Table 1.

Relationship between three-color parameters in the presence of acceptor blinking and two-color or pre-determined parameters.

Excitation	Acceptor dark state	3-color Parameter	2-color parametera		Pre-determined parameterb
			DA1	DA2
Donor	A2 dark	ε1Sbd	${\epsilon }_S^{\text{DA1}}\left(1-{\epsilon }_{\text{d}12}\right)$
		ε2Sbd	${\epsilon }_S^{\text{DA1}}{\epsilon }_{\text{d}12}$
	A1 dark	ε1Sdb		$\left(1-{\epsilon }_S^{\text{DA2}}\right){\epsilon }_{\text{d}1}$
		ε2Sdb		${\epsilon }_S^{\text{DA2}}$
	A1, A2 dark	ε1Sdd			εd1
		ε2Sdd			εd2
A1	A1 dark	ε12Sbd			εd12
	A2 dark	ε12Sdb			ε12db
	A1, A2 dark	ε12Sdd			ε12dd

^a${\epsilon }_S^{\text{DA1}}=\left(n_{\text{A}1}+n_{\text{A}2}\right)/\left(n_{\text{D}}+n_{\text{A}1}+n_{\text{A}2}\right)$ and ${\epsilon }_S^{\text{DA2}}={\eta }_{\text{A}2}/\left(n_{\text{D}}+n_{\text{A}1}+n_{\text{A}2}\right)$ (see eq 26).

^bε_d1 (ε_d2) is the fraction of photons detected in A1 (A2) channel after donor excitation when A1 and A2 are in the dark state, which are pre-determined from the donor-only segments. ${\epsilon }_{\text{d}1}=n_{\text{A1}}^0/(n_{\text{D}}^0+n_{\text{A1}}^0+n_{\text{A2}}^0)$ and ${\epsilon }_{\text{d}2}=n_{\text{A2}}^0/(n_{\text{D}}^0+n_{\text{A1}}^{\text{0}}+n_{\text{A2}}^0)$, where $n_{\text{D}}^0,n_{\text{A1}}^{\text{0}},\text{ and }{n}_{\text{A2}}^0$ are the count rates in D, A1 and A2 channels, respectively, of the donor-only segment. Note that ε_d1, ε_d2, and ε_d12 are not corrected for background photons, and therefore, are different from the leak values l₁, l₂, and l₁₂ in eq 31. ε_d12 is the fraction of A2 photons detected after A1 excitation when A2 is in the dark state, which is pre-determined from DA1 segments by A1 excitation. ${\epsilon }_{12\text{db}}=n_{\text{A2}}^{\text{Aex}0}/(n_{\text{A1}}^{\text{Aex}0}+n_{\text{A2}}^{\text{Aex}0}),$ where $n_{\text{A1}}^{\text{Aex0}}\text{ and }{n}_{\text{A2}}^{\text{Aex0}}$ are the count rates in A1 and A2 channels, respectively, of the A2 only segments by the A1 excitation laser. ε_12dd is determined by background photons in both A1 and A2 channels.