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%%%%%%%%
% Goal: show enthousiasm, knowledge and drive about the field

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\title[STEP-UP: Interferometry in GRAND]{% and BEACON]{
	{ \large STEP'UP Interview}\\
	{
		Investigating interferometry in\\%
		GRAND\footnote{ Giant Radio Array for Neutrino Detection}
		% and BEACON\footnote{Beam forming Elevated Array for COsmic Neutrinos}
	}
}

\date{June, 2023}

\author[E.T. de Boone]{
	E.T. de Boone
%	\\
%	\vspace{2em}
%	Advisors: Olivier Martineau, LPNHE\\
%	\quad\quad\quad\quad\quad\, Harm Schoorlemmer, IMAPP
	}

\begin{document}
{
\setbeamertemplate{footline}{} % no page number here
\frame{	\titlepage }
}

\section{My Background}
\begin{frame}{My Background}
	Studies @Radboud University, Nijmegen
	\begin{itemize}
		\item Master's Physics and Astronomy {\small (\textit{1yr courses + 1yr internship})}\\
			\quad { \small Specialisation: Particle and Astrophysics }\\
			\quad { \small Minor: Computational Data Science }\\

		\vspace*{1em}

		\item Master's Internship: \\
			\quad {\small Supervisor: Harm Schoorlemmer, IMAPP, Radboud University}\\
			\quad {\small ``Enhancing Timing Accuracy in Air Shower Radio Detectors'' }\\
	\end{itemize}
\end{frame}
\note[itemize]{
	\item Interests since Bachelor's, continued in Master's
	\begin{itemize}
		\item Ultra High Energy particles
		\item Radio detection \& Hardware experimenting
	\end{itemize}

	\item Now wrapping up Master and full year's worth of internship

	\item Why start internship? (Experimental)
}


% Cosmic Rays and Radio
%%%%%%%%%
\section{Radio and Airshowers}
\begin{frame}{Ultra High Energy particles}
	\begin{figure}
		\includegraphics[width=\textwidth]{grand/astroparticletypes_grand.jpg}%
		\imagecite{GRAND:2018iaj}
	\end{figure}
\end{frame}
\note[itemize]
{
\item Ultra High Energies (EeV $10^{18}$ eV) (Sources)
\item Propagation effects (Magnetic Field deflections, Horizons)
\item Multiple classes (Different combinations of effects)
}

%%
\begin{frame}{Air Showers: Atmospheric Depth \& Composition}
	\begin{columns}
		\begin{column}{0.45\textwidth}
			\begin{figure}
				\hspace*{-1em}
				\includegraphics[width=\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf}%
				\imagecredit{H. Schoorlemmer}
			\end{figure}
		\end{column}
		\begin{column}{0.45\textwidth}
			Enhanced Xmax measurement with Interferometry\\
				$\mapsto$ particle identification\\
			\begin{figure}
				\centering
				\includegraphics[width=\textwidth]{2006.10348/fig03_b.png}%
				\imagecite{Schoorlemmer:2020low}
			\end{figure}
		\end{column}
	\end{columns}
\end{frame}
\note[itemize]
{
\item Statistical discrimation: high Z at high altitudes
\item FD claims 20 g/cm2, Fe/p ~ 50 g/cm2
\item Radio Interferometry helps in Xmax measurement
}

\section{Radio Interferometry and Timing}
\begin{frame}{Effect of Timing Synchronisation}
	%\vspace*{-2em}
	Interferometry: Amplitude + Timing information of the $\vec{E}$-field\\
	\vspace*{ 0.8em }

	\begin{columns}
		%\hfill
		\begin{column}{0.4\textwidth}
			\vfill
			\hyperlink{fig:sine:repairments}{\includegraphics[width=1.1\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_none.axis.trace_overlap.repair_none.pdf}}%
			\vspace*{\fill}
			\hyperlink{fig:sine:grid_power}{\includegraphics[width=1.1\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_none.scale4d.pdf}}
		\end{column}
		\hfill
		\begin{column}{0.4\textwidth}
			\vfill
			\hyperlink{fig:sine:repairments}{\includegraphics[width=1.1\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_full.axis.trace_overlap.repair_full.pdf}}%
			\vspace*{\fill}
			\hyperlink{fig:sine:grid_power}{\includegraphics[width=1.1\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf}}%
		\end{column}
		\hfill
	\end{columns}
\end{frame}
\note{
}

\begin{frame}{Timing Synchronisation: Beacon}
	\begin{columns}
		\begin{column}{0.6\textwidth}
			\hspace*{1em}
			Required time accuracy $\sim 1 \mathrm{ns}$\\
			\vspace*{1em}
			\hspace*{1em}
			\visible<2->{
				\textcolor{red}{GNSS},  in Auger $\gtrsim 5 \mathrm{ns}$\\
			}
			\hspace*{1em}
			\vspace*{1em}
			\visible<2->{
				\textcolor{blue}{Beacon}: Pulse or Sine
				}
			\vspace*{\fill}
	\begin{figure}
		\hspace*{-2em}
		\begin{tikzpicture}
			\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}; }
				\draw[red, ultra thick, visible on=<{2-}>] (0.85,0.87) circle [radius=8mm];
				\draw[blue, ultra thick, visible on=<{2-}>] (0.23,0.32) circle [radius=8mm];
			\end{scope}
		\end{tikzpicture}
		\imagecredit{H. Schoorlemmer}
	\end{figure}
		\end{column}
		\begin{column}{0.5\textwidth}
			\centering
			\vspace*{\fill}
			\onslide<3->{\hyperlink{fig:pulse:accuracy}{\includegraphics[width=\textwidth]{pulse/time_res_vs_snr_multiple_dt_small.pdf}}}%
			\vspace*{\fill}
			\onslide<3->{\hyperlink{fig:sine:accuracy}{\includegraphics[width=\textwidth]{beacon/time_res_vs_snr_f67.pdf}}}%
			\vspace*{\fill}
		\end{column}
	\end{columns}
\end{frame}
\note{
	Single frequency interest due to Auger (TV@67MHz)
}

\section{Radio Interferometry in GRAND}
\begin{frame}{Radio Interferometry in GRAND}
	\begin{figure}
		\centering
		\vspace*{\fill}
		\hspace*{-2em}
		\includegraphics[width=1.13\textwidth]{grand/roadmap-per-2023-01-shortened.jpg}%
		%\includegraphics<2->[width=0.5\textwidth]{grand/roadmap-per-2023-01-shortened.jpg}%
		\imagesource{Adapted from \url{https://grand.cnrs.fr/overview/roadmap/}}
	\end{figure}
\end{frame}

% GRAND
%%%%%%%%%%%%%%%
%\note[itemize]
%{
%	\item GRAND radio-only, heavy development
%	\item pathfinders upto 2026 (Auger reference, Europe testbed, China array)
%	\item ultra high energy has low hits, need large area
%}


\begin{frame}{Radio Interferometry in GRAND in Conclusion}
	\begin{columns}
		\begin{column}{0.4\textwidth}
		\hspace*{-1.2em}
		\begin{figure}
			\vspace*{\fill}
			\vspace*{2.4em}
			\includegraphics[width=1\textwidth]{grand/roadmap-per-2023-01-shortened-prototyping.jpg}%
			\imagesource{Adapted from \url{https://grand.cnrs.fr/overview/roadmap/}}
			\vspace*{\fill}
		\end{figure}
		\end{column}
		\hspace*{-2em}
		\begin{column}{0.65\textwidth}
			\begin{enumerate}
				\item Timing Requirement in~Hardware\\
					\quad test beacon at Auger/GP300
					\vspace*{2em}
				\item Setup Interferometric Analyses\\
					\quad adapt to GRAND
					\vspace*{2em}
				\item Particle ID through Xmax\\
					and Shower Axis reconstruction
			\end{enumerate}
			\vspace*{1em}
		\end{column}
	\end{columns}
\end{frame}

%	\only<2-> {
%	Timing Requirements:\\
%		\quad synchronisation schemes investigated in internship,\\
%		\quad opportunity to implement and test (e.g.~Nan\c{c}ay)\\
%	}
%
%	\only<3-> {
%	\vspace*{1em}
%	Interferometric Analyses:\\
%		\quad enhances Xmax resolution\\
%	}
%
%	\vspace{\stretch{100}}

	%\vspace*{2em}
	%GRAND Goals:\\
	%	\quad Largest UHECR observatory, \\
	%	\quad Multi-messenger science case,\\
	%	\quad meaningful contribution to a new experiment\\
%\end{frame}
%\begin{frame}{Radio Interferometry in GRAND}

%			\visible<2->{
%				\vspace*{\fill}
%				\begin{center}
%				\begin{minipage}{.6\textwidth}
%					\hrule
%					\centering
%					\vspace{ 2em }
%					\textit{Thank you!}
%				\end{minipage}
%				\end{center}
%				%\vspace{ 4em }
%			}


%%%%%%%%%%%%%%%
% Backup slides
%%%%%%%%%%%%%%%
\appendix
\begin{frame}[c]
	\centering
	\Large {
		\textcolor{blue} {
	Supplemental material
	}
	}
\end{frame}

\section*{Table of Contents}
\begin{frame}{Table of Contents}
	\tableofcontents
\end{frame}

\begin{frame}{GRAND}
	\begin{figure}
		\includegraphics[width=1\textwidth]{grand/GRAND-detection-principle-1.png}%
		\imagecite{GRAND:2018iaj}
	\end{figure}
\end{frame}

\section{Radio Emission}
\begin{frame}{Airshower development}
	\begin{figure}
		\includegraphics[width=0.9\textwidth]{1607.08781/fig02a_airshower+detectors.png}
		\imagecite{Schroder:2016hrv}
	\end{figure}
\end{frame}

\begin{frame}{Polarised Radio Emission}
	\begin{columns}
		\begin{column}{0.2\textwidth}
			\centering
			Geosynchrotron
		\end{column}
		\begin{column}{0.7\textwidth}
			\centering
			\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_geomagnetic.png}%
		\end{column}
	\end{columns}
	\vfill
	\begin{columns}
		\begin{column}{0.2\textwidth}
			\centering
			Askaryan
		\end{column}
		\begin{column}{0.7\textwidth}
			\centering
			\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_askaryan.png}%
			\imagecite{Huege:2017bqv}
		\end{column}
	\end{columns}
%	\vfill
\end{frame}

\section{Radio Interferometry}
\begin{frame}{Radio Interferometry: Concept}
	\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}

\begin{frame}{Radio Interferometry: Xmax Resolution vs Timing Resolution}
	\begin{figure}
		\centering
		\includegraphics[width=0.7\textwidth]{2006.10348/fig03_b.png}%
		\imagecite{Schoorlemmer:2020low}
	\end{figure}
\end{frame}

\section{Time Synchronisation}
\subsection{Expected Time Accuracies vs SNR}
\subsubsection{Sine}
\begin{frame}{Sine wave: Accuracy}
	\begin{figure}
		\includegraphics[width=\textwidth]{beacon/time_res_vs_snr.pdf}
		\label{fig:sine:accuracy}
	\end{figure}
\end{frame}
\begin{frame}{Sine wave: SNR}
	\includegraphics[width=\textwidth]{ZH_simulation/signal_to_noise_definition.pdf}
\end{frame}

\subsubsection{Pulse}
\begin{frame}{Pulse Template}
	\begin{figure}
		\includegraphics[width=\textwidth]{pulse/time_res_vs_snr_multiple_dt.pdf}
		\label{fig:pulse:accuracy}
	\end{figure}
\end{frame}
\begin{frame}{Pulse Template: SNR}
	\begin{columns}
		\begin{column}{0.45\textwidth}
			\centering
			Signal to Noise
			\includegraphics[width=\textwidth]{pulse/antenna_signal_to_noise_6.pdf}
		\end{column}
		\hfill
		\begin{column}{0.45\textwidth}
			\centering
			Impulse Response
			\includegraphics[width=\textwidth]{pulse/filter_response.pdf}
		\end{column}
	\end{columns}
\end{frame}
\begin{frame}{Pulse Template: Timing}
	\begin{figure}
		\includegraphics[width=\textwidth]{pulse/correlation_tdt0.2_zoom.pdf}
		\label{fig:pulse:correlation}
	\end{figure}
\end{frame}



%%%%%%%%%
\subsection{Single Frequency Beacon}
\begin{frame}{Short period beacon 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}{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}

\begin{frame}{Time resolving short period beacon}
	\begin{figure}
		\centering
		\includegraphics<1>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_none.scale4d.pdf}
		\includegraphics<2>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf}
		\includegraphics<3>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf}
		\includegraphics<4>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.no_offset.scale4d.pdf}
		\label{fig:sine:grid_power}
	\end{figure}
\end{frame}

%%%%%%%%%%
\section{GNSS clock stability}
\begin{frame}{GNSS clock stability I}
	\begin{columns}
		\begin{column}{0.4\textwidth}
			\begin{figure}
				\centering
				\includegraphics[width=0.8\textwidth]{grand/setup/antenna-to-adc.pdf}
				\caption{
					GRAND Digitizer Unit's ADC to antennae
				}
			\end{figure}
		\end{column}
		\hfill
		\begin{column}{0.5\textwidth}
			\begin{figure}
				\includegraphics[width=\textwidth]{grand/setup/channel-delay-setup.pdf}%
				\caption{
					Channel filterchain delay experiment 
				}
			\end{figure}
		\end{column}
	\end{columns}
\end{frame}

\begin{frame}{GNSS filterchain delay experiment}
	\begin{columns}
		\begin{column}{0.5\textwidth}
			\centering
			Pulse
			\includegraphics[width=\textwidth]{grand/split-cable/split-cable-delays-ch1ch4.pdf}
		\end{column}
		\begin{column}{0.5\textwidth}
			\centering
			50MHz Sinewave
			\includegraphics[width=\textwidth]{grand/split-cable/split-cable-delay-ch1ch2-50mhz-200mVpp.pdf}
			%\includegraphics[width=\textwidth]{fourier/04_signal_to_noise_fig04.png}

				Delay $ \lesssim 150\mathrm{ps}$
		\end{column}
	\end{columns}

\end{frame}

\begin{frame}{GNSS clock stability II}
	\begin{figure}
		\centering
		\includegraphics[width=0.7\textwidth]{grand/setup/grand-gps-setup.pdf}
		\caption{
			GNSS stability experiment
		}
	\end{figure}
\end{frame}

\subsection{In the field}
\begin{frame}{GNSS clock stability II}
	\begin{columns}
		\begin{column}{0.5\textwidth}
			\includegraphics[width=\textwidth]{images/IMG_20220819_154801.jpg}
		\end{column}
		\begin{column}{0.5\textwidth}
			\includegraphics[width=\textwidth]{images/IMG_20220815_161244.jpg}
		\end{column}
	\end{columns}
\end{frame}

\subsection{White Rabbit}
\begin{frame}{White Rabbit: GNSS}
	\begin{figure}
		\includegraphics<1>[width=0.85\textwidth]{gnss/phase-delocked-gps-white-rabbit-setup-colored.pdf}%
		\includegraphics<2>[width=0.8\textwidth]{gnss/phase-locked-gps-white-rabbit-setup-colored.pdf}%
	\end{figure}
\end{frame}
\begin{frame}{White Rabbit: Precision Time Protocol}
	\begin{figure}
		\includegraphics[height=0.8\textheight]{white-rabbit/protocol/wrptpMSGs_1.pdf}
		\imagecite{WRPTP}
	\end{figure}
\end{frame}
\begin{frame}{White Rabbit: Delay model}
	\begin{figure}
		\includegraphics[width=\textwidth]{white-rabbit/protocol/delaymodel.pdf}
		\imagecite{WRPTP}
	\end{figure}
\end{frame}
\begin{frame}{White Rabbit: Clocks Reference}
	\begin{figure}
		\centering
		\hspace*{-5em}
		\includegraphics[width=1.35\textwidth]{clocks/wr-clocks.pdf}
	\end{figure}
\end{frame}

%%%%%%%%%%%%%%
% Bibliography
%%%%%%%%%%%%%%
\section*{References}
\begin{frame}[allowframebreaks]
	\frametitle{References}
	\printbibliography
\end{frame}
\end{document}

