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

# ModeratorTzeroLinear v1¶

## Summary¶

Corrects the time of flight of an indirect geometry instrument by a time offset that is linearly dependent on the wavelength of the neutron after passing through the moderator.

ModeratorTzero

## Properties¶

Name

Direction

Type

Default

Description

InputWorkspace

Input

MatrixWorkspace

Mandatory

The name of the input workspace, containing events and/or histogram data, in units of time-of-flight

Input

number

Optional

Wavelength dependent TOF shift, units in microsec/Angstrom. Overrides the value stored in the instrument object

Intercept

Input

number

Optional

TOF shift, units in microseconds. Overrides the valuestored in the instrument object

OutputWorkspace

Output

MatrixWorkspace

Mandatory

The name of the output workspace

## Description¶

This algorithm Corrects the time of flight (TOF) of an indirect geometry instrument by substracting a time offset $$t_0$$ linearly dependent on the wavelength of the neutron when emitted through the moderator. This algorithm is suitable to data reduction of indirect instruments featuring a neutron flux with a narrow distribution of wavelengths. A empirical formula for the correction, stored in the instrument definition file, is taken as linear on the initial neutron wavelength $$\lambda_i$$: $$t_0 = a * \lambda_i + b$$. Gradient $$a$$ is in units of microsec/Angstrom and Intercept $$b$$ is in units of microsec. Below is the example XML code included in BASIS beamline parameters file.

<!-- Moderator Tzero/LambdaZero Parameters  -->
<value val="11.967"/>
</parameter>
<parameter name="Moderator.TimeZero.Intercept">
<value val="-5.0"/>
</parameter>

The recorded TOF: $$TOF = t_0 + t_i + t_f$$, with

• $$t_0$$: emission time from the moderator

• $$t_i$$: time from moderator to sample

• $$t_f$$: time from sample to detector

This algorithm will replace TOF with $$TOF' = TOF-t_0 = t_i + t_f$$

For an indirect geometry instrument, $$\lambda_i$$ is not known but the final energy, $$E_f$$, selected by the analyzers is known. For this geometry:

• $$t_f = L_f/v_f$$, with $$L_f$$: distance from sample to detector, $$v_f$$: final velocity derived from $$E_f$$

• $$t_i = L_i/v_i$$, with $$L_i$$: distance from moderator to sample, $$v_i$$: initial velocity unknown

• $$t_0 = a'/v_i+b'$$, with $$a'$$ and $$b'$$ constants derived from the aforementioned empirical formula $$a' = a \cdot 3.956 \cdot 10^{-3}$$ with $$a'$$ in units of meters

and $$b' = b$$ with $$b'$$ in units of microseconds.

Putting all together: $$TOF' = \frac{L_i}{L_i+a'} \cdot (TOF-t_f-b') + t_f$$, with [TOF’]=microsec

If the detector is a monitor, then we can treat it as both sample and detector. Thus, we use the previous formula inserting the time from sample to detector $$t_f = 0$$ and with the initial fligh path $$L_i$$ as the distance from source to monitor.