= Optimal Förster distance for two-state contrast
{title2=$R_{0,\mathrm{opt}}=\sqrt{AB}$}
For <FRET efficiency> $E(R)=1/[1+(R/R_0)^6]$ and distinct positive reporter distances A and B, the absolute contrast is maximized at the geometric mean <Förster distance> $R_0=\sqrt{AB}$. Substitution of $x=R_0^6$ makes the derivative have the sign of $A^6B^6-x^2$. The maximum is $|B^3-A^3|/(B^3+A^3)$ and the two efficiencies then sum to one. If $A=B$, every choice gives zero contrast and there is no unique optimum.
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