Effect of Spectral Degradation and Spatio-Energy Correlation in X-Ray PCD for Imaging

Charge sharing, scatter, and fluorescence events in a photon counting detector can result in counting of a single incident photon in multiple neighboring pixels, each at a fraction of the true energy. This causes energy distortion and correlation of data across energy bins in neighboring pixels (spatio-energy correlation), with the severity depending on the detector pixel size and detector material. If a “macro-pixel” is formed by combining the counts from multiple adjacent small pixels, it will exhibit correlations across its energy bins. Understanding these effects can be crucial for detector design and for model-based imaging applications. This paper investigates the impact of these effects in basis material and effective monoenergetic estimates using the Cramér-Rao Lower Bound. To do so, we derive a correlation model for the multi-counting events. CdTe detectors with grids of pixels with side length of <inline-formula> <tex-math notation="LaTeX">$250~\mu \text{m}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$500~\mu \text{m}$ </tex-math></inline-formula>, and 1 mm were compared, with binning of <inline-formula> <tex-math notation="LaTeX">$4\times4$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$2\times2$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$1\times1$ </tex-math></inline-formula> pixels, respectively, to keep the same net 1 mm² aperture constant. The same flux was applied to each. The mean and covariance matrix of measured photon counts were derived analytically using spatio-energy response functions precomputed from Monte Carlo simulations. Our results show that a 1 mm² macro-pixel with <inline-formula> <tex-math notation="LaTeX">$250\times 250\,\,\mu \text{m}^{\textsf {2}}$ </tex-math></inline-formula> sub-pixels shows 35% higher standard deviation than a single 1 mm² pixel for material-specific imaging, while the penalty for effective monoenergetic imaging is <10% compared with a single 1 mm<inline-formula> <tex-math notation="LaTeX">$^{\textsf {2}}$ </tex-math></inline-formula> pixel. Potential benefits of sub-pixels (higher spatial resolution and lower pulse pile-up effects) are important but were not investigated here.