Quasi-continuous re-binning of measured spectra and associated uncertainties

As part of an evaluation of gamma-ray spectra or other spectra, the need to adapt the binning quasi-continuously may arise. Often, the re-distribution of measured events to a new energy scale may be required. The necessity to change the energy scale can have several reasons. Frequently, a drift of the detector or the amplifier leads to different energy scales of measured spectra in time. In order to calculate difference spectra or sum spectra, the energy axis and binning of all spectra has to be adapted. Moreover, before a spectrum is unfolded, its energy axis also has to be adapted to the energy scale of the response matrix. Widespread commercial software packages, which are commonly used for the analysis of spectra, do not include an algorithm which solves this task. Three algorithms are presented in this work after shedding light on the mathematical background. An analysis of the statistical uncertainty of the counts of re-binned or remapped spectra completes this paper.