Effect of spatio-energy correlation in PCD due to charge sharing, scatter, and secondary photons

Charge sharing, scatter and fluorescence events in a photon counting detector (PCD) can result in multiple counting of a single incident photon in neighboring pixels. This causes energy distortion and correlation of data across energy bins in neighboring pixels (spatio-energy correlation). If a "macro-pixel" is formed by combining multiple small pixels, it will exhibit correlations across its energy bins. Charge sharing and fluorescence escape are dependent on pixel size and detector material. Accurately modeling these effects can be crucial for detector design and for model based imaging applications. This study derives a correlation model for the multi-counting events and investigates the effect in virtual non-contrast and effective monoenergetic imaging. Three versions of 1 mm² square CdTe macro-pixel were compared: a 4×4 grid, 2×2 grid, or 1×1 composed of pixels with side length 250 μm, 500 μm, or 1 mm, respectively. The same flux was applied to each pixel, and pulse pile-up was ignored. The mean and covariance matrix of measured photon counts is derived analytically using pre-computed spatio-energy response functions (SERF) estimated from Monte Carlo simulations. Based on the Cramer-Rao Lower Bound, a macro-pixel with 250×250 μm² sub-pixels shows ∼2.2 times worse variance than a single 1 mm² pixel for spectral imaging, while its penalty for effective monoenergetic imaging is <10% compared to a single 1 mm² pixel.