Precision of mono-exponential decay estimates from rapid lifetime determination in the presence of signal photon and background noise

Precision of mono-exponential decay time estimates using the rapid lifetime determination (RLD) method is analyzed, taking into account both signal photon shot noise and Gaussian background noise. Analytical expressions are derived that enable selection of optimum gate width and inter-gate delay values, and the range of validity of these expressions is tested with random number simulations. The analysis includes both the general case when gates are allowed to overlap in time and the specific case when they do not overlap. The analysis is also applicable to whole decay measurements, from which two gates are selected afterwards for lifetime estimation.