{1}{A_{s,sc}} \left( I_{sc}^E - I_c^E K_c \frac{A_{c,sc}}{A_{c,c}} \right)\]

\[I_s = \frac{1}{A_{s,s}} \left( I_{sc}^E \right) - \frac{1}{A_{c,c}} \left( I_{c}^E \right)\]

The variables that are not defined above are

Variable	Parameter Name	Default
\(I_s\)	OutputWorkspace	N/A
\(I_{sc}^E\)	SampleWorkspace	N/A
\(I_{c}^E\)	CanWorkspace	0
\(K_c\)	CanScaleFactor	1
\(A_{a,b}\)	CorrectionsWorkspace	1

The workflow diagrams below are another representation of the equation above with the simplifications for when the various terms are missing or one.

Workflow

Depending on the input workspaces and correction factors provided to the algorithm it may operate in one of four ways, each of which is described on a separate workflow diagram.

Container Scale Only

In the case where only a container workspace and no correction factors are provided.

Sample Corrections Only

In the case where only correction factors and no container workspace is provided.

Two-Factor Approximation

In the case where a container workspace, along with the \(A_{s,s}\) and \(A_{c, c}\) factors are provided.

Full Corrections

In the case where a container workspace, along with the \(A_{s,sc}\), \(A_{c,c}\) and \(A_{c,sc}\) factors are provided.

Usage

Example: using with legacy indirect corrections data

# Load the sample and can
sample_ws = Load('irs26176_graphite002_red.nxs')
can_ws = Load('irs26173_graphite002_red.nxs')

# Convert sample and container workspaces to wavelength
sample_ws = ConvertUnits(InputWorkspace=sample_ws,
                         Target='Wavelength',
                         EMode='Indirect',
                         EFixed=1.845)
can_ws = ConvertUnits(InputWorkspace=can_ws,
                      Target='Wavelength',
                      EMode='Indirect',
                      EFixed=1.845)

# Load the corrections workspace
corrections_ws = Load('irs26176_graphite002_cyl_Abs.nxs')

# Interpolate each of the correction factor workspaces to match the
# binning of the sample
# Required to use corrections from the old indirect calculate
# corrections routines
for factor_ws in corrections_ws:
    SplineInterpolation(WorkspaceToMatch=sample_ws,
                        WorkspaceToInterpolate=factor_ws,
                        OutputWorkspace=factor_ws,
                        OutputWorkspaceDeriv='')

corr = ApplyPaalmanPingsCorrection(SampleWorkspace=sample_ws,
                                   CorrectionsWorkspace=corrections_ws,
                                   CanWorkspace=can_ws)

print('Corrected workspace has {} spectra over {} bins'.format(corr.getNumberHistograms(), corr.blocksize()))

print('Type of correction applied: {}'.format(corr.getRun()['corrections_type'].value))

Output:

Corrected workspace has 10 spectra over 1905 bins
Type of correction applied: sample_and_can_corrections

Related Algorithms

PaalmanPingsMonteCarloAbsorption calculates the partial absorption factors for simple shapes using Monte Carlo simulation.

FlatPlatePaalmanPingsCorrection calculates the partial absorption factors in flat plate geometry using numerical integration.

CylinderPaalmanPingsCorrection calculates the partial absorption factors in cylindrical geometry using numerical integration.

PaalmanPingsAbsorptionCorrection calculates the partial absorption factors for generic shapes using numerical integration.

References

1. H. H. Paalman, and C. J. Pings. Numerical Evaluation of X‐Ray Absorption Factors for Cylindrical Samples and Annular Sample Cells, Journal of Applied Physics 33.8 (1962) 2635–2639 doi: 10.1063/1.1729034

Categories: AlgorithmIndex | Workflow\MIDAS

Source

Python: ApplyPaalmanPingsCorrection.py