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Tex/experiment.tex

@@ -1,6 +1,6 @@
 \chapter{Experimental Verification}
 \label{chap:experiment}
-Using the knowledge gained by the simulation, an experiment at the beamline 3 of the SACLA FEL is performed. The experiment consisted of three parts: First, reproducing the results of Nakumura et al. and imaging projection of the focal volume of the FEL by using metal foils as samples, performing a measurement of the K$\alpha$  fluorescence and an reconstruction in the small angle regime. Second, moving to a smaller length scale and trying to image nanoparticles. And Third, leaving the small angle regime and recording the fluorescence of a single crystal and perform a reciprocal space reconstruction.
+Using the knowledge gained by the simulation, an experiment at the beamline 3 of the SACLA FEL is performed. The experiment consists of three parts: First, reproducing the results of Nakumura et al. and imaging projection of the focal volume of the FEL by using metal foils as samples, performing a measurement of the K$\alpha$  fluorescence and an reconstruction in the small angle regime. Second, moving to a smaller length scale and trying to image nanoparticles. And Third, leaving the small angle regime and recording the fluorescence of a single crystal and perform a reciprocal space reconstruction.
 \section{Sample Preparation and Characterization}
 As a nanoparticle sample, spherical iron oxide nanoparticles are chosen for their commercial availability in high quality. To improve the number of detected fluorescence photons per FEL shot, a preparation allowing (statistically) multiple particles inside the focus is chosen. This greatly reduces the possibility of having shots without any particles inside the focus as well.
 
@@ -134,7 +134,7 @@ \section{Setup of the Experiment}
 The sample is mounted in a 45° angle to the beam on a stack of two rotational/two translational/two rotational/three translational stage to allow scanning of the sample, to ensure perpendicularly of the scanning directions to the beam to stay within the Rayleigh length (approx. 100\,um horizontal/200\,um vertical) while also ensuring a parallel alignment of the sample surface to one of the detectors. Overall, two MPCCD detectors are used: A dual detector with two tiles, each 512x1024 pixels perpendicular to the FEL beam in a distance of 1\,m and a "Short Working Distance" octal detector, consisting of eight 512x1024 tiles, parallel to the sample surface in a distance $d_{octal}=$14-50\,cm. To suppress absorption and more importantly, air scattering, a vacuum pipe with Kapton windows is installed in between the sample and the dual detector.
 An L-shaped aluminum plate is installed to reduce stray light as well as to allow mounting of the beamstop and filters between sample and the detectors.
 
-The samples are scanned with a mean step size of 20\,um in horizontal direction (fast scanning direction) and 20\,um in vertical direction.between shots. The step size was chosen based on the crater size visible with an optical microscope of approximately 5-10\,um for the samples and energies used in the experiment.
+The samples are scanned with a mean step size of 20\,um in horizontal direction (fast scanning direction) and 20\,um in vertical direction.between shots. The step size is chosen based on the crater size visible with an optical microscope of approximately 5-10\,um for the samples and energies used in the experiment.
 
 \begin{figure}
 	\centering
@@ -197,7 +197,7 @@ \subsection{Preprocessing}
 \end{figure}
 
 \paragraph{Detector Artifacts}
-During the experiment, an unnoticed failure of the electronics of the octal detector has occurred, manifesting as periodic noise on most of the detector tiles at a much higher level than expected (see \fref{fig:octalissue} for an illustration). Not all columns of a tile are affected (in contrast to common-mode effects commonly encountered with different detectors). As the overall affected area of the detector is substantial and the noise leaks through the photon counting scheme by slightly influencing the probability of a pixel being considered a photon hit, causing correlations and therefore artifacts in the reconstruction in one direction, a correction was applied to the affected columns of affected tiles of the detector. For the correction, affected columns are first identified by filtering on the Fourier transform, neighboring effected columns are considered as a block and the medians over those block is calculated and subtracted. This scheme is chosen instead of the more commonly used portwise common modes due to the uneven strength of the artifact (see \fref{fig:app_correction} for a comparison). Using this correction reduces the artifact, but does not completely remove it. As the remaining artifact in the reconstructions is limited to low $q$ compared to the expected positions of the features of the samples and only two orthogonal lines, it can be masked out.
+During the experiment, an unnoticed failure of the electronics of the octal detector has occurred, manifesting as periodic noise on most of the detector tiles at a much higher level than expected (see \fref{fig:octalissue} for an illustration). Not all columns of a tile are affected (in contrast to common-mode effects commonly encountered with different detectors). As the overall affected area of the detector is substantial and the noise leaks through the photon counting scheme by slightly influencing the probability of a pixel being considered a photon hit, causing correlations and therefore artifacts in the reconstruction in one direction, a correction is applied to the affected columns of affected tiles of the detector. For the correction, affected columns are first identified by filtering on the Fourier transform, neighboring effected columns are considered as a block and the medians over those block is calculated and subtracted. This scheme is chosen instead of the more commonly used portwise common modes due to the uneven strength of the artifact (see \fref{fig:app_correction} for a comparison). Using this correction reduces the artifact, but does not completely remove it. As the remaining artifact in the reconstructions is limited to low $q$ compared to the expected positions of the features of the samples and only two orthogonal lines, it can be masked out.
 
 
 
@@ -252,7 +252,7 @@ \subsection{Preprocessing}
 
 
 \paragraph{Crystal orientation}
-For determining the relative orientation of the crystal with regards to the detector, Kossel lines as described in \fref{sec:kossel} can be used.  A semi-automatic alignment program was developed (\fref{fig:kosselfit}) to aid with the procedure.
+For determining the relative orientation of the crystal with regards to the detector, Kossel lines as described in \fref{sec:kossel} can be used.  A semi-automatic alignment program has been 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 (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,
 

Tex/simulation.tex

@@ -1,7 +1,7 @@
 \chapter{Simulations}
 \label{chap:simulation}
 To illustrate the working principle of IDI and to examine the Signal-to-Noise characteristics, the results of different simulations will be shown:\\
-First, it is assumed that the object to be imaged consists of discrete emitters, each emitting monochromatic spherical waves with a randomly chosen phase, and the speckle image on a pixelated detector was simulated by the addition of scalar electric fields with random initial phase propagated to the detector and Poisson sampling in each pixel. In this time independent configuration, the speckle images of a single particle with randomly positioned emitters inside (approximating a single particle imaging setup), a focal volume filled with randomly positioned (non intersecting) hard spheres consisting of randomly positioned atoms (approximating, for example, many spherical nanoparticles imaged simultaneously) as well as a crystalline structure with emitters positioned within a lattice are simulated. In the first two cases, a small-angle regime was chosen, and the reconstruction was performed in 2D and as a 1D radial profile. For the crystalline structure, a realistic lattice constant in the same order of magnitude as the K$\alpha$ wavelength moves the reconstruction out of the small-angle regime, and a 3D reconstruction of the reciprocal space is performed. Additionally, in these simulations the effect of under-sampling is studied.\\
+First, it is assumed that the object to be imaged consists of discrete emitters, each emitting monochromatic spherical waves with a randomly chosen phase, and the speckle image on a pixelated detector is simulated by the addition of scalar electric fields with random initial phase propagated to the detector and Poisson sampling in each pixel. In this time independent configuration, the speckle images of a single particle with randomly positioned emitters inside (approximating a single particle imaging setup), a focal volume filled with randomly positioned (non intersecting) hard spheres consisting of randomly positioned atoms (approximating, for example, many spherical nanoparticles imaged simultaneously) as well as a crystalline structure with emitters positioned within a lattice are simulated. In the first two cases, a small-angle regime is chosen, and the reconstruction is performed in 2D and as a 1D radial profile. For the crystalline structure, a realistic lattice constant in the same order of magnitude as the K$\alpha$ wavelength moves the reconstruction out of the small-angle regime, and a 3D reconstruction of the reciprocal space is performed. Additionally, in these simulations the effect of under-sampling is studied.\\
 Secondly, to examine the influence of the finite fluorescence lifetime and pulse width, and the validity of approximating  this influence by the overlay of a discrete number of speckle images according to the estimated number of modes, a time-resolved simulation is performed.
 
 Ultimately, the results of these simulations are used to estimate the parameters for an experimental setup.
@@ -151,7 +151,7 @@ \subsection{Accessible Reciprocal Space}
 
 \subsection{Detector Size and SNR}
 
-	To asses the influence of the number of pixels of an detector on the SNR, a simulation for a 1\,um thick Copper foil in an 100\,nm FWHM focus is performed. The detector size was varied from 64x64 to 3072x3072 pixels and always placed at the same distance of 1\,m, keeping the mean photon count per pixel constant. The number of correlation averaged over in the reconstruction increases linear with the number of pixels. For the SNR calculations, the signal is defined as peak intensity, the noise as the standard deviation over independent simulations.  As show in \fref{fig:SNRdetsize}, under these conditions, the SNR is proportional to the square root of the number of pixels of the detector. 
+	To asses the influence of the number of pixels of an detector on the SNR, a simulation for a 1\,um thick Copper foil in an 100\,nm FWHM focus is performed. The detector size is varied from 64x64 to 3072x3072 pixels and always placed at the same distance of 1\,m, keeping the mean photon count per pixel constant. The number of correlation averaged over in the reconstruction increases linear with the number of pixels. For the SNR calculations, the signal is defined as peak intensity, the noise as the standard deviation over independent simulations.  As show in \fref{fig:SNRdetsize}, under these conditions, the SNR is proportional to the square root of the number of pixels of the detector.