Nonlinearity intersection points
The additive line – the zeroth and first order member of the nonlinearity – is to shift or “shear” the curve such that it intersects the X axis at two specific points (where zero nonlinearity is reached, as shown by the green triangles).
The user can select from Optimum, Linear fit or User defined intersection (or baseline) determination modes. The figure shows the same nonlinearity analysis as in section “ Nonlinearity curve”, but with Optimum baseline instead of Linear fit. HyperLab uses the Optimum mode by default, because in this case the maximum absolute deviance from zero nonlinearity will be minimized in the whole energy range (minimax condition).
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The Linear fit option will use no additive line (or, equivalently it uses the first measurements' line – as it is selected as zero slope and offset).
In User defined mode the user is able to set her own intersection points (thus defining the additional line).
Notes:
If you want to compare percentage nonlinearity values of different measurement systems, or the overall goodness of the same system at two different times, use Optimum method, because this provides the smallest possible percentage value.
If you want to compare the shape of nonlinearity of two systems, apply User defined mode, and set intersection to the same values. This way the same shifting is applied to the curves, and their differences in shape will be immediately visible.
If you want to check whether a linear energy calibration gives the same deviations from the calibration curve as the points on the nonlinearity curve, use Linear fit method with one single measurement.
For energy calibration purposes, in essence there is no big difference between the methods, as the line of the linear energy calibration is able to compensate any setting of baseline. We suggest using the Optimum or Linear fit method in this case.
Bug note: a rarely occurring bug exists in HyperLab's minimax intersection determination algorithm. If you have a measurement system which has a nearly linear response almost in the whole range, the minimax fit sometimes results in the same intersection values for both intersection points. This is indicated by the nonlinearity display: only one green intersection triangle is visible instead of two, because they are at the same position. In this rare case please use the Linear fit or the User defined method.
