X-ray tube spectra measurement and correction using a CdTe detector and an analytic response matrix for photon energies up to 160 keV

The aims of our work were: i) to measure selected normalized X-ray beam spectra with the commercially available cadmium telluride detector based spectrometry system; ii) to construct the approximate response matrix of the detector using a simple algebraic model approach; iii) to reconstruct the physical energy spectra from the measured instrumental spectra using the detector response matrix; iv) to compare the obtained spectra parameters with the published and reference data in order to verify the model and to optimize the measurement setup if necessary. In particular, the spectra of five “narrow-spectrum series” beams, namely N60 to N150, were measured with a spectrometry system consisting of the Amptek XR-100T X-ray semiconductor detector and the PX5 multichannel analyser. Two different measuring geometries were used. The response matrix R(E, E′) of the detector was constructed which quantifies the energy dependence of the relative detection efficiency of the detector, the probabilities of the escape effects, and the probability of the Compton effect. A single matrix operation was applied to recover the physical energy spectra from the measured instrumental ones. The parameters of the corrected spectra were compared with the published and reference data. Despite the fact that the effect of incomplete charge collection was not implemented in the detector model, a fully satisfying quantitative correspondence was observed between the measured corrected spectra and the available reference data.