  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.
