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EstimateResolutionDiffraction v1¶

$../_images/EstimateResolutionDiffraction-v1_dlg.png$

EstimateResolutionDiffraction dialog.

Table of Contents

Summary
- See Also
Properties
Description
Instrument resolution
Factor Sheet
- NOMAD
- POWGEN
Usage
Source

Summary ¶

Estimate the resolution of each detector pixel for a powder diffractometer

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,

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

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

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

Source ¶

C++ header: EstimateResolutionDiffraction.h (last modified: 2021-03-31)

C++ source: EstimateResolutionDiffraction.cpp (last modified: 2021-03-31)