The energy calibration concept in HyperLab
A basic assumption of HyperLab is that every measurement system has an inherent and characteristic nonlinearity, which is rarely and slowly varying in time. We also assume that this is very different from the daily shift of the linear calibration values, and may be separated from it.
Thus the nonlinearity function should only be determined occasionally, e.g. with a multi-isotope, multi-measurement calibration set, serving a high precision nonlinearity curve. This nonlinearity curve can be used in the daily work for a longer period – e.g. for a half year or a whole year –, and only the linear part of the calibration should be adjusted daily. This way a convenient and high-precision energy calibration may be used. This figure shows the effect of applying a real nonlinearity curve in addition to the same linear calibration as seen on the figure in section “Linear and nonlinear calibration”. Please note that the nonlinearity virtually disappeared throughout the whole energy range, and much smaller unwanted shifts may be observed in peak positions. As you can see the abrupt change of the green ±1σ error curve after the last calibration point, HyperLab does not use nonlinearity curves for extrapolation. When a nonlinearity value is requested for an energy, which is outside the energy range of the linear calibration points, the nonlinearity value of the closest point (first or last linear calibration point) will be used.
Further benefits
By utilizing a separated nonlinearity curve for the system, it also provides further benefits:
• the uncertainty calculation contains the incremental effect of the system nonlinearity, and
• it is possible to apply the precise nonlinearity even when the spectrum has a small number of calibration peaks.
As the nonlinearity calibration takes only a few minutes to create, and provides peak positions with much higher precision, our advice is to always use the nonlinearity part of energy calibration.
In fact, this process is almost fully automatic: during loading a spectrum file, HyperLab is able to assign the actual nonlinearity curve to the measurement's energy calibration. After this step, all computations involving this energy calibration will automatically utilize the compensation.