Number of energy windows for photon counting detectors: is more actually more?

It has been debated whether photon counting detectors (PCDs) with moderate numbers of energy windows ( $N_E$ ) perform better than PCDs with higher $N_E$ . A higher $N_E$ results in fewer photons in each energy window, which degrades the signal-to-noise ratio of each datum. Unlike energy-integrating detectors, PCDs add very little electronic noise to measured counts; however, there exists electronic noise on the pulse train, to which multiple energy thresholds are applied to count photons. The noise may increase the uncertainty of counts within energy windows; however, this effect has not been studied in the context of spectral imaging tasks. We aim to investigate the effect of $N_E$ on the quality of the spectral information in the presence of electronic noise.

We obtained the following three types of PCD data with various $N_E$ (= 2 to 24) and noise levels using a Monte Carlo simulation: (A) A PCD with no electronic noise; (B) realistic PCDs with electronic noise added to the pulse train; and (C) hypothetical PCDs with electronic noise added to each energy window's output, similar to energy-integrating detectors. We evaluated the Cramér-Rao lower bound (CRLB) of estimation for the following two spectral imaging tasks: (a) water-bone material decomposition and (b) K-edge imaging.

For both the e-noise-free and realistic PCDs, the CRLB improved monotonically with increasing $N_E$ for both tasks. In contrast, a moderate $N_E$ provided the best CRLB for the hypothetical PCDs, and the optimal $N_E$ was smaller when electronic noise was larger. Adding one energy window to the minimum necessary $N_E$ for a given task gained 66.2% to 68.7% of the improvement $N_E=24$ provided.

For realistic PCDs, the quality of the spectral information monotonically improves with increasing $N_E$ .