From inverse error function to resolution enhancement: hardware-efficient virtual subdivision in single photon counting detectors

Abstract

Single-photon counting hybrid pixel X-ray detectors combine a wide dynamic range with effective noise suppression, but their spatial resolution is degraded by charge sharing, which intensifies as the pixel pitch shrinks. The charge fractions registered by neighbouring pixels can, however, be exploited to estimate the photon interaction position with subpixel precision. This work presents a fully digital, in-pixel algorithm that reconstructs the interaction position from the digitised readings of a 3 × 3 pixel neighbourhood, assigning each event to one of 2 × 2 or 3 × 3 virtual subdivisions. An exact reconstruction based on the inverse error function is reformulated into the ratio-based virtual subdivision allocation (RVSA) algorithm, which replaces the per-event division and erf^-1 evaluation with a single integer ratio test. Simulations against a behavioural front-end model with noise and converter non-idealities show that RVSA matches the floating-point reference, reducing the mean allocation error from 0.38 of the pixel pitch for conventional single-photon counting to 0.14 in the 3 × 3 mode. Synthesized in a 40 nm CMOS process, the RVSA datapath occupies about 1740 µm² and dissipates 1.42 µW per pixel, fitting within a 50 × 50 µm² pixel alongside the analogue front-end.