A fundamental limit on timing performance with scintillation detectors

A new lower bound on the mean-squared error of postdetection γ-ray time-of-flight estimators has been derived. Previously, the Cramer-Rao bound has been used, but for nearly exponentially decaying scintillation pulses it gives an extremely optimistic picture of the achievable performance, depending critically on the dark current and photomultiplier characteristics. The new bound has been derived under the assumption that excited states in the scintillator leading to the emission of scintillation photons have an exponential lifetime density. The bound is a function of the mean state lifetime, the spectrum of energy deposited, and the energy conversion efficiency of the scintillator, and it is exact for the observation of a mono-exponentially decaying photoelectron rate at the first dynode of the photomultiplier tube given the γ-ray arrival time