$$\renewcommand\AA{\unicode{x212B}}$$

# EstimateResolutionDiffraction v1¶

## Summary¶

Estimate the resolution of each detector pixel for a powder diffractometer

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

Output

number

DeltaT as the resolution of TOF with unit microsecond

DeltaTOFOverTOF

Input

number

Optional

DeltaT/T as the full term in the equation

SourceDeltaL

Input

number

0

Uncertainty in the path length due to the source in unit of meters

SourceDeltaTheta

Input

number

0

Uncertainty in angle due to the source in unit of radians

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. If the input workspace has summed detectors, the resolution of the individual pixels with be added in quadrature.

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, or pulse width, generally from moderator dimensions. If supplied through DeltaTOF parameter, the center wavelength is used to calculate the center time-of-flight. Alternatively, one can specify DeltaTOFOverTOF.

• $$\Delta\theta$$ is the uncertainty in angle due to the source size and coverage of the detector. The former is supplied through the SourceDeltaTheta parameter. The latter can be approximated from the square root of the solid angle of the detector to sample or is taken from the DivergenceWorkspace

• $$\Delta L$$ is the uncertainty in the flight path due to the source position and detector position. The former can be supplied through the SourceDeltaL parameter. The latter is calculated from the detector pixel dimensions.

• $$L$$ is the total flight path of the neutron from source-to-sample (L1) and sample to detector (L2)

• $$\theta$$ 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¶

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
# 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