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.