Nonlinearity curve

The nonlinearity of a measurement system at a specific point of time is characterized by a so called nonlinearity curve. This describes the system's deviation from the linear calibration line, as shown in the picture below.

The figure shows the nonlinearity curve of HyperLab's Nonlinearity module for the 152Eu lines of a calibration measurement.

The curve itself is depicted by a red line, its ±1σ limit with blue lines, while the data points are from the centroid shift of the fitted peaks.

The green triangles show the points where the curve reaches the zero nonlinearity value.

In HyperLab, the system nonlinearity curve always uses the channel-channel scale, as with these units the nonlinearity characteristics are supposed to be slowly varying with the time.

The calculated nonlinearity may be used for several purposes:

The curve provides the “fine tuning” part of the energy calibration, because it transforms the system's response to nearly linear. Thus, when applied together with a linear channel-position calibration line, it serves more exact energy values. See section “Energy calibration editor” for more details about applying a previously created nonlinearity calibration to an existing linear energy calibration.
Helps to compare the absolute nonlinearity of different measurement systems. As HyperLab also calculates an absolute percentage nonlinearity value, a simple comparison of two numbers may reveal the differences between them.
Helps to characterize the aging or other changes in a specific measurement system for quality assurance purposes. With consecutive nonlinearity evaluations, the percentage nonlinearity values may be used to monitor the changes in characteristics of the measurement system.