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\subsection{Event recognition and overlapping events}  Typical single photon events detected with the EBCCDat 8 kV acceleration voltage and maximum read-out gain  are shown in Fig~\ref{fig1}. Fig~\ref{fig1}c,d.  The central peak is high with small wings, and the events are wider in the horizontal direction. Brighter, larger ion  events are also detected, caused by a photoelectron hitting a gas molecule in the imperfect vacuum inside the EBCCD tube, leading to the gas molecule being ionised and accelerated towards the photocathode. photocathode (Fig~\ref{fig1}c,d, top). The data also contains some overlapping photons events (Fig~\ref{fig1}c,d, bottom left).  \begin{itemize}  \item Ion The ion  events \item Multi-emitter fitting analysis  \item Table: Photon count statistics  \item Images: detected cause problems with event recognition algorithms that find a threshold for each frame separately; the high brightness causes the threshold to be set too high and the photon  events with/without MFA  \end{itemize} discarded as noise. The raw data was therefore preprocessed using ImageJ's tools by setting the intensity of all bright pixels in the ion events to a grey value slightly above the maximum intensity of the photons events. The ion events are then incorrectly localised as photon events, but the relatively rare occurrence of ion events compared to photon events (around 1 ion event / 1000 photon events ??? - check this) does not have a noticeable effect on the results.  \subsection{FPN *** Something about the event recognition methods  and centroiding accuracy} how well they work with our data... ***  - Result images In traditional photon counting imaging  and cross-sections centroiding with simple one-iteration algorithms, it is usually ensured that the frames do not contain images of photons that have any overlap. However, in biological imaging with super-resolution microscopy the image acquisition speed is a critical parameter which can be shortened by imaging as many molecules as possible in each frame. While simple one-iteration center-of-mass algorithms are not capable  of bars Fig~\ref{fig_results} guessing which proportion of the detected intensity in a pixel that contains overlapping intensity from more than one photon belongs to which photon event, the separation of overlapping events is possible with algorithms that fit several point-spread functions to an area containing overlapping events. ThunderSTORM's option for Multi-emitter Fitting Analysis (MFA) produces excellent results with recognising and separating overlapping EBCCD photon events, as shown in Fig~\ref{fig_mfa}.  - Pixel images (and maybe histograms) Fig~\ref{fig_pixelimages}