Cram\'er-Rao analysis of lifetime estimations in time-resolved fluorescence microscopy

TL;DR

This paper applies Fisher information theory to determine the fundamental limits of lifetime estimation precision in time-resolved fluorescence microscopy, considering various noise sources and experimental parameters.

Contribution

It introduces a Cramér-Rao bound analysis for lifetime estimations, including background noise and IRF effects, with an open-source tool for practical application.

Findings

Lower bounds on lifetime estimation precision derived

Impact of background noise and IRF analyzed

Open-source code provided for experimental optimization

Abstract

Measuring the lifetime of fluorescent emitters by time-correlated single photon counting (TCSPC) is a routine procedure in many research areas spanning from nanophotonics to biology. The precision of such measurement depends on the number of detected photons but also on the various sources of noise arising from the measurement process. Using Fisher information theory, we calculate the lower bound on the precision of lifetime estimations for mono-exponential and bi-exponential distributions. We analyse the dependence of the lifetime estimation precision on experimentally relevant parameters, including the contribution of a non-uniform background noise and the instrument response funtion (IRF) of the setup. We also provide an open-source code to determine the lower bound on the estimation precision for any experimental conditions. Two practical examples illustrate how this tool can be used to reach optimal precision in time-resolved fluorescence microscopy.