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