  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.
