Error Analysis of the Rapid Lifetime Determination Method for Double-Exponential Decays and New Windowing Schemes

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Abstract
The rapid lifetime determination method (RLD) is a mathematical technique for extremely rapid evaluations of lifetimes in exponential decays. It has been applied in luminescence microscopy and single-molecule lifetime evaluation. To date, the primary application has been in single-exponential evaluations. We present extensions of the method to double exponentials. Using Monte Carlo simulations, we assess the performance of both the double-exponential decay with known lifetimes and the double-exponential decay with unknown preexponential factors and lifetimes. Precision is evaluated as a function of the noise level (Poisson statistics), the ratios of the lifetimes, the ratios of their preexponential factors, and the fitting window. Optimum measurement conditions are determined. RLD is shown to work well over a wide range of practical experimental conditions. If the lifetimes are known, the preexponential factors can be determined with good precision even at low total counts (104). With unknown preexponential factors and lifetimes, precisions decrease but are still acceptable. A new gating scheme (overlapped gating) is shown to offer improved precision for the case of a single-exponential decay. Theoretical predictions are tested against actual experimental data from a laser-based lifetime instrument.