Investigation of the statistical distribution of noise in fluorescence lifetime imaging microscopy (FLIM) measurements

Fluorescence Lifetime Imaging Microscopy (FLIM) is an advanced imaging modality that extends traditional fluorescence microscopy by capturing the decay rate of excited fluorophores. However, accurate lifetime measurement in FLIM depends critically on accounting for its unique noise properties, which often become non-Gaussian and non-Poisson at low photon counts. In this paper, we develop a comprehensive theoretical framework to describe the underlying noise distributions for frequency-domain and time-domain FLIM, considering one-photon and two-photon excitations. We derive closed-form expressions for the statistical moments of the in-phase, quadrature, and total intensity components under different demodulation strategies, showing how factors like higher-order harmonics, photon flux, and demodulation techniques contribute to the statistical properties of FLIM measurements. Monte Carlo simulations validate our analytical results, confirming that these noise distributions transition from significantly skewed at low photon counts to nearly Gaussian at higher signal levels. These findings offer valuable guidance for designing improved FLIM estimators and reconstruction algorithms, especially in challenging scenarios with a limited photon budget.