.
The superscript 
refers to spectra of (sample+environment), (environment) or (vanadium+environment).
The scattering geometry is defined here:
Vanadium is known to be an entirely incoherent scatterer, and hence
is used to correct for relative detector efficiencies. For many purposes,
it is not necessary to perform this normalisation of the spectra, reducing
errors introduced into the data reduction. We shall assume that our data
has been normalised and is represented as a function of angle and time
by 
and 
.
For a spectrum recorded for a total time 
,
with an incident neutron flux 
,
impinging on a sample consisting of 
scattering
centres, then
,with 
and 
referring to the solid angle subtended by the detector and the time channel
width, respectively.
The physics of the system is encapsulated in the scattering law (e.g. Squires: Introduction to the Theory of Thermal Neutron Scattering):
.which we can extract from the experimental data using the fact that
the energy, 
,
of a neutron is related to the time it leaves the sample and the distance, 
,
from sample to detector via 
.
Using the time taken for an elastically scattered neutron to arrive at
the detectors as 
,
while 
represents
the time taken for neutrons that have suffered inelastic scattering events,
we arrive at the defining equation:
