Cascaded systems analysis of charge sharing in cadmium telluride photon-counting x-ray detectors

Single-photon-counting (SPC) and spectroscopic x-ray detectors are under development in academic and industry laboratories for medical imaging applications. The spatial resolution of SPC and spectroscopic x-ray detectors is an important design criterion. The purpose of this article was to extend the cascaded systems approach to include a description of the spatial resolution of SPC and spectroscopic x-ray imaging detectors.

A cascaded systems approach was used to model reabsorption of characteristic x rays, Coulomb repulsion, and diffusion in SPC and spectroscopic x-ray detectors. In addition to reabsorption, diffusion, and Coulomb repulsion, the model accounted for x-ray conversion to electron-hole (e-h) pairs, integration of e-h pairs in detector elements, electronic noise, and energy thresholding. The probability density function (PDF) describing the number of e-h pairs was propagated through each stage of the model and was used to derive new theoretical expressions for the large-area gain and modulation transfer function (MTF) of CdTe SPC x-ray detectors, and the energy bin sensitivity functions and MTFs of CdTe spectroscopic detectors. Theoretical predictions were compared with the results of MATLAB-based Monte Carlo (MC) simulations and published data. Comparisons were also made with the MTF of energy-integrating systems.

Under general radiographic conditions, reabsorption, diffusion, and Coulomb repulsion together artificially inflate count rates by 20% to 50%. For thicker converters (e.g. 1000 μm) and larger detector elements (e.g. 500 μm pixel pitch) these processes result in modest inflation (i.e. ∼10%) in apparent count rates. Our theoretical and MC analyses predict that SPC MTFs will be degraded relative to those of energy-integrating systems for fluoroscopic, general radiographic, and CT imaging conditions. In most cases, this degradation is modest (i.e., ∼10% at the Nyquist frequency). However, for thicker converters, the SPC MTF can be degraded by up to 25% at the Nyquist frequency relative to EI systems. Additionally, unlike EI systems, the MTF of spectroscopic systems is strongly dependent on photon energy, which results in energy-bin-dependent spatial resolution in spectroscopic systems.

The PDF-transfer approach to modeling signal transfer through SPC and spectroscopic x-ray imaging systems provides a framework for understanding system performance. Application of this approach demonstrated that charge sharing artificially inflates the SPC image signal and degrades the MTF of SPC and spectroscopic systems relative to energy-integrating systems. These results further motivate the need for anticharge-sharing circuits to mitigate the effects of charge sharing on SPC and spectroscopic x-ray image quality.