6.4

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EstimateResolutionDiffraction v1

../_images/EstimateResolutionDiffraction-v1_dlg.png

EstimateResolutionDiffraction dialog.

Summary

Estimate the resolution of each detector pixel for a powder diffractometer

See Also

EstimateDivergence

This algorithm is also known as: EstimatePDDetectorResolution

Properties

Name Direction Type Default Description
InputWorkspace Input MatrixWorkspace Mandatory Name of the workspace to have detector resolution calculated
DivergenceWorkspace Input MatrixWorkspace   Workspace containing the divergence
OutputWorkspace Output MatrixWorkspace Mandatory Name of the output workspace containing delta(d)/d of each detector/spectrum
DeltaTOF Input number Mandatory DeltaT as the resolution of TOF with unit microsecond
Wavelength Input number Optional Wavelength setting in Angstroms. This overrides what is in the dataset.
PartialResolutionWorkspaces Output WorkspaceGroup Mandatory Workspaces created showing the various resolution terms

Instrument resolution

Resolution of a detector in d-spacing is defined as \(\frac{\Delta d}{d}\), which is constant for an individual detector.

Starting from the Bragg equation for T.O.F. diffractometer,

\[d = \frac{t}{252.777\cdot L\cdot2\sin\theta}\]

as

\[\Delta d = \sqrt{\left(\Delta T \frac{\partial d}{\partial T}\right)^2 + \left(\Delta L \frac{\partial d}{\partial L}\right)^2 + \left(\Delta \theta \frac{\partial d}{\partial \theta}\right)^2}\]

and thus

\[\frac{\Delta d}{d} = \sqrt{\left(\frac{\Delta T}{T}\right)^2 + \left(\frac{\Delta L}{L}\right)^2 + \left(\Delta\theta\cdot\cot(\theta)\right)^2}\]

where,

  • \(\Delta T\) is the time resolution from moderator
  • \(\Delta\theta\) is the coverage of the detector, and can be approximated from the square root of the solid angle of the detector to sample
  • \(L\) is the flight path of the neutron from source to detector
  • \(\theta\) is half the Bragg angle \(2 \theta\), or half of the angle from the downstream beam

The optional DivergenceWorkspace specifies the values of \(\Delta\theta\) to use rather than those derived from the solid angle of the detectors. EstimateDivergence can be used for estimating the divergence.

PartialResolutionWorkspaces is a collection of partial resolution functions where _tof is the time-of-flight term, _length is the path length term, and _angle is the angular term. Note that the total resolution is these terms added in quadriture.

Note that \(\frac{\Delta d}{d} = \frac{\Delta Q}{Q}\). When fitting peaks in time-of-flight the resolution is \(\frac{\Delta T}{T} = \frac{\Delta d}{d}\).

Factor Sheet

NOMAD

Detector size

  • vertical: 1 meter / 128 pixel
  • Horizontal: half inch or 1 inch

POWGEN

Detector size: 0.005 x 0.0543

Range of \(\Delta\theta\cot\theta\): \((0.00170783, 0.0167497)\)

Usage

Example - estimate PG3 partial detectors’ resolution:

# Load a Nexus file
Load(Filename="PG3_2538_2k.nxs", OutputWorkspace="PG3_2538")
# Run the algorithm to estimate detector's resolution
EstimateResolutionDiffraction(InputWorkspace="PG3_2538", DeltaTOF=40.0, OutputWorkspace="PG3_Resolution",
                              PartialResolutionWorkspaces="PG3_Resolution_partials")
resws = mtd["PG3_Resolution"]

print("Size of workspace 'PG3_Resolution' =  {}".format(resws.getNumberHistograms()))
print("Estimated resolution of detector of spectrum 0 =  {:.14f}".format(resws.readY(0)[0]))
print("Estimated resolution of detector of spectrum 100 =  {:.14f}".format(resws.readY(100)[0]))
print("Estimated resolution of detector of spectrum 999 =  {:.14f}".format(resws.readY(999)[0]))

Output:

Size of workspace 'PG3_Resolution' =  1000
Estimated resolution of detector of spectrum 0 =  0.00323913137315
Estimated resolution of detector of spectrum 100 =  0.00323608260137
Estimated resolution of detector of spectrum 999 =  0.00354849176520

See also

Algorithms EstimateDivergence v1.

Categories: AlgorithmIndex | Diffraction\Utility