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\verb|bg.exp_fit| estimates the background using a maximum likelihood estimation
(MLE) of the delays distribution. Additional fitting functions are available in
\verb|bg| namespace
(i.e. the \verb|background|
modulw, module, \href{http://fretbursts.readthedocs.org/en/latest/background.html}
{link}). The second argument, \verb|time_s|, is the
\textit{background period} (section~\ref{sec:bg_intro}) and the third, \verb|tail_min_us|,
is the inter-photon delay threshold above which the distribution is assumed exponential.
It is possible to use different thresholds for each photon stream, passing a
tuple (i.e. a comma-separated list of values, \href{https://docs.python.org/3.5/tutorial/datastructures.html#tuples-and-sequences}{link}) instead of a scalar.
Finally, it is possible to use a heuristic estimation of the threshold using
\verb|tail_min_us='auto'|. For more details refer to the \verb|calc_bg| documentation
(\href{http://fretbursts.readthedocs.org/en/latest/data\_class.html#fretbursts.burstlib.Data.calc_bg}{link}).
After FRETBursts provides are two kind of plots to represent the
background has been estimated, it background. One is
useful to compare the
histogram histograms
of inter-photon delays
with an compared to the fitted exponential distribution
as shown reported in
figure~\ref{fig:bg_dist_all} figure~\ref{fig:bg_dist_all}) (see
section~\ref{sec:bg_intro}). section~\ref{sec:bg_intro} for details on the inter-photon distribution).
This plot is performed
with: with the command:
\begin{lstlisting}
dplot(d, hist_bg, bp=0)
...
Figure~\ref{fig:bg_dist_all} allows to quickly identify pathological cases when the
background fitting procedure returns unreasonable values.
Another useful The second background-related plot is the timetrace of the estimated
background, background rates,
as shown in figure~\ref{fig:bg_timetrace}. This plot allows to monitor background changes
taking place during the measurement.
In our experience, coverglass This plot is obtained with the commans:
\begin{lstlisting}
dplot(d, timetrace_bg)
\end{lstlisting}
Coverglass impurities can contribute to the background even when focusing
deep into the sample
(10um (10μm or more),
and these These impurities tend to bleach on timescales of minutes resulting in
background variations
during the course of the measurement, such as
the one shown in figure~\ref{fig:bg_timetrace}a.
Another source of background variation, visible in figure~\ref{fig:bg_timetrace}b, is
the evaporation in case Additionally, when the sample
is placed on the coverglass without in not sealed in an
enclosure (gasket). observation chamber,
evaporation can contribute to background variations, similar to the
one shown in figure~\ref{fig:bg_timetrace}b.
\paragraph{Python details} For an ALEX measurement, the tuple passed to
\verb|tail_min_us| to define the thresholds, is required to have have
5 values corresponding the 5 photon streams.
The
ordering order of the photon streams can be obtained from
the \verb|Data.ph_streams|
attributes attribute (i.e. \verb|d.ph_streams| in our example).
The estimated background rates are stored in the \verb|Data| attributes
\verb|bg_dd|, \verb|bg_ad| and \verb|bg_aa|, corresponding to the photon
streams \verb|Ph_sel(Dex='Dem')|, \verb|Ph_sel(Dex='Aem')| and \verb|Ph_sel(Aex='Aem')|
respectively. These attributes are lists of arrays (one array per excitation spot).
The arrays contain the estimated background rates in the different background periods.
\subsubsection{Error metric and optimal threshold}
The functions that fit the background also return an estimation of the
