The sector involves splitting up the 
plane into four
sectors: left, right, up, and down. These sectors are shown in figure
.
Figure: Illustration of the sectors in the 
plane used
for categorizing the direction of neutron scattering.
The asymmetries are found by comparing the number of scatters in each sector. If we consider a vertically polarized beam and a constant detector acceptance then the distribution of hits can be written as [Mer93]
where the explicit dependence on 
had been suppressed. The number
of particles scattered into the left and right sectors are
respectively, where N is the number of counts scattered between
and 
. Solving for the asymmetry:
The 
-direction asymmetry is similarly expressed as
