Energy calibration and gain correction of pixelated spectroscopic x-ray detectors using correlation optimised warping

We describe the implementation of a reliable, robust and flexible gain correction and energy calibration algorithm for pixelated spectroscopic x-ray detectors. This algorithm uses a data processing method known as correlation optimised warping which aligns shifted datasets by means of a segmental linear stretching and compression of the spectral data in order to best correlate with a reference spectrum. We found the algorithm to be very robust against low-count spectroscopy, and was reliable in a range of different spectroscopic applications. Analysis of the integrated spectrum over all pixels for a Cerium K-alpha x-ray emission (at 34.72 keV) yielded a peak width of 2.45 keV before alignment and 1.11 keV after alignment. This compares favourably with the best in class pixel peak width of 0.76 keV and the mean peak width for all pixels of 1.00 keV. We also found the algorithm to be more user friendly than other peak-search algorithms because there is less external input. A key advantage of this algorithm is that it requires no prior knowledge of the input spectral characteristics, shape or quality of the data. This therefore lends itself to being useful for in-line processing and potentially removes the need for a separate calibration standard (e.g. a radioactive source). This algorithm can be used for any system that simultaneously collects large numbers of spectral data—including multi-element detectors.