The lower bound on the timing resolution of scintillation detectors

The timing performance of scintillation detectors is ultimately limited by photon counting statistics. In fact, photon counting statistics form a dominant contribution to the overall timing resolution of many state-of-the-art detectors. A common approach to investigate this contribution is to calculate the variance in the registration times of individual scintillation photons within the photosensor. However, in general the single-photon variance is not equal to the intrinsic limit on the timing resolution, since in principle one can make use of the timing information carried by all photons detected. In this work, the Cramér-Rao lower bound on the timing resolution of a scintillation detector, based on the information contained in the full set of registered photons, is calculated. The results appear to be in good agreement with trends observed in the literature. Furthermore, it is shown that the timestamp obtained from any single scintillation photon never yields the optimum timing resolution for realistic scintillation detectors. Yet, it appears that the intrinsic timing resolution limit can be approached closely by making use of the timestamps from a relatively small number of photons emitted during the initial part of the scintillation pulse.