We have developed a framework for assessing the performance of photon-counting energy-resolving detectors and shown that the matrix-valued NEQ and DQE metrics contain sufficient information for calculating the dose efficiency for both detection and quantification tasks, the task having any spatial and energy dependence. This framework will be beneficial for the development and optimization of photon-counting x-ray detectors.

Purpose: Charge sharing and migration of scattered and fluorescence photons in an energy discriminating photon counting detector (PCD) degrade the detector's energy response and can cause a single incident photon to be registered as multiple events at different energies among neighboring pixels, leading to spatio-energetic correlation. Such a correlation in conventional linear, space-invariant imaging system can be usefully characterized by the frequency dependent detective quantum efficiency DQE(f). Defining and estimating DQE(f) for PCDs in a manner consistent with that of conventional detectors is complicated because the traditional definition of DQE(f) does not address spectral information. Methods: We introduce the concept of presampling spectroscopic detective quantum efficiency, DQE s (f), and present an analysis of it for CdTe PCDs using a spatial domain method that starts from a previously described analytic computation of spatio-energetic crosstalk. DQE s (f) is estimated as the squared signal-to-noise ratio of the amplitude of a small-signal sinusoidal modulation of the object (cortical bone) thickness at frequency f estimated using data from the detector under consideration compared that obtained from the photon distribution incident on the detector. DQE s for material decomposition (spectral) and effective monoenergetic imaging tasks for different pixel pitch is studied based on the multipixel Cram er-Rao lower bound (CRLB) that accounts for inter pixel basis material correlation. Effective monoenergetic DQE s is estimated from the CRLB of a linear weighted combination of basis materials, and its energy dependence is also studied. Results: Zero frequency DQE s for the spectral task was~18%, 25%, and 34% for 250 lm, 500 lm, and 1 mm detector pixels respectively. Inter pixel signal correlation results in positive noise correlation between same basis material estimates of neighboring pixels, resulting in least impact on DQE s at the detector's Nyquist frequency. Effective monoenergetic DQE s (0) at the optimal energy is relatively tolerant of spectral degradation (85-91% depending on pixel size), but is highly dependent on the selected effective energy, with maximum variation (in 250 lm pixels) of 17% to 85% for effective energy between 30 to 120 keV. Conclusions: Our results show that spatio-energetic correlations degrade DQE s (f) beyond what is lost by poor spectral response in a single detector element. The positive correlation between computed single basis material values in neighboring pixels results in the penalty to DQE s (f) to be the least at the Nyquist frequency of the detector. It is desirable to reduce spectral degradation and crosstalk to minimize the impact on system performance. Larger pixels sizes have better spatio-energetic response due to lower charge sharing and escape of scatter and K-fluorescence photons, and therefore higher DQE s (0). Effective monoenergetic DQE s (0) at the optimal energy is much less affected by spectral degradation and crosstalk compared to DQE s for spectra...

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The detector pixel size is an important design consideration in CdTe detectors. Smaller pixels allow for improved capabilities at high flux but increase charge sharing, which in turn compromises spectral performance. The optimal pixel size will depend on the specific task and on the charge shaping time.