Improvement of the detector resolution in X-ray spectrometry by using the maximum entropy method

In every X-ray spectroscopy measurement the influence of the detection system causes loss of information. Different mechanisms contribute to form the so-called detector response function (DRF): the detector efficiency, the escape of photons as a consequence of photoelectric or scattering interactions, the spectrum smearing due to the energy resolution, and, in solid states detectors (SSD), the charge collection artifacts. To recover the original spectrum, it is necessary to remove the detector influence by solving the so-called inverse problem. The maximum entropy unfolding technique solves this problem by imposing a set of constraints, taking advantage of the known a priori information and preserving the positive-defined character of the X-ray spectrum. This method has been included in the tool UMESTRAT (Unfolding Maximum Entropy STRATegy), which adopts a semi-automatic strategy to solve the unfolding problem based on a suitable combination of the codes MAXED and GRAVEL, developed at PTB. In the past UMESTRAT proved the capability to resolve characteristic peaks which were revealed as overlapped by a Si SSD, giving good qualitative results. In order to obtain quantitative results, UMESTRAT has been modified to include the additional constraint of the total number of photons of the spectrum, which can be easily determined by inverting the diagonal efficiency matrix. The features of the improved code are illustrated with some examples of unfolding from three commonly used SSD like Si, Ge, and CdTe. The quantitative unfolding can be considered as a software improvement of the detector resolution.