Bragg reflections excited in the calibration crystal are recorded in the upper and lower
detector channels as a function of the monochromator motor step position. These motor step
positions are converted into an approximate or pseudo energy scale, 
.
Given that 
is vertical and (
) points back down the incident beam, 
and 
pairs will be excited in the upper and lower channels of the detector
respectively. For 
these reflection
pairs will be matched in energy. Thus establishing the value of 
becomes a matter of
either matching the energies of and pairs or accurately measuring the extent
of their energy splitting in the monochromator energy space. This measurement will be accurate if the
splitting is small. The 
angle may be found in a similar manner by matching the
energies of and 
pairs.
Figure 
shows a map of all reflections which appear in the calibrator detector
for a fixed as a function of energy and 
. The positions on the map where lines
intersect are , degeneracies and may be used to
obtain a value for 
.
These values of 
and along with Eqs. and yield
the true energies, 
of all diffraction lines excited in the crystal.
Plotting 
against allows the construction of a calibration curve
which may then be used to calibrate the whole energy range covered by the calibration markers.
Figure: Map of all reflections appearing in the detector for with
varying energy and 
angle.