small changes

Tex/conclusion.tex

@@ -1,27 +1,18 @@
 \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.
-
+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.
 
 \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.
 
-
-
-
-
 \paragraph{Experimental Improvements}
+As previously published results for the foil samples could be reproduced but, as the experiments using nanoparticle and crystal samples have been inconclusive so far, the proof of high resolution imaging using IDI is still outstanding, further refinements in the experimental design are necessary.
 
-As previously published results for the foil samples could be reproduced but the proof of high resolution imaging using IDI is still outstanding, further refinements in the experimental design are necessary.
-
-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. 
+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 are lithographically produced nanogratings 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.  
-
+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 nanoscale.  
 
 
 \begin{figure}[p]
@@ -36,22 +27,24 @@ \chapter{Conclusion and Outlook}
 		\caption{AAO membrane  }
 		\label{fig:outlook_aao}
 	\end{subfigure}
-	\caption[Simulations in Preparation of LV65 Experiment]{Examples of simulations performed with the tools developed in this thesis in preparation of the LCLS free electron laser experiment LV65, which will use nano-gratings and AAO membranes with metal filled self-organized pores as samples for an IDI measurement. The simulations were used to chose an optimized sample geometry and to estimate the feasibility with respect to the expected SNR. The images shown are the calculated fluorescence intensity correlations between pixels of a quarter of an Jungfrau 4M detector placed at a distance of 70\,cm (grating) and 1\,m (membrane) respectively. The simulated grating has a pitch of 80\,nm, 40\,nm line width and 40\,nm thickness; 20\% excitation and 4 modes were simulated. The AAO membrane has and inter pore distance 105\,nm, the pores are filled with vanadium and 20\% excitation are assumed. For both samples, the average over 100 images is shown.}
+	\caption[Simulations in preparation of LV65 Experiment]{Examples of simulations performed with the tools developed in this thesis in preparation of the LCLS free electron laser experiment LV65, which will use nano-gratings and AAO membranes with metal filled self-organized pores as samples for an IDI measurement. The simulations were used to chose an optimized sample geometry and to estimate the feasibility with respect to the expected SNR. The images shown are the calculated fluorescence intensity correlations between pixels of a quarter of an Jungfrau 4M detector placed at a distance of 70\,cm (grating) and 1\,m (membrane) respectively. The simulated grating has a pitch of 80\,nm, 40\,nm line width and 40\,nm thickness; 20\% excitation and 4 modes were simulated. The AAO membrane has and inter pore distance 105\,nm, the pores are filled with vanadium and 20\% excitation are assumed. For both samples, the average over 100 images is shown.}
 \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).
+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 successfully 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.}
+	\label{fig:outlook_vanadium}
 \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}.
+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 certain positions termed \textit{Magic Poisition} \cite{schneider2018,thiel2007}. A future application of this scheme in the analysis of the already recorded fluorescence patterns might lead to a significant increase in the SNR.
+$$\\$$
+$$\\$$
+Overall, the methods presented will help pushing the experimental implementation of IDI forward. Before considering the method as non-suitable for high resolution imaging, the results of experiments implementing the improvements described above should be awaited.

Tex/discussion.tex

@@ -1,13 +1,12 @@
 \chapter{Discussion}
 The promise of IDI to allow three-dimensional, high resolution, element-specific imaging of nanoscale samples could not yet be fulfilled by the experimental implementation.
 
-The estimated number of independent modes from the spectra seems lower than expected. However, one must keep in mind that the used regression scheme has a low sensitivity for higher $M$ values due to the diminishing gradient and might underestimate the number of modes. Nevertheless, this indicates that the number of modes is much higher than the "optimal" value for unpolarized light ($M=2$), resulting in severely reduced contrast. 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 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 estimated number of independent modes from the foil spectra is lower than expected. However, one must keep in mind that the used regression scheme has a low sensitivity for higher $M$ values due to the diminishing gradient and might underestimate the number of modes. Nevertheless, this indicates that the number of modes is much higher than the "optimal" value for unpolarized light ($M=2$), resulting in severely reduced contrast. 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 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 nanoparticle samples had much less prominent features according to the SAXS measurements than initially planned and compared to the structure factor for non-interacting spheres. 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, 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, which would introduce additional complexity to the experimental setup.
+The nanoparticle samples have much less prominent features according to the SAXS measurements than initially planned and compared to the structure factor for non-interacting spheres, leading to an overestimation of the SNR in the simulations. The SAXS measurements give a reasonably good insight into the expected results of the IDI measurement of the same sample, but the latter will differ due to the iron specificity of the reconstructed structure factor and the smaller focal volume capturing less aggregates. 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, 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, which would introduce additional complexity to the experimental setup.
 
-The achieved alignment of the crystalline samples after determination of the mean orientation, and translational offset is still worse than the resolution of the reconstruction and the size of the expected Bragg peaks, resulting most likely in a reduction of the signal contrast through averaging of different pixel pairs not belonging to the same true $\vec{q}$. Additionally, the regression has only been performed on the average image; thus, variations over the scanning of the sample are not corrected. Mounting of the sample on the window might as well as the damage done during the measurement by the focused beam might have resulted in stress, slight bending of the thin glass stabilizing the crystal sheet, and stress in the lattice. Additionally, thermal motion of the gallium will have reduced the contrast.
-
-Severe detector artifacts reduced the amount of usable data significantly, which, unfortunately, has not been noticed during the experiment - showing the necessity of better continuous online monitoring of the recorded data. The photon-counting applied to the raw images improves the fidelity of the focal images. Depending on the PSF of the detectors and sufficiently low photon counts, more sophisticated droplet schemes based on error minimization allowing for subpixel resolution, incorporating the scattering photons into the droplet algorithm or using a neural network trained on synthetic images could reduce the influence of noise and undersampling \cite{baumann2018,collaboration2014,schayck2020,sun2020}.
+The achieved alignment of the crystalline samples after determination of the mean orientation, and translational offset is still worse than the resolution of the reconstruction and the size of the expected Bragg peaks, resulting most likely in a reduction of the signal contrast through averaging of different pixel pairs not belonging to the same true $\vec{q}$. As the regression has only been performed on the average image variations over the scanning of the sample are not corrected. Mounting of the sample on the window might as well as the damage done during the measurement by the focused beam might have resulted in stress, slight bending of the thin glass stabilizing the crystal sheet, and stress in the lattice. Additionally, thermal motion of the gallium will have reduced the contrast. The energy of the excitation X-ray being close to the gallium K$_\alpha$ energy (to avoid excitation of the aresenic) makes it impossible to quantify or filter coherent scattering in the recorded data. Combined, these effects might have resulted in a reduction of the the peak intensity below the noise level. Furthermore, it has proved to be difficult to ensure that the orientation correction works as designed and the Bragg peaks would be reconstructed at the positions chosen as regions-of-interest. A non-comprehensive search using local maxima filter (as used to determine the Bragg peak positions in the simulated correlations for \fref{fig:accesiblebraggq}) has not lead to reasonable, i.e. symmetric and at the correct $\left|\vec{q}\right|$, candidates at other positions.
 
+Severe detector artifacts reduced the amount of usable data significantly, which, unfortunately, has not been noticed during the experiment -- showing the necessity of better continuous online monitoring of the recorded data. The photon-counting applied to the raw images improves the fidelity of the focal images. Depending on the PSF of the detectors and sufficiently low photon counts, more sophisticated droplet schemes based on error minimization allowing for subpixel resolution, incorporating the scattering photons into the droplet algorithm or using a neural network trained on synthetic images could further reduce the influence of noise and undersampling and might increase the contrast in for the single crystal images \cite{baumann2018,collaboration2014,schayck2020,sun2020}.\\
 Even though the application of non-uniform FFT (NUFFT) based correlation estimators with sophisticated interpolation kernels, which have successfully been used in other fields, would require more memory, the reduction in under-sampling by making full use of the smaller $\vec{q}$ spacing at higher detector angles could make it a worthwhile extension of the used 3d reconstruction \cite{laguna1998,yang2008,chang2020}. Another possible avenue for improvement of the implementation might be to reconstruct only relevant parts of the reciprocal space, significantly reducing computational time and memory requirements.