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