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SangYoon Chung edited Burst_Variance_Analysis.tex
about 8 years ago
Commit id: efd5e990aa1c701035683fca91aa6b454da6ce49
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A FRET peak originating from a single static FRET efficiency has the minimum width and
the sub-bursts acceptor counts ($N_a$) will ideally follow a binomial distribution of
eq.~\ref{eq:binom_dist}, where $n$ is the number of photons in each sub-burst and
$E$ is the FRET efficiency. (In practice, Proximity ratio is used as
$E$.) $E$) Since, as mentioned, $N_a$ will follow a binomial distribution and $E$ = {$N_a$}/\textit{n}, we expect the standard deviation of $E$ for the sub-bursts to be distributed according to eq.~\ref{eq:binom_std}. This is an approximation because background counts (both from sample and detector's dark counts) add additional variance that is not taken into account.
However, the approximation works well in practical cases because the background contribution
is normally a small fraction of the total number of counts (therefore it marginally contributes to the variance).