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fzimmermann89 committed Jun 6, 2021
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10 changes: 9 additions & 1 deletion Tex/app_plots.tex
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Expand Up @@ -15,8 +15,16 @@ \section{Simulation}
\end{table}
\section{Experiment}

\begin{figure}
\centering
\includegraphics[width=0.8\linewidth]{images/kossel_gaas.png}
\caption{Mean images of 5000 shots after background subtraction for sample 1 (left) and sample 2 (right)}
\label{fig:kosselgaasmean}
\end{figure}


\begin{table}
\caption{Miller Indices considered in Kossel line least squares regression of GaAs sample 1 (left) and sample 2 (right). Not all possible Kossel lines are visible in the recorded images.}
\caption[Miller Indices considered in Kossel line least squares regression of GaAs sample]{Miller Indices considered in Kossel line least squares regression of GaAs sample 1 (left) and sample 2 (right). Not all possible Kossel lines are visible in the recorded images.}
\begin{tabular}[t]{lll}
\toprule
h& k & l \\
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21 changes: 10 additions & 11 deletions Tex/experiment.tex
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Expand Up @@ -205,25 +205,23 @@ \subsection{Preprocessing}
\paragraph{Crystal orientation}
For determining the relative orientation of the crystal with regards to the detector, Kossel lines as described in \fref{chap:kossel} can be used. A semi-automatic alignment program was developed (\fref{fig:kosselfit}) to aid with the procedure:

For each sample, the images are split into sets of 5000 shots and (after filtering for hot pixels and cutting bellow a noise threshold of 2\,keV), the mean is taken. To better distinguish the Kossel lines from uniform fluorescence, a Gaussian blurred version ($\sigma$=20\, px) is subtracted. Kossel lines are identified visually and the local maxima in the 20x20\,px surrounding block of a selected Kossel line are considered as points on the Kossel line. A least-square regression is performed to minimize the sum of the distances of identified points from Kossel lines by varying the rotation angles and detector translation.
As initial parameters, a 5.65\,\AA\, lattice constant, 9.25\,keV energy and 2800\,px detector distance and the result of a 2D cubic fit to the fluorescence background for the values of the translational shift are used.
For each sample, the images are split into sets of 5000 shots and (after filtering for hot pixels and cutting bellow a noise threshold of 2\,keV), the mean is taken. To better distinguish the Kossel lines from uniform fluorescence, a Gaussian blurred version ($\sigma$=20\, px) is subtracted (see \fref{fig:kosselgaasmean} for examples). The Kossel lines are identified visually and the local maxima in the 20x20\,px surrounding block of a selected Kossel line are considered as points on the Kossel line. A least-square regression is performed by varying the rotation angles and detector translation as described in \fref{chap:kossel}.
As initial parameters, a 5.65\,\AA\, lattice constant, 9.25\,keV energy, 14\,cm detector distance and the result of a 2D cubic fit to the fluorescence background for the values of the x- and y-shifts are used.

The results are shown in \fref{tab:kosselfit} as mean over the sets for each sample and maximum deviation from the mean as an error estimation.
The used lines are shown in \fref{fig:kosselgaaslines} and \fref{tab:kosselpeaks}, the results are shown in \fref{tab:kosselfit} as mean over the sets for each sample and maximum deviation from the mean as an error estimation.

The detector shift is corrected before calculating the correlations, the rotation angles are used afterwards to determine the expected position of Bragg peaks in the reconstruction.
\begin{figure}
\centering
\includegraphics[width=0.8\linewidth]{images/kosselfit.png}
\caption{Program for fitting Kossel lines to experimental data}
\label{fig:kosselfit}
\end{figure}

\begin{figure}
\centering
\begin{subfigure}{0.7\textwidth}
\includegraphics[width=\linewidth]{images/kossel_gaas.png}
\caption{Mean images after background subtraction for sample 1 (left) and sample 2 (right)}
\end{subfigure}
\\



\begin{figure}
\begin{subfigure}{0.35\textwidth}
\includegraphics[width=\linewidth]{images/kossel_gaas1.pdf}
\caption{Indexed lines on sample 1}
Expand All @@ -233,7 +231,8 @@ \subsection{Preprocessing}
\includegraphics[width=\linewidth]{images/kossel_gaas2.pdf}
\caption{Indexed lines on sample 2}
\end{subfigure}
\caption[Kossel lines on GaAs samples]{Kossel lines on GaAs samples after background subtraction (a) and the indexed lines overlaid in the determined orientation (b and c).}
\caption[Kossel lines on GaAs samples]{Indexed Kossel lines in the determined orientation overlaid over the mean of 5000 shots after background subtraction. For a list of all considered indices, see \fref{tab:kosselpeaks}.}
\label{fig:kosselgaasline}
\end{figure}

\begin{table}[]
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2 changes: 1 addition & 1 deletion Tex/simulation.tex
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Expand Up @@ -232,7 +232,7 @@ \subsection{Multiple Samples}
\caption{IDI Reconstruction \\ $ $}
\label{fig:multisphere2}
\end{subfigure}
\caption{Structure factors of a sphere with 20\,nm radius, a 200\,nm Gaussian focus and a random distribution of points at least 50\,nm apart (a), the structure factor of different numbers of hard 20\,nm radius spheres with an additional 5\,nm separating layer on each sphere inside the focal volume (b), and the result of an IDI simulation assuming iron fluorescence, a mean of $5*10^4$ excited atoms per sphere, a 1024x1024 pixel (100\,um pixelsize) detector in a distance of 30\,cm (resulting in approximately 1\% of the emitted photons being captured), and using 5000 images (c). The shaded area is the standard error of the mean over images, the markers show the discrete $q$ steps in the reconstruction.}
\caption[Structure factors and reconstructions for multiple spherical samples]{Structure factors of a sphere with 20\,nm radius, a 200\,nm Gaussian focus and a random distribution of points at least 50\,nm apart (a), the structure factor of different numbers of hard 20\,nm radius spheres with an additional 5\,nm separating layer on each sphere inside the focal volume (b), and the result of an IDI simulation assuming iron fluorescence, a mean of $5*10^4$ excited atoms per sphere, a 1024x1024 pixel (100\,um pixelsize) detector in a distance of 30\,cm (resulting in approximately 1\% of the emitted photons being captured), and using 5000 images (c). The shaded area is the standard error of the mean over images, the markers show the discrete $q$ steps in the reconstruction.}

\end{figure}

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2 changes: 1 addition & 1 deletion Tex/theory.tex
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Expand Up @@ -274,7 +274,7 @@ \subsection{Signal}
\caption{Photon Statistics}
\label{fig:stat}
\end{subfigure}
\caption{Temporal Modes for a Lorentzian Spectrum and Gaussian excitation (a): In the limit of longer excitation pulses, the number of modes increases linear with the pulse duration. Photon statistics with different numbers of modes $M$ and equal mean of 0.1\,photons (b): A lower number of modes corresponds the an higher probability of observing multi photon events. The limit of a high number of modes is a Poisson distribution.}
\caption[Temporal Modes and Photons statistics]{Temporal Modes for a Lorentzian Spectrum and Gaussian excitation (a): In the limit of longer excitation pulses, the number of modes increases linear with the pulse duration. Photon statistics with different numbers of modes $M$ and equal mean of 0.1\,photons (b): A lower number of modes corresponds the an higher probability of observing multi photon events. The limit of a high number of modes is a Poisson distribution.}
\end{figure}

The experimentally indistinguishable fluorescence energies $K_\alpha,1$ and $K_\alpha,2$ (as well as $K_\beta$ if no filter is used for suppression) give additional independent modes $M_E$
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