Spatio‐energetic cross‐talk in photon counting detectors: N × N binning and sub‐pixel masking

Purpose Smaller pixel sizes of x‐ray photon counting detectors ( PCD s) benefit count rate capabilities but increase cross‐talk and “double‐counting” between neighboring PCD pixels. When an x‐ray photon produces multiple ( n ) counts at neighboring (sub‐)pixels and they are added during post‐acquisition N  ×  N binning process, the variance of the final PCD output‐pixel will be larger than its mean. In the meantime, anti‐scatter grids are placed at the pixel boundaries in most of x‐ray CT systems and will decrease cross‐talk between sub‐pixels because the grids mask sub‐pixels underneath them, block the primary x‐rays, and increase the separation distance between active sub‐pixels. The aim of this paper was, first, to study the PCD statistics with various N  ×  N binning schemes and three different masking methods in the presence of cross‐talks, and second, to assess one of the most fundamental performances of x‐ray CT : soft tissue contrast visibility. Methods We used a PCD cross‐talk model (Photon counting toolkit, Pc TK ) and produced cross‐talk data between 3 × 3 neighboring sub‐pixels and calculated the mean, variance, and covariance of output‐pixels with each of N  ×  N binning scheme [4 × 4 binning, 2 × 2 binning, and 1 × 1 binning (i.e., no binning)] and three different sub‐pixel masking methods (no mask, 1‐D mask, and 2‐D mask). We then set up simulation to evaluate the soft tissue contrast visibility. X‐rays of 120 kV p were attenuated by 10–40 cm‐thick water, with the right side of PCD s having 0.5 cm thicker water than the left side. A pair of output‐pixels across the left‐right boundary were used to assess the sensitivity index ( SI or d′ ), which typically ranges 0–1 and is a generalized signal‐to‐noise ratio and a statistics used in signal detection theory. Results Binning a larger number of sub‐pixels resulted in larger mean counts and larger variance‐to‐mean ratio when the lower threshold of the energy window was lower than the half of the incident energy. Mean counts are in the order of no mask (the largest), 1‐D mask, and 2‐D mask but the difference in variance‐to‐mean ratio was small. For a given sub‐pixel size and masking method, binning more sub‐pixels degraded the normalized SI values but the difference between 4 × 4 binning and 1 × 1 binning was typically less than 0.06. 1‐D mask provided better normalized SI values than no mask and 2‐D mask for side‐by‐side case and the improvements were larger with fewer binnings, although the difference was less than 0.10. 2‐D mask was the best for embedded case. The normalized SI values of combined binning, sub‐pixel size, and masking were in the order of 1 × 1 (900 μm) 2 binning, 2 × 2 (450 μm) 2 binning, and 4 × 4 (225 μm) 2 binning for a given masking method but the difference between each of them were typically 0.02–0.05. Conclusion We have evaluated the effect of double‐counting between PCD sub‐pixels with various binning and masking methods. SI values were better with fewer number of binning and larger sub‐pixels. The difference among various binning and masking methods, however, was typically less than 0.06, which might result in a dose penalty of 13% if the CT system were linear.