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\caption{\label{tab:ph_sel_alex}Photon selection syntax (ALEX)}  \end{table}  \subsection{Background periods} definitions}  \label{sec:bg_intro}  Even when no molecule is crossing the excitation volume, there are “background counts” due to detectors dark counts, out of focus molecules and sample scattering and/or auto-fluorescence. Figure~\ref{fig:bgdist} shows the typical distribution of timestamps delays (i.e. the 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 minimal timestamp delay threshold above which the distribution can be considered exponential. We also need to chose a fitting method, for example the Maximum Likelihood Estimation (MLE) or a curve fit of the histogram via non-linear least squares (NLSQ).