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IQTransform v1

Summary

This algorithm provides various functions that are sometimes used to linearise the output of a ‘SANS’ data reduction prior to fitting it.

Properties

Name	Direction	Type	Default	Description
InputWorkspace	Input	MatrixWorkspace	Mandatory	The input workspace must be a distribution with units of Q
OutputWorkspace	Output	MatrixWorkspace	Mandatory	The name of the output workspace
TransformType	Input	string	Mandatory	The name of the transformation to be performed on the workspace. Allowed values: [‘Debye-Bueche’, ‘General’, ‘Guinier (rods)’, ‘Guinier (sheets)’, ‘Guinier (spheres)’, ‘Holtzer’, ‘Kratky’, ‘Log-Log’, ‘Porod’, ‘Zimm’]
BackgroundValue	Input	number	0	A constant value to subtract from the data prior to its transformation
BackgroundWorkspace	Input	MatrixWorkspace		A workspace to subtract from the input workspace prior to its transformation.Must be compatible with the input (as for the Minus algorithm).
GeneralFunctionConstants	Input	dbl list		A set of 10 constants to be used (only) with the ‘General’ transformation

Description

This algorithm is intended to take the output of a SANS reduction and apply a transformation to the data in an attempt to linearise the curve. Optionally, a background can be subtracted from the input data prior to transformation. This can be either a constant value, another workspace or both. Note that this expects a single spectrum input; if the input workspace contains multiple spectra, only the first will be transformed and appear in the output workspace.

A SANS reduction results in data in the form I(Q) vs Q, where Q is Momentum Transfer and I denotes intensity (the actual unit on the Y axis is 1/cm). These abbreviations are used in the descriptions of the transformations which follow. If the input is a histogram, the mid-point of the X (i.e. Q) bins will be taken. The output of this algorithm is always point data.

Transformation Name	Y	X
Guinier (spheres)	\(\ln (I)\)	\(Q^2\)
Guinier (rods)	\(\ln (IQ)\)	\(Q^2\)
Guinier (sheets)	\(\ln (IQ^2)\)	\(Q^2\)
Zimm	\(\frac{1}{I}\)	\(Q^2\)
Debye-Bueche	\(\frac{1}{\sqrt{I}}\)	\(Q^2\)
Holtzer	\(I \times Q\)	\(Q\)
Kratky	\(I \times Q^2\)	\(Q\)
Porod	\(I \times Q^4\)	\(Q\)
Log-Log	\(\ln(I)\)	\(\ln(Q)\)
General [*]	\(Q^{C_1} \times I^{C_2} \times \ln{\left( Q^{C_3} \times I^{C_4} \times C_5 \right)}\)	\(Q^{C_6} \times I^{C_7} \times \ln{\left( Q^{C_8} \times I^{C_9} \times C_{10} \right)}\)

[*]

The constants \(C_1 - C_{10}\) are, in subscript order, the ten constants passed to the GeneralFunctionConstants property.

Usage

Example - Zimm transformation:

x = [1,2,3]
y = [1,2,3]
input = CreateWorkspace(x,y)
input.getAxis(0).setUnit("MomentumTransfer")
input.setDistribution(True)

output = IQTransform(input, 'Zimm')

print('Output Y: {}'.format(output.readY(0)))
print('Output X: {}'.format(output.readX(0)))

Output:

Output Y: [1.         0.5        0.33333333]
Output X: [1. 4. 9.]

Example - Zimm transformation and background:

x = [1,2,3]
y = [1,2,3]
input = CreateWorkspace(x,y)
input.getAxis(0).setUnit("MomentumTransfer")
input.setDistribution(True)

output = IQTransform(input, 'Zimm', BackgroundValue=0.5)

print('Output Y: {}'.format(output.readY(0)))
print('Output X: {}'.format(output.readX(0)))

Output:

Output Y: [2.         0.66666667 0.4       ]
Output X: [1. 4. 9.]

Example - General transformation:

import math

x = [1,2,3]
y = [1,2,3]
input = CreateWorkspace(x,y)
input.getAxis(0).setUnit("MomentumTransfer")
input.setDistribution(True)

constants = [2,2,0,0,math.e,3,0,0,0,math.e]
output = IQTransform(input, 'General', GeneralFunctionConstants=constants)

print('Output Y: {}'.format(output.readY(0)))
print('Output X: {}'.format(output.readX(0)))

Output:

Output Y: [ 1. 16. 81.]
Output X: [ 1.  8. 27.]

Categories: AlgorithmIndex | SANS

Source

C++ header: IQTransform.h

C++ source: IQTransform.cpp