deletions | additions       diff --git a/smFRET data analysis.tex b/smFRET data analysis.tex  index f40658b..ec81d81 100644  --- a/smFRET data analysis.tex  +++ b/smFRET data analysis.tex 
...
\subsection{Background periods}  \label{sec:bg_intro}  Even when no molecule is crossing the excitation volume, there are “background counts” originating from detectors dark counting rates (DCR), samples scattering and auto-fluorescence. Figure~\ref{fig:bg_dist} Figure~\ref{fig:bgdist}  shows the typical distribution of timestamps delays (waiting times between two subsequent timestamps) in a smFRET measurement. The “tail” of the distribution (a line in semi-log scale) corresponds to exponentially-distributed delays, indicating that those counts are generated by a \href{http://en.wikipedia.org/wiki/Poisson_process}{Poisson process}. At short timescales, the distribution departs from the exponential due to the bursts of photons from diffusing single-molecules (the signal). To estimate the background rate, (i.e. the exponential time constant) we need to select a minimum threshold above which the distribution can be considered exponential. Then, we need to chose a fit method, for example the Maximum Likelihood Estimation (MLE) or a curve fit of the histogram via non-linear least squares (NLSQ). In practice, for burst search and burst correction, the background rates for all the different photon streams are needed. Furthermore, since the background rate can typically change during the measurement on time scales of tens of seconds or minutes, we want to estimate it periodically. FRETBursts splits the data in uniform time slices called \textit{background periods} and compute the background rates for each of these slices (see section~\ref{sec:bg_calc}). The slicing in background periods is also used during burst search to compute a background-dependent threshold and to apply the burst correction (section~\ref{sec:burstsearch}).