Sensitivity of photon-counting K-edge imaging: Dependence on atomic number and object size

The feasibility of K-edge x-ray CT imaging has been demonstrated both by simulations and by experiments performed on energy-resolved, photon-counting data. The method is based on detecting the difference in attenuation above and below the K-edge of elements with high atomic number Z measured with energy-sensitive, photon counting devices. So far, the sensitivity of this technique has been probed only for a handful of scenarios. In this paper, we thoroughly investigate the dependence of the sensitivity of K- edge imaging on the atomic number Z of the contrast material, on the object size D and on the spectral response function of the x-ray detector. We assume a photon-counting detector equipped with 6 adjustable energy thresholds. The various physical effects leading to a degradation of the energy resolution of the detector are taken into account using the concept of a spectral response function R(E, U) for which we assume four different models: infinite energy resolution, a shift-invariant Gaussian response with 10 keV FWHM, a (measured) shift-invariant energy response featuring a photo-peak and a K- escape peak and, finally, an experimentally determined response function from a detector calibration at the synchrotron. The dependence on the values of the energy thresholds is taken into account by optimizing the achievable signal with respect to the threshold values. We find that for a given x-ray spectrum there exists an atomic number Z for which the signal-to-noise ratio (SNR) in the high-Z basis material image is maximal. The SNR dependence on the object thickness is an exponential decrease with particularly deteriorating effects in the case where the beam-hardening from the object itself causes a signal loss below the K-edge. The influence of the energy-response of the detector is very strong and increases for responses with tailing towards lower energies.