WuotD: Still Missing Introduction

presentations/2023-07-06_final_masters/2023-Masters.tex

@@ -15,6 +15,7 @@
 \usepackage{graphicx}
 \usepackage{tikz}
 \usepackage{xurl}
+\usepackage{physics}
 \graphicspath{{.}{./figures/}{../../figures/}}
 \usepackage{todo}
 
@@ -26,6 +27,7 @@
   {\usebibmacro{citeindex}%
    \usebibmacro{cite}
    \newunit
+   \clearfield{eprintclass}
    \usebibmacro{eprint}}
   {\multicitedelim}
   {\usebibmacro{postnote}}
@@ -95,25 +97,50 @@
 \def\thesissubtitle{}
 \def\thesisauthorfirst{E.T.}
 \def\thesisauthorsecond{de Boone}
-\def\thesisauthoremail{}
+\def\thesisauthoremailraw{ericteunis@deboone.nl}
+\def\thesisauthoremail{\href{mailto:\thesisauthoremailraw}{\thesisauthoremailraw}}
 \def\thesissupervisorfirst{dr. Harm}
 \def\thesissupervisorsecond{Schoorlemmer}
-\def\thesissupervisoremail{}
+\def\thesissupervisoremailraw{}
+\def\thesissupervisoremail{\href{mailto:\thesissupervisoremailraw}{\thesissupervisoremailraw}}
 
-\title[]{Enhancing Timing Accuracy in Air Shower Radio Detectors}
+\title[\thesistitle]{\thesistitle}
 
 \date{July, 2023}
 
 \author[\thesisauthorfirst\space\thesisauthorsecond]{%
-	\thesisauthorfirst\space\thesisauthorsecond\thanks{\thesisauthoremail}\\
+	\texorpdfstring{\thesisauthorfirst\space\thesisauthorsecond\thanks{e-mail: \thesisauthoremail}\\
-	\vspace*{2em}
+	\vspace*{0.5em}
-	{Supervisor: \thesissupervisorfirst\space\thesissupervisorsecond\thanks{\thesissupervisoremail} }
+	{Supervisor: \thesissupervisorfirst\space\thesissupervisorsecond }
+	}{\thesisauthorfirst\space\thesisauthorsecond<\thesisauthoremailraw>}
 	}
 
 % >>> Meta data
 
+\newcommand{\tclock}{\ensuremath{t_\mathrm{clock}}}
+\newcommand{\ns}{\ensuremath{\mathrm{ns}}}
+
+\newcommand{\pTrue}{\phi}
+\newcommand{\PTrue}{\Phi}
+\newcommand{\pMeas}{\varphi}
+
+\newcommand{\pTrueEmit}{\pTrue_0}
+\newcommand{\pTrueArriv}{\pTrueArriv'}
+\newcommand{\pMeasArriv}{\pMeas_0}
+\newcommand{\pProp}{\pTrue_d}
+\newcommand{\pClock}{\pTrue_c}
+
 \begin{document}
 { % Titlepage <<<
+\setbeamertemplate{background}
+{%
+	\parbox[c][\paperheight][c]{\paperwidth}{%
+		\centering%
+		\vfill%
+		\includegraphics[width=\textwidth]{beacon/array_setup_gps_transmitter_cows.png}%
+		\vspace*{2em}
+	}%
+}
 \setbeamertemplate{footline}{} % no page number here
 \frame{	\titlepage }
 } % >>>
@@ -121,18 +148,72 @@
 %%%%%%%%%%%%%%%
 % Start of slides <<<
 %%%%%%%%%%%%%%%
-\section{Cosmic Particles}% <<<<
+\section{Cosmic Particle Detection}% <<<<
 % Sources, Types, Propagation, Observables
 % Flux -> Large instrumentation area
 % Detection methods of Auger
 %  - FD, SD
 % AERA / AugerPrime RD or GRAND
-\begin{frame}
+\begin{frame}{Ultra High Energy particles}
 \end{frame}
 
+\begin{frame}{Air Showers}
+% Observables
+\end{frame}
+
+\begin{frame}{UHE particle flux}
+\end{frame}
+
+\begin{frame}{Detection methods}
+\end{frame}
+
+\begin{frame}{Radio Emission}
+\end{frame}
+
+
 % >>>>
 \section{Radio Interferometry}% <<<<
-\begin{frame}
+\begin{frame}{Radio Interferometry: Concept}
+	Interferometry: Amplitude + Timing information of the $\vec{E}$-field\\
+	\vspace*{ 0.8em }
+	\begin{columns}
+		\begin{column}{0.4\textwidth}
+			\begin{figure}
+				\includegraphics<1>[width=\textwidth]{radio_interferometry/rit_schematic_base.pdf}%
+				\includegraphics<2>[width=\textwidth]{radio_interferometry/rit_schematic_far.pdf}%
+				\includegraphics<3>[width=\textwidth]{radio_interferometry/rit_schematic_close.pdf}%
+				\includegraphics<4>[width=\textwidth]{radio_interferometry/rit_schematic_true.pdf}%
+			\end{figure}
+		\end{column}
+		\begin{column}{0.6\textwidth}
+			\vspace*{\fill}
+			\begin{itemize}
+				\item<1-> Measure signal $S_i(t)$ at antenna $\vec{a_i}$
+
+				\item<2-> Calculate light travel time \\[5pt]
+					\quad $\Delta_i(\vec{x}) = \frac{ \left| \vec{x} - \vec{a_i} \right| }{c} n_{eff}$
+
+				\item<2-> Sum waveforms accounting \\
+					for time delay \\[5pt]
+					\quad $S(\vec{x}, t) = \sum S_i( t + \Delta_i(\vec{x}) )$
+			\end{itemize}
+			\vspace*{\fill}
+			\begin{figure}% Spatially
+				\includegraphics<1>[width=0.8\textwidth]{radio_interferometry/single_trace.png}%
+				\includegraphics<2>[width=0.8\textwidth]{radio_interferometry/trace_overlap_bad.png}%
+				\includegraphics<3>[width=0.8\textwidth]{radio_interferometry/trace_overlap_medium.png}%
+				\includegraphics<4>[width=0.8\textwidth]{radio_interferometry/trace_overlap_best.png}%
+			\end{figure}
+		\end{column}
+	\end{columns}
+\end{frame}
+
+\begin{frame}{Radio Interferometry: Image}
+	\begin{figure}
+		\centering
+		\includegraphics[width=0.7\textwidth]{2006.10348/fig01.png}%
+		\imagecite{Schoorlemmer:2020low}
+	\end{figure}
 \end{frame}
 
 % >>>>
@@ -140,7 +221,32 @@
 % GNSS
 % reference system: White Rabbit, AERA beacon, (ADS-B?)
 % GRAND setup and measurements
-\begin{frame}
+\begin{frame}{Timing in Radio Detectors: GNSS}
+% Geometry
+	Default Timing mechanism: Global Navigation Satellite Systems\\
+	\begin{columns}
+		\begin{column}{0.5\textwidth}
+			\vfill
+			\begin{figure}
+				\begin{tikzpicture}[scale=1]
+					\clip (2.5 , 0) rectangle ( 6, 2.5);
+					\node[anchor=south west, inner sep=0] (image) at (0,0) {\includegraphics[width=\textwidth]{beacon/array_setup_gps_transmitter_cows.png}};
+					%\draw[help lines,xstep=1,ystep=1] (0,0) grid (11,5);
+				\end{tikzpicture}
+				\imagecredit{H. Schoorlemmer}
+			\end{figure}
+		\end{column}
+		\hfill
+		\begin{column}{0.45\textwidth}
+			In AERA, $ \Delta \tclock \gtrsim 10\ns$
+			\\
+			\begin{figure}
+				\centering
+				\includegraphics[width=\textwidth]{gnss/auger/1512.02216.figure3.gnss-time-differences.png}
+				\imagecite{PierreAuger:2015aqe}
+			\end{figure}
+		\end{column}
+	\end{columns}
 \end{frame}
 
 % >>>>
@@ -148,13 +254,173 @@
 % Geometry
 % Pulse method + SNR
 % Sine method + SNR
-\begin{frame}
+\begin{frame}{Beacon Synchronisation}
+% Geometry
+	\vspace*{0em}
+	{
+		{ \color{red} GNSS } 
+		+ 
+		Extra Timing mechanism: {\color{blue} Beacon}%, {\color{green} ADS-B}
+	}
+	\\
+	\vspace*{2em}
+	\begin{figure}
+		\hspace*{-2em}
+		\begin{tikzpicture}
+			[circle/.style={circle, ultra thick, radius=8mm}]
+			\node[anchor=south west, inner sep=0] (image) at (0,0) {\includegraphics[width=\textwidth]{beacon/array_setup_gps_transmitter_cows.png}};
+			\begin{scope}[x={(image.south east)}, y={(image.north west)}]
+				%\draw[help lines,xstep=.1,ystep=.1] (0,0) grid (1,1);
+				%\foreach \x in {0,1,...,9} { \node [anchor=north] at (\x/10,0) {0.\x}; }
+				%\foreach \y in {0,1,...,9} { \node [anchor=east] at (0,\y/10) {0.\y}; }
+				\node (transmitter) at (0.23, 0.32) {};
+				\node (gnss) at (0.85, 0.87) {};
+				%\node (aeroplane) at (0.3, 0.67) {\includegraphics[width=1.5cm]{templates/aeroplane.png}};
+				%\draw[green, ultra thick, visible on=<{1-}>] (aeroplane.center)    circle[radius=8mm];
+				\draw[red,   ultra thick, visible on=<{1-}>] (gnss.center)         circle[radius=8mm];
+				\draw[blue,  ultra thick, visible on=<{1-}>] (transmitter.center)  circle[radius=8mm];
+			\end{scope}
+		\end{tikzpicture}
+		\imagecredit{H. Schoorlemmer}
+	\end{figure}
+\end{frame}
+
+\subsection{Pulse Beacon}
+\begin{frame}{Pulse Beacon}
+	\begin{figure}
+		\includegraphics[width=\textwidth]{pulse/antenna_signals_tdt0.2_zoom.pdf}
+	\end{figure}
+	\vfill
+\end{frame}
+\begin{frame}{Pulse Beacon}
+	Correlation: similarity between two signals.\\
+	\begin{figure}
+		\includegraphics[width=\textwidth]{pulse/correlation_tdt0.2_zoom.pdf}
+	\end{figure}
+\end{frame}
+\begin{frame}{Pulse Beacon Timing}
+	\begin{figure}
+		\includegraphics[width=0.8\textwidth]{pulse/time_res_vs_snr_multiple_dt_small.pdf}
+	\end{figure}
+\end{frame}
+
+\subsection{Sine Beacon}
+\begin{frame}{(Multi)Sine Beacon}
+	\begin{equation*}
+		\Delta \tclock = \left[ \frac{\varphi}{2\pi} \; + \; k \right] T
+	\end{equation*}
+	\begin{figure}
+		\includegraphics[width=.45\textwidth]{methods/fourier/waveform.pdf}
+		\hfill
+		\includegraphics[width=.45\textwidth]{methods/fourier/noisy_spectrum.pdf}
+	\end{figure}
+\end{frame}
+\begin{frame}{(Multi)Sine Beacon Timing}
+	\begin{figure}
+		\includegraphics[width=0.8\textwidth]{beacon/time_res_vs_snr.pdf}
+	\end{figure}
+	\begin{columns}
+		\begin{column}{0.3\textwidth}
+		\end{column}
+		\begin{column}{0.7\textwidth}
+			\tiny\begin{equation*}
+	p_\PTrue(\pTrue; s, \sigma) =
+		\frac{ e^{-\left(\frac{s^2}{2\sigma^2}\right)} }{ 2 \pi }
+		+
+		\sqrt{\frac{1}{2\pi}}
+		\frac{s}{\sigma}
+		e^{-\left( \frac{s^2}{2\sigma^2}\sin^2{\pTrue} \right)}
+		\frac{\left(
+			1 + \erf{ \frac{s \cos{\pTrue}}{\sqrt{2} \sigma }}
+		\right)}{2}
+		\cos{\pTrue}
+			\end{equation*}
+		
+		\tiny{Random Phasor Sum: ``Statistical Optics'', J. Goodman}
+		\end{column}
+	\end{columns}
+
 \end{frame}
 
 % >>>>
 \section{Single Sine Synchronisation}% <<<<
 % Sine method + Radio Interferometry
-\begin{frame}
+\begin{frame}{Single Sine Synchronisation}
+	\begin{figure}
+		%\centering
+		\hspace*{-5em}
+		\includegraphics<1>[width=1.3\textwidth]{beacon/08_beacon_sync_timing_outline.pdf}%
+		\includegraphics<2>[width=1.3\textwidth]{beacon/08_beacon_sync_synchronised_outline.pdf}%
+		\includegraphics<3>[width=1.3\textwidth]{beacon/08_beacon_sync_synchronised_period_alignment.pdf}%
+	\end{figure}
+\end{frame}
+
+\begin{frame}{Single Sine Synchronisation Simulation}
+	Air Shower detected on a grid of 100x100 antennas.
+
+	\begin{columns}
+		\begin{column}{0.5\textwidth}
+			\begin{itemize}
+				\item Add beacon to antenna
+				\item Randomise clocks
+				\item Measure phase
+				\item Repair clocks for small offsets
+				\item Iteratively find best $k_{ij}$
+			\end{itemize}
+		\end{column}
+		\hfill
+		\begin{column}{0.4\textwidth}
+			\begin{figure}
+				\includegraphics<1>[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.pdf}%
+				\includegraphics<2>[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.masked.pdf}%
+			\end{figure}
+		\end{column}
+	\end{columns}
+\end{frame}
+
+\begin{frame}{Simulation: Period $k_i$}
+	\small{
+	Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$
+	\\
+	Iterative process: \\
+	\; Scan positions finding the best $\{k_i\}$ set, then zoom in on strongest.
+	}
+
+	\only<1-4>{\begin{figure}
+	\includegraphics<1>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i5.loc8.0-2795.4-7816.0.pdf}
+	\includegraphics<2>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i99.loc8.0-2795.4-7816.0.pdf}
+	\includegraphics<3>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf}
+	\includegraphics<4>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf}
+	\end{figure}}
+	\only<5>{\begin{figure}
+		\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf}
+		\hfill
+		\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf}
+		\vspace{0.5cm}
+		\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run1.pdf}
+		\hfill
+		\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run1.power.pdf}
+	\end{figure}}
+\end{frame}
+
+
+\begin{frame}{Time resolving short period beacon: phase vs full}
+	\begin{columns}
+		\begin{column}{0.45\textwidth}
+			{ Phase reparation }
+			\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_phases.axis.trace_overlap.repair_phases.pdf}%
+			\vfill
+			\includegraphics[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf}%
+			\label{fig:sine:repairments}
+		\end{column}
+		\hfill
+		\begin{column}{0.45\textwidth}
+			{ Phase + Period reparation }
+			\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_full.axis.trace_overlap.repair_full.pdf}%
+			\vfill
+			\includegraphics[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf}%
+		\end{column}
+	\end{columns}
 \end{frame}
 
 % >>>>
@@ -163,7 +429,7 @@
 % Outlook: Parasitic/Active vs Pulse/Sine table
 % Parasitic Single Sine: 67MHz Auger
 % Implementation for GRAND?
-\begin{frame}
+\begin{frame}{Conclusion and Outlook}
 \end{frame}
 
 % >>>>