Generalization of the polar representation in time domain fluorescence lifetime imaging microscopy for biological applications: practical implementation

The polar representation or phasor, which provides a fast and visual indication on the number of exponentials present in the intensity decay of the fluorescence lifetime images is increasingly used in time domain fluorescence lifetime imaging microscopy experiments. The calculations of the polar coordinates in time domain fluorescence lifetime imaging microscopy experiments involve several experimental parameters (e.g. instrumental response function, background, angular frequency, number of temporal channels) whose role has not been exhaustively investigated. Here, we study theoretically, computationally and experimentally the influence of each parameter on the polar calculations and suggest parameter optimization for minimizing errors. We identify several sources of mistakes that may occur in the calculations of the polar coordinates and propose adapted corrections to compensate for them. For instance, we demonstrate that the numerical integration method employed for integrals calculations may induce errors when the number of temporal channels is low. We report theoretical generalized expressions to compensate for these deviations and conserve the semicircle integrity, facilitating the comparison between fluorescence lifetime imaging microscopy images acquired with distinct channels number. These theoretical generalized expressions were finally corroborated with both Monte Carlo simulations and experiments.