ideas

Tex/conclusion.tex

@@ -1,46 +1,49 @@
 \chapter{Conclusion and Outlook}
+There is still an ongoing discussion about the feasibility, optimal sample and beam requirements of a proof-of-principle experiment of IDI at the nanoscale as well as about in which areas IDI can provide new information. More thorough theoretical studies , further improvements in experimental design and data analysis will be beneficial.
 
-\section{Developed tools for CDI/IDI experiments}
+
+\paragraph{Developed tools for CDI/IDI experiments}
 Both the GPU-accelerated simulation code and the reconstruction code developed for this thesis are open source\footnote{available under \url{https;//github.com/fzimmermann89/idi}} and will be used for planning and analyzing future IDI experiments. The simulation code allows to compare IDI and CDI experiments for the same sample, comparison for different samples and experimental parameters as shown in \fref{chap:simulation}.
 The analysis code implements 2d, 3d and radial correlations for small and wide angle experiments with different normalization approaches as well as library of commonly needed auxiliary functions, such as dark and mask generation for pixel detectors, a new common mode correction with adaptive block sizes, photon counting procedures, different regression tools as well as tools for center finding and similar tasks.
-Furthermore, the Kossel line alignment tool with its graphical user interface allows easy analysis of the detector orientation for future experiments with strict alignment margins.
 
 
-\section{Using Incoherent Imaging for Online Beam Diagnostic}
 
 
 
-The posibility to run an IDI setup in parallel with other detectors would allow for a combination of IDI with CDI
 
-Larger detectors
 
-Short pulses
 
-Element specific 
+\paragraph{Results of the Experiment}
 
+The previously published results for the foil samples could be reproduced.
+By using the presented preparation of nanoparticle samples in polymer matrix, aggregation could not be prevented, resulting in less pronounced features in higher $q$ instead of providing a structure factor similiar to non-interacting spheres as determined by the SAXS measurement. 
 
-Even just the ability to image to focal volume might be an useful diagnostic tool in certain experiments
 
 
+Furthermore, the Kossel line alignment tool with its graphical user interface allows easy analysis of the detector orientation for future experiments with strict alignment margins.
 
 
-\begin{figure}
-	\centering
-	\includegraphics[width=\linewidth]{images/lv65_vanadium.pdf}
-	\label{fig:outlook_vanadium}
-	\caption[Focus finding using IDI]{Preliminary results of the $g^2(\vec{q})$ calculation of the fluorescence of a 4\,um vanadium foil, placed at 4 different positions along the x-ray beam at the CXI experimental hutch (LCLS, running in an experimental configuration for short pulse duration under 1\,fs \cite{subfs2017,argosecond}) using the "100 nm" KB focusing (optimal theoretical focus size 90\,nm x 150\,nm, theoretical beam divergence 2 mrad x 1 mrad) on one tile of a Jungfrau detector (75\,um pixelsize, placed 480\,mm downstream of the sample). The axis are in detector pixels. Shown are averages over ~2000 shots with minimal shot based filtering. The position captioned "0" was determined during the experiment as the focus based on these results, the other positions are 250\,um and 500\,um further downstream and 250\,um upstream (this position was previously determined as the focus by imprints).  Some astigmatism is visible.}
-\end{figure}
 
-\section{Experimental Improvements}
+\paragraph{Experimental Improvements}
+
+
+
+The posibility to run an IDI setup in parallel with other detectors would allow for a combination of IDI with CDI
 
-Recently, we performed an experiment using sub-1\,fs pulses at the CXI beamline at the LCLS free electron laser. In this experiment, three major improvements made over the SACLA experiment: First, the shorter pulse length reduces the number of temporal modes and a shot-by-shot high resolution spectrometer allows for better filtering of the x-ray pulses by estimated pulse length and intensity. Second, the data was recorded in forward direction, solving the undersampling issue and reducing the spatial modes. And third, two new, signal optimized samples were chosen: Anodic aluminum oxide (AAO) membranes with regular spaced 20\,nm or 30\,nm wide pores, with are filled with Nickel or Vanadium using atomic layer deposition, creating an array of hexagonal placed 500\,nm long cylinders 60\,nm/100\,nm apart \cite{carina2019}. As the range of the order of the self-organizing pores is smaller than the total area used in the experiment, the simulated reconstruction shows rings (\fref{fig:outlook_aao}). 
+Larger detectors
+
+Short pulses
+
+Element specific 
+
+Recently, we performed an experiment using sub-1\,fs pulses at the CXI beamline at the LCLS free electron laser. In this experiment, three major improvements over the SACLA experiment were implemented: First, the shorter pulse length reduces the number of temporal modes and a shot-by-shot high resolution spectrometer allows for better filtering of the x-ray pulses by estimated pulse length and intensity. Second, the data was recorded in forward direction, solving the undersampling issue and reducing the spatial modes. And third, two new, signal optimized samples were chosen: Anodic aluminum oxide (AAO) membranes with regular spaced 20\,nm or 30\,nm wide pores, with are filled with Nickel or Vanadium using atomic layer deposition, creating an array of hexagonal placed 500\,nm long cylinders 60\,nm/100\,nm apart \cite{carina2019}. As the range of the order of the self-organizing pores is smaller than the total area used in the experiment, the simulated reconstruction shows rings (\fref{fig:outlook_aao}). 
 The other sample is will be lithographically produced gratings with two diffferent pitches, 60\,nm  and 80\,nm \cite{mojarad2015}. For these samples, a simulation is shown in \fref{fig:outlook_grating}. Both samples combine the advantages of a single crystal sample (namely intense features) while providing more signal and requiring less accessible reciprocal space. 
 Based on the simulations, it can be estimated, that a few hundred images taken with sub-fs pulses exciting 20\% of the atoms would suffice to reach a SNR of >3.
 We were able to record full datasets on multiple samples. The data analysis of this experiment has not yet been completed and might result in the first experimental proof of using fluorescence intensity correlation for structural imaging at the nano-scale.  
 
 
 
-\begin{figure}
+\begin{figure}[p]
 	\centering
 	\begin{subfigure}[b]{0.50\textwidth}
 		\includegraphics[width=\linewidth]{images/lv65simA.pdf}
@@ -56,5 +59,18 @@ \section{Experimental Improvements}
 \end{figure}
 
 
+\paragraph{Using Incoherent Imaging for Online Beam Diagnostic}
+
+Extending on the results obtained for both determining the focal volume as well as using the contrast to estimate the pulse length promises to be an useful diagnostic tool in future FEL experiments with ultra-short pulses and/or tight foci \cite{nakumura2020,inoue2019}. In the aforementioned LCLS experiment it has already been used successful during tuning to find the focal spot along the beam direction (see \fref{fig:outlook_vanadium} for examples of the online analysis).
+
+
+\begin{figure}[p]
+	\centering
+	\includegraphics[width=\linewidth]{images/lv65_vanadium.pdf}
+	\label{fig:outlook_vanadium}
+	\caption[Focus finding using IDI]{Preliminary results of the $g^2(\vec{q})$ calculation of the fluorescence of a 4\,um vanadium foil, placed at 4 different positions along the X-ray beam at the CXI experimental hutch (LCLS, running in an experimental configuration for short pulse duration under 1\,fs \cite{subfs2017,argosecond}) using the "100 nm" KB focusing (optimal theoretical focus size 90\,nm x 150\,nm, theoretical beam divergence 2 mrad x 1 mrad) on one tile of a Jungfrau detector (75\,um pixelsize, placed 480\,mm downstream of the sample). The axis are in detector pixels. Shown are averages over ~2000 shots with minimal shot based filtering. The position captioned "0" was determined during the experiment as the focus based on these results, the other positions are 250\,um and 500\,um further downstream and 250\,um upstream (this position was previously determined as the focus by imprints).  Some astigmatism is visible.}
+\end{figure}
+
+\paragraph{Higher Order Correlations}
 
 Extending the Hanbury-Brown and Twiss experiment to higher order correlations allows the usage of prior knowledge about the distribution of the spatial frequencies in the sample as an effective filter by fixing some terms in the correlation function at what certain positions termed  \textit{Magic Poisition}. A future application of this scheme in the analysis of the already recorded fluorescence patterns might lead to a significant increase in the SNR and resolution \cite{schneider2018,thiel2007}.

Tex/discussion.tex

@@ -6,13 +6,16 @@ \chapter{Discussion}
 
 Due to limitations in the placement of the detectors, the undersampling
 
+The amplitude of the intensity correlations observed in the foil samples is a factor of 2-4 less than previously measured by Inoue et al and suggests more than 200 modes. This might be the combination of a longer pulse length due to a less strict filtering of the shots (a different trade-off chosen with regards to peak contrast vs. noise reduction by averaging over more images) and the only partially by the regression corrected undersampling creating additional spatial modes.
 
 The severe detector artifacts reduced the amount of usable data significantly, which, unfortunately, has not been noticed during the experiment. This show the necessity of better continuous online monitoring of the recorded data.
 
 
-The nanoparticle samples had a much less pronounced features according to the SAXS measurements than initially planned. An optimization of the preparation method leading to either higher concentrations of non-aggregating particles or to complete aggregation might lead to stronger features. Also, using liquid injectors might be an option, even though, partially due to the tight focus, short Rayleigh length and therefore difficult to achieve spatial overlap of the beam and sample, this would introduce additional complexity to the experimental setup.
 
 
+The estimated number of independent modes seems lower than expected, but one has to keep in mind that the used regression scheme as a low sensitivity for higher $M$ values due to the diminishing gradient and might underestimate the number of modes. Nevertheless, this is an indicator that the number of modes is much higher than the "optimal" value for unpolarized light ($M=2$), resulting in severely reduced signal and therefore SNR.
+
+The nanoparticle samples had a much less pronounced features according to the SAXS measurements than initially planned and compared to the structure factor for non-interacting spheres. An optimization of the preparation method leading to either higher concentrations of non-aggregating particles or to complete aggregation and the  formation of quasi-crystals, might lead to stronger features. Also, using liquid injectors might be an option, even though, partially due to the tight focus, short Rayleigh length and therefore difficult to achieve spatial overlap of the beam and sample, this would introduce additional complexity to the experimental setup.