Figure 2: Determining correction factors for acceptor direct excitation (δ) and donor cross talk (α).

Using the apparent fluorescence stoichiometry ratio, $\widehat{S}$, it is possible to identify bursts from molecules with either only active donor (i.e., $\widehat{S}$ ≈ 1) or only active acceptor (i.e., $\widehat{S}$ ≈ 0) fluorophores. The apparent mean transfer efficiency, $\langle \widehat{E}\rangle$, of the donor-only subpopulation is used to determine the correction factor for cross-talk, $\alpha =\frac{\langle {\widehat{E}}_{\mathit{\text{donor}}-\mathit{\text{only}}}\rangle }{1-\langle {\widehat{E}}_{\mathit{\text{donor}}-\mathit{\text{only}}}\rangle }$. The apparent mean fluorescence stoichiometry ratio, $\langle \widehat{S}\rangle$, associated with the acceptor-only subpopulation is used to determine the correction factor for direct excitation, $\delta =\frac{\langle {\widehat{S}}_{\mathit{\text{acceptor}}-\mathit{\text{only}}}\rangle }{1-\langle {\widehat{S}}_{\mathit{\text{acceptor}}-\mathit{\text{only}}}\rangle }$ (due to background correction, Ê values for the acceptor-only bursts extend beyond the range shown). With pulsed interleaved excitation (PIE), time-correlated single-photon counting, and four-channel detection, it is also possible to obtain time-resolved fluorescence intensity and anisotropy decay plots from the parallel and perpendicular emission of the donor-only subpopulation after donor excitation (i.e., ∥ ${\widehat{N}}_D^d$ and ⊥ ${\widehat{N}}_D^d$) and the parallel and perpendicular emission of the acceptor-only subpopulations after acceptor excitation (i.e, ∥ ${\widehat{N}}_{tot}^a$ and ⊥ ${\widehat{N}}_{tot}^a$). This information is then used to determine the fluorescence lifetimes of donor and acceptor fluorophores and the time-resolved and the steady-state anisotropies (r_ss) of the fluorophores.