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 250μm , 500μm , and 1 mm were compared, with binning of 4×4 , 2×2 , and 1×1 pixels, respectively, to keep the same net 1 mm ² 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 mm ² macro-pixel with 250× 250 mu;m ² sub-pixels shows 35% higher standard deviation than a single 1 mm ² pixel for material-specific imaging, while the penalty for effective monoenergetic imaging is <10% compared with a single 1 mm ² pixel. Potential benefits of sub-pixels (higher spatial resolution and lower pulse pile-up effects) are important but were not investigated here.