Fundamental bound on scintillation timing

Derive the Cramer-Rao lower bound (the minimum variance any unbiased estimator can reach) on timing precision for a scintillation detector including non-exponential rise and decay, position-dependent light transport inside the crystal, photodetector single-photon time response and dark counts, and construct an estimator reaching it. An answer is the bound as a function of photon yield, rise time, decay time and transit-time spread, plus a realizable estimator.

A derivation with an estimator demonstrated in simulation and on bench data to approach the bound.