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 uni-versal semicircle. The effects of IRF offset, decay truncation and gate shape are also discussed. Finally, modified expressions for the phase and modulus lifetimes are pro-vided for some simple cases. A discussion of a modified phasor calibration approach is presented, and illustration of the new concepts with examples from the literature conclude this work.