TOFSANSResolutionByPixel v1

../_images/TOFSANSResolutionByPixel-v1_dlg.png

TOFSANSResolutionByPixel dialog.

Summary

Calculate the Q resolution for TOF SANS data for each pixel.

Properties

Name Direction Type Default Description
InputWorkspace Input MatrixWorkspace Mandatory Name the workspace to calculate the resolution for, for each pixel and wavelength
OutputWorkspace Output Workspace Mandatory Name of the newly created workspace which contains the Q resolution.
DeltaR Input number 0 Virtual ring width on the detector (mm).
SampleApertureRadius Input number 0 Sample aperture radius, R2 (mm).
SourceApertureRadius Input number 0 Source aperture radius, R1 (mm).
SigmaModerator Input MatrixWorkspace Mandatory Moderator time spread (microseconds) as afunction of wavelength (Angstroms).
CollimationLength Input number 0 Collimation length (m)
AccountForGravity Input boolean False Whether to correct for the effects of gravity
ExtraLength Input number 0 Additional length for gravity correction.

Description

Calculates the Q-resolution per pixel according to Mildner and Carpenter equation

(\sigma_Q )^2 = \frac{4\pi^2}{12\lambda^2} [ 3(\frac{R_1}{L_1})^2 + 3(\frac{R_2}{L_3})^2 + (\frac{\Delta R}{L_2})^2 ] + Q^2(\frac{\sigma_{\lambda}}{\lambda})^2

where L1 and L2 are the collimation length and sample-to-detector distance respectively and

\frac{1}{L_3} = \frac{1}{L_1} + \frac{1}{L_2}

and

(\sigma_{\lambda})^2 = (\Delta \lambda )^2 / 12 + (\sigma_{moderator})^2

where \sigma_{\lambda} is the overall effective standard deviation in wavelength. \Delta \lambda values are found from the wavelength binning of the InputWorkspace, \sigma_{moderator} is the moderator time spread (the variation in time for the moderator to emit neutrons of a given wavelength). Note that \Delta \lambda may be imposed by wavelength steps set elsewhere in Mantid which should be at least as large as the equivalent time bins used in the original histogram data collection. For event mode data \Delta \lambda is in theory very small, but in practice a histogram in time has to be generated (perhaps using monitor time bins or specifically set event-time-bins), before a rebinning into user provided wavelength steps in InputWorkspace. Again the latter steps should be the largest.

Q values needed here are calculated in the same way as for Q1D, including correction for gravity for which detector coordinates are assumed centred at zero wavelength.

\sigma_Q is returned as the y-values of the InputWorkspace, and the remaining variables in the main equation above are related to parameters of this algorithm as follows:

  • R_1 equals SourceApertureRadius
  • R_2 equals SampleApertureRadius
  • \Delta R equals DeltaR
  • \sigma_{moderator} equals SigmaModerator
  • \L_1 equals CollimationLength

\lambda in the equation is the midpoint of wavelength histogram bin values of InputWorkspace.

Collimation length L_1 in metres in the equation here is the distance between the first beam defining pinhole (Radius R_1) and the sample aperture (radius R_2). (Beware that L_1 is more often the moderator to sample distance.)

For rectangular collimation apertures, size H x W, Mildner & Carpenter say to use R = \sqrt{( H^2 +W^2)/6 }. Note that we are assuming isotropically averaged, scalar Q, and making some small angle approximations. Results on higher angle detectors may not be accurate. For data reduction sliced in different directions on the detector (e.g. GISANS) adjust the calling parameters to suit the collimation in that direction.

Note that \Delta is the full width of a rectangular distribution in radius or wavelength, for which the standard deviation is \sigma=\Delta/\sqrt{12}. For a Gaussian distribution the FWHM (full width at half maximum) is \sqrt{8\ln{2}}\sigma=2.35482\sigma. For an exponential decay e^{-t/\tau}, the standard deviation (and the mean) is \tau. For non-rectangular distributions these equations allow the equivalent \Delta to be entered as \Delta=\sqrt{12}\sigma.

This version of the algorithm neglects wavelength-dependent detector detection depth effects.

Categories: AlgorithmIndex | SANS

Source

C++ source: TOFSANSResolutionByPixel.cpp (last modified: 2019-07-17)

C++ header: TOFSANSResolutionByPixel.h (last modified: 2018-10-05)