TOFSANSResolutionByPixel v1¶

TOFSANSResolutionByPixel dialog.

Table of Contents

Summary
Properties
Description
Source

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 wavelength std from TOF binning and moderator, $\Delta \lambda$ is taken from the binning of the InputWorkspace and the $\sigma_{moderator}$ is the wavelenght spread from the moderator.

where $\sigma_{\lambda}$ is the effective standard deviation, and $\Delta \lambda$ , originating from the TOF binning of the InputWorkspace, is the (rectangular) width, of the moderator wavelength distribution. $\sigma_{moderator}$ is the moderator time spread (the variation in time for the moderator to emit neutrons of a given 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.