deletions | additions       diff --git a/Results1.tex b/Results1.tex  index 4f35da2..057f9c5 100644  --- a/Results1.tex  +++ b/Results1.tex 
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\section{Results \& Discussion}  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 hitting ionising  a residual  gas molecule in the imperfect vacuum inside the EBCCD tube, leading to the gas molecule resulting ion  beingionised and  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 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 (around 1 ion event per 600 photon events) this does not have a noticeable effect on the results.  The 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 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 (around 1 ion event per 600 photon events) this does not have a noticeable effect on the results. Photon counting images of the USAF test chart are shown in Fig~\ref{fig_results}. As the photon events are relatively dim compared to the high camera background noise, the sum of the frames without any processing produces a noisy image (Fig~\ref{fig_results}b), while centroiding with one pixel accuracy removescamera  the camera  background and produces a clearer image (Fig~\ref{fig_results}c). Centroiding with 1/5-pixel accuracy (Fig~\ref{fig_results}d) recovers 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 event shape and the centroiding function can lead to fixed pattern noise which can be seen as bright and dark stripes in the centroided image. The level of fixed pattern noise can be quantified by  \begin{equation} 
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Several of ThunderSTORM's centroiding algorithms were tested to find an algorithm that leads to a minimum amount of fixed pattern noise (see Table~\ref{table:results}). The distributions of centroided positions are shown in Fig~\ref{fig_pixelimages}, where the pixels are further divided into a 13$\times$13 grid. Maximum likelihood (ML) fitting with a Gaussian PSF produces the most uniform distribution of localised positions (Fig~\ref{fig_pixelimages}a-c), as well as the finding the highest number of photons. As reported previously,\cite{Hirvonen2014_rsi} the horizontal widening of the photon events, most likely caused by the CCD read-out, causes a bias in the centroided positions and photons are most likely to be found towards the right edge of the pixel. Other methods produce results with similar distribution of centroided positions but with higher FPN and lower photon count (an example of weighted LS fit with integrated Gaussian PSF is shown in Fig~\ref{fig_pixelimages}d), with the exception of the radial symmetry method, which changes the bias to the vertical direction (Fig~\ref{fig_pixelimages}e).