deletions | additions       diff --git a/Results: Centroiding.tex b/Results: Centroiding.tex  index 7017698..647d448 100644  --- a/Results: Centroiding.tex  +++ b/Results: Centroiding.tex 
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\subsection{FPN and centroiding accuracy}  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 removes camera the background and produces a clearer image (Fig~\ref{fig_results}c). Centroiding with 1/5-pixel resolution accuracy  (Fig~\ref{fig_results}d-f) recovers some of the resolution lost by the electron diffusion in the sensor, as shown in Fig~\ref{fig_results}g.\begin{figure}[tbp]  \centerline{\includegraphics[width=1\columnwidth]{fig2}}  \caption{\label{fig_results} Images of USAF test pattern obtained by single photon counting with an EBCCD. (a) Imaged area of USAF test pattern, (b) sum of frames, (c) 1-pixel centroiding, (d) ML with Gaussian PSF, (e) weighted LS with Intergrated Gaussian PSF, (f) radial symmetry, and (g) line profiles of the area indicated in (a) by the orange rectangle. }  \end{figure}  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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\end{equation}  where $N_{max}$, $N_{min}$, and $N_{mean}$ are the maximum, minimum and average number of counts in the 5$\times$5 array of subpixel positions, respectively. For a completely random distribution, this number should approach zero with increasing number of photons.  Several of ThunderSTORM's centroiding algorithms were tested to find an algorithm that leads to a minimum amount of fixed pattern noise. noise (see Table~\ref{table:results}).  The distributions of centroided positions are shown in Fig~\ref{fig_pixelimages}, where the pixels are further divided into a 13$\times$13 grid.The results are summarised in Table~\ref{table:results}.  Maximum likelihood (ML) fitting with a Gaussian PSF produces the most uniform distribution of localised positions (Fig~\ref{fig_pixelimages}a) with FPN of 71\%, 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. Radial symmetry method produces similar results with a slightly higher FPN of 91\%, but changes the bias to the vertical direction (Fig~\ref{fig_pixelimages}c). Other methods produce results with similar distribution of centroided positions as ML (an example of weighted LS fit with integrated Gaussian PSF is shown in Fig~\ref{fig_pixelimages}b), but with higher FPN and lower photon count.