minor

Tex/ffz.bib

@@ -813,7 +813,6 @@ @Book{butz2015
   title     = {Fourier Transformation for Pedestrians},
   year      = {2015},
   isbn      = {9783319169859},
-  series    = {Undergraduate Lecture Notes in Physics},
 }
 
 @Article{goodman1976,
@@ -1570,7 +1569,7 @@ @InBook{oppenheim2009
 with relatively short life spans.},
 }
 
-@Article{yanoda2015,
+@Article{yoneda2015,
   author        = {Yoneda, Hitoki and Inubushi, Yuichi and Nagamine, Kazunori and Michine, Yurina and Ohashi, Haruhiko and Yumoto, Hirokatsu and Yamauchi, Kazuto and Mimura, Hidekazu and Kitamura, Hikaru and Katayama, Tetsuo and Ishikawa, Tetsuya and Yabashi, Makina},
   journal       = {Nature},
   title         = {Atomic inner-shell laser at 1.5-{\aa}ngstr{\"o}m wavelength pumped by an X-ray free-electron laser},

Tex/main.tex

@@ -31,7 +31,7 @@
 \usepackage{blindtext} %Einfügen von Blindtext über \blindtext
 \usepackage{siunitx} %Einstellungen für Dezimaltrennzeichen und Definitionen in siunitx.cfg
 \usepackage[autostyle=true,german=quotes]{csquotes} %Verwendung von Anführungszeichen über \enquote{Text}
-\usepackage[toc,page]{appendix} %um eine Titelseite "Anhang" vor dem eigentlichen Anhang einfügen zu können
+\usepackage[toc]{appendix} %um eine Titelseite "Anhang" vor dem eigentlichen Anhang einfügen zu können
 
 %Druckt den Hinweis "Entwurf" mit Datum auf jede Seite. Zum deaktivieren printwatermark=false setzen
 \usepackage[printwatermark=true]{xwatermark}
@@ -360,7 +360,7 @@ \chapter*{List of Abbreviations}
 \bibliography{ffz}
 \bibliographystyle{ffz}
 \addcontentsline{toc}{chapter}{Bibliography}
-\cleardoublepage
+%\cleardoublepage
 
 
 \include{thanks}

Tex/theory.tex

@@ -4,7 +4,7 @@ \chapter{Theory}
 
 
 \section{X-Ray Fluorescence}
-X-ray fluorescence is emitted if atoms are ionised leaving vacancies in the inner shells, which are subsequently filled by electrons of higher energy levels while the energy difference is emitted as photons  (see \fref{fig:levels} for the usual naming convention), compared to the non-radiating Auger decay which, for K-shell vacancies, is more likely for lighter atoms up to atomic number ~30 \cite{santra2009}.  The finite lifetime of the excited states cause a predominantly Lorentzian line shape \cite{attwood1999,van2001}. In the experimental section, iron, copper and gallium atoms are considered - the relevant emission energies, the (experimental) line widths and relative intensities are shown in \fref{tab:elements}.   Roughly, the $K_\alpha$ line widths correspond to coherence times in the 0.4-0.8\,fs range \cite{krause1979}. The cross section for $K$-fluorescence is the highest just above the $K$-absorption edge and, for example for iron, an order of magnitude higher than the coherent cross section (see \fref{fig:cross}).
+X-ray fluorescence is emitted if atoms are ionised leaving vacancies in the inner shells, which are subsequently filled by electrons of higher energy levels while the energy difference is emitted as photons  (see \fref{fig:levels} for the usual naming convention), compared to the non-radiating Auger decay which, for K-shell vacancies, is more likely for lighter atoms (up to atomic number ~30) \cite{santra2009}.  The finite lifetime of the excited states cause a predominantly Lorentzian line shape \cite{attwood1999,van2001}. In the experimental section, iron, copper and gallium atoms are considered - the relevant emission energies, the (experimental) line widths and relative intensities are shown in \fref{tab:elements}.   Roughly, the $K_\alpha$ line widths correspond to coherence times in the 0.4-0.8\,fs range \cite{krause1979}. The cross section for $K$-fluorescence is the highest just above the $K$-absorption edge and, for example for iron, an order of magnitude higher than the coherent cross section (see \fref{fig:cross}).
 
 \begin{figure}
 	\centering
@@ -36,7 +36,7 @@ \section{X-Ray Fluorescence}
 \end{table}
 
 \section{Basic Concepts of Coherence}
-In the following, for simplicity, all considered fields are initially assumed to be both stationary and ergodic: A process $f(t)$ is wide-sense stationary, if the expectation value $E[f(t)]$ is independent of the time $t$ and $E[f(t_1)f(t_2)]$ depends only on the time difference $\tau=f_1-f_2$. A process, for which the time average and the ensemble average are equal is called ergodic. Stationarity is a necessity for ergodicity \cite{goodman2000}. It can be shown, that the basic principles hold for non-stationary fields with the main difference being, that all expectation values have to be taken over different realizations \cite{lajunen04}.
+In the following, for simplicity, all considered fields are initially assumed to be both stationary and ergodic: A process $f(t)$ is wide-sense stationary, if the expectation value $E[f(t)]$ is independent of the time $t$ and $E[f(t_1)f(t_2)]$ depends only on the time difference $\tau=f_1-f_2$. A process, for which the time average and the ensemble average are equal is called ergodic. Stationarity is a necessity for ergodicity \cite{goodman2000}. It can be shown, that the basic principles hold for non-ergodic fields with the main difference being, that all expectation values have to be taken over different realizations  \cite{lajunen04}.
 
 Spherical waves as solutions wave equation in spherical coordinates,
 \begin{equation}
@@ -124,7 +124,7 @@ \section{Basic Concepts of Coherence}
 \end{equation}
 If the distances from $\vec{r}$ to the two slits are (approximately) equal, $R_{1}\approx R_{2} \approx d$, the intensity at $\vec{r}$ is
 \begin{align*}
-	\left\langle I_{P}\left(\vec{r}, t^{\prime}\right)\right\rangle&=\left\langle\left|E\left(\vec{r}_{1}, t\right)\right|^{2}\right\rangle+\left\langle\left|E\left(\vec{r}_{2}, t\right)\right|^{2}\right\rangle 
+	\left\langle I\left(\vec{r}, t^{\prime}\right)\right\rangle&=\left\langle\left|E\left(\vec{r}_{1}, t\right)\right|^{2}\right\rangle+\left\langle\left|E\left(\vec{r}_{2}, t\right)\right|^{2}\right\rangle 
 	+\left[\left\langle E^{*}\left(\vec{r}_{1}, t\right) E\left(\vec{r}_{2}, t\right)\right\rangle e^{i\left(\vec{k}_{1}-\vec{k}_{2}\right) \cdot \vec{r}+i \Delta \phi}+\text{c.c}\right] \\
 	& \propto 1+
 	\frac{2 \sqrt{\left< I\left(\vec{r}_{1}, t\right)\right>\left< I\left(\vec{r}_{2}, t\right)\right>}}
@@ -245,11 +245,7 @@ \section{Hanbury-Brown Twiss Experiment}
 \end{figure}
 
 \section{Photon Statistics}
-Considering a complex sum of many phasors (e.g. the superposition of many electrical fields or probability amplitudes) of constant amplitude $A$ and independent uniformly in $(-\pi,\pi]$ distributed phases $\phi_k$,
-\begin{align}
-	c=\sum^N_k A e^{i\phi_k}
-\end{align}
-for sufficiently large numbers of $N$, the real and imaginary parts
+Considering a complex sum of many phasors (e.g. the superposition of many electrical fields or probability amplitudes) of constant amplitude $A$ and independent uniformly in $(-\pi,\pi]$ distributed phases $\phi_k$, $c=\sum^N_k A e^{i\phi_k}$, for sufficiently large numbers of $N$, the real and imaginary parts
 \begin{align*}
 	r&=\Re c =  A \sum^N_k \cos(\phi_k) &
 	i&= \Im c =A \sum^N_k \sin(\phi_k)