Linear and nonlinear calibration

In most cases, a simple linear channel – energy function is not acceptable for post-processing, as this would lead to two adverse effects:

Inexact energy positions. This is due the inherent nonlinearity of the measurement systems, and finally would cause improper nuclide identification in post-processing of the peak lists. If nonlinearity correction is not applied – that is, solely the linear calibration function is used – peak positions of the fitted peak positions may differ as much as 1-3 channels from their expected value.
Improper uncertainties. If only the linear calibration function is used, the reported uncertainties on peak positions are smaller than the real values, thus would make the isotope identification unreliable for activity calculation and calibration purposes.

This picture shows the case when only a linear energy calibration is used for a typical measurement system. This is a measurement of a 152Eu source, in the 121 keV – 1408 keV range.

The green squares depict the difference (the residual) of the calibration points' position from the linear calibration (red line).

Despite multiple calibration points, a clear tendency shows that the system has a significant nonlinear response, which reaches 0.35 keV at in the vicinity of 1408 keV.

If these discrepancies are not acceptable, the purely linear energy calibration is not enough: a correction is needed to eliminate the nonlinearity of the measurement system.