deletions | additions       diff --git a/Results1.tex b/Results1.tex  index 781f90f..f1c300f 100644  --- a/Results1.tex  +++ b/Results1.tex 
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Typical single photon events detected with the EBCCD are shown in Fig~\ref{fig1}c,d. The central peak is high with small wings: during the diffusion of the electrons from the back of the sensor to the front, the charge spills over into adjacent pixels. Brighter, larger ion events are also detected, caused by a photoelectron ionising a residual gas molecule in the imperfect vacuum inside the EBCCD tube, leading to the resulting ion being accelerated towards the photocathode (Fig~\ref{fig1}c,d, top). These ion events 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 are 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 due to the relatively rare occurrence of ion events compared to photon events (i.e.\ an ion event every few frames) this does not have a noticeable effect on the results.  hoton Photon  counting images of the USAF test chart with 30,000 frames are shown in Fig~\ref{fig_results}. The sum of the frames without any processing includes the camera noise and produces a very noisy image (Fig~\ref{fig_results}b), while centroiding with one pixel accuracy, where the photon is assigned to the center pixel the event and the edges ignored, removes the camera background and produces a much clearer image (Fig~\ref{fig_results}c). Each pixel was then divided into 5$\times$5 subpixels, and each photon event was assigned a sub-pixel according to the centroid position calculated by sub-pixel localisation algorithm. This method of centroiding with 1/5-pixel accuracy results in an even better image (Fig~\ref{fig_results}d) as it seems to recover some of the resolution lost by the electron diffusion in the sensor, as shown in Fig~\ref{fig_results}e. The mismatch between the photon event shape and the centroiding function can lead to fixed pattern noise (FPN) which can be seen as bright and dark stripes in the centroided image.\cite{Suhling1999} The level of FPN can be quantified by  \begin{equation}