An overview of continuous and discrete phasor analysis of binned or time-gated periodic decays

Time-resolved analysis of periodically excited luminescence decays by the phasor method in the presence of time-gating or binning is revisited. Analytical expressions for discrete configurations of square gates are derived and the locus of the phasors of such modified periodic single-exponential decays is compared to the canonical universal semicircle. The effects of IRF offset, decay truncation and gate shape are also discussed. Finally, modified expressions for the phase and modulus lifetimes are provided for some simple cases. A discussion of a modified phasor calibration approach is presented.