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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}
				%\scriptsize{TODO: Xmax figure showing difference for photon/proton}
				%\includegraphics[width=\textwidth]{1607.08781/fig02b_longitudinal_shower_profile.png}%
				%\imagecite{Schroder:2016hrv}
				\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\\
				$\mapsto$ composition measurement\\
			\begin{figure}
				\centering
				\includegraphics[width=\textwidth]{2006.10348/fig03_b.png}%
				\imagecite{Schoorlemmer:2020low}
			\end{figure}
			%photon/proton/Fe differences\\
	%\begin{figure}
	%	\centering
	%	\includegraphics[width=0.7\textwidth]{2006.10348/fig01.png}%
	%	\imagecite{Schoorlemmer:2020low}
	%\end{figure}
			%\vspace*{1em}
		\end{column}
	\end{columns}
\end{frame}
\note[itemize]
{
\item Statistical discrimation: high Z at high altitudes
\item Radio Interferometry helps in Xmax measurement
}

% GRAND
%%%%%%%%%%%%%%%
\section{GRAND}
\begin{frame}{Giant Radio Array for Neutrino Detection}
	%\begin{columns}
	%	\begin{column}{0.45\textwidth}
	%   		\begin{figure}
	%			\hspace*{-2em}
	%   			\includegraphics[width=1.3\textwidth]{grand/roadmap-per-2023-01-shortened.jpg}%
	%   		\end{figure}
	%		\vfill
	%	\end{column}
	%	\hfill
	%	\begin{column}{0.45\textwidth}
		   	\begin{figure}
	%			\hspace*{-2em}
				\includegraphics[width=1\textwidth]{grand/GRAND-detection-principle-1.png}%
				\imagecite{GRAND:2018iaj}
			\end{figure}
	%	\end{column}
	%\end{columns}
	%200 000 Radio Antennas $\mapsto$ largest Cosmic Ray observatory\\
\end{frame}
\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
}

% RI in GRAND
%%%%%%%%%%%%%
%\section{Radio Interferometry}
%\begin{frame}{Radio Interferometry}
%	\begin{columns}
%		\begin{column}{0.6\textwidth}
%			Enhanced measurements:
%			\begin{itemize}
%				\item Shower depth \\
%					  $\mapsto$ composition measurement\\
%				\item Shower axis reconstruction
%				\item Detector noise suppression\\
%			\end{itemize}
%
%			\vspace*{2em}
%	
%			Problem: synchronisation $\Delta t < \frac{1}{4f}$\\
%		\end{column}
%		\begin{column}{0.4\textwidth}
%			\begin{figure}
%				\centering
%				\includegraphics[width=\textwidth]{2006.10348/fig01_a.png}%
%				\imagecite{Schoorlemmer:2020low}
%			\end{figure}
%		\end{column}
%	\end{columns}
%\end{frame}

\section{Implementing Interferometry in GRAND}
\begin{frame}{Time synchronisation}
	%\vspace*{-2em}
	Interferometry: Amplitude + Timing information of the $\vec{E}$-field\\
	\vspace*{ 0.8em }

	Required time accuracy $< \frac{1}{4f} \sim 1 \mathrm{ns}$ (GNSS $\gtrsim 5 \mathrm{ns}$)
	\vspace*{ 0.8em }
	%Problem: Interferometry requires $\Delta t < \frac{1}{4f}$\\
	%\vspace*{1em}

	Internship: \\
		\quad schemes to synchronise using extra physics band signal\\
%		\quad synchronisation with a single beacon in simulations\\ (algorithm)
%		\quad (pulse and single frequency)

	\vspace*{ 0.5em }

	\begin{columns}
		%\hfill
		\begin{column}{0.3\textwidth}
			\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}%
			\vfill
			\includegraphics[width=1.1\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_none.scale4d.pdf}%
		\end{column}
		\hfill
		\begin{column}{0.3\textwidth}
			\includegraphics[width=1.1\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_phases.axis.trace_overlap.repair_phases.pdf}%
			\vfill
			\includegraphics[width=1.1\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf}%
		\end{column}
		\hfill
		\begin{column}{0.3\textwidth}
			\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}%
			\vfill
			\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}

\begin{frame}{Timing Synchronisation: Beacon}
	\begin{figure}
		\begin{tikzpicture}
			\node[anchor=south west, inner sep=0] (image) at (0,0) {\includegraphics[width=0.8\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[green, ultra thick, visible on=<3>] (0.23,0.32) circle [radius=8mm];
			\end{scope}
		\end{tikzpicture}
		\imagecredit{H. Schoorlemmer}
	\end{figure}

\end{frame}
\note{
	Single frequency interest due to Auger (TV@67MHz)
}

\begin{frame}{Radio Interferometry in GRAND}
	\begin{figure}
		\centering
		\only<1>{\hspace*{-2em}}
		\includegraphics<1>[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}

	\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 }
%			}
\end{frame}


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

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

\subsection{Radio Emission}
\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}

\subsubsection{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}


%%%%%%%%%
\subsection{Synchronisation: 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}
	\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}
	\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}%
		\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}

\subsection{Synchronisation: Expected Time Accuracies vs SNR}
\begin{frame}
	\begin{figure}
		\includegraphics[width=\textwidth]{beacon/time_res_vs_snr.pdf}
	\end{figure}
\end{frame}
\begin{frame}
	\begin{figure}
		\includegraphics[width=\textwidth]{pulse/time_res_vs_snr_multiple_dt.pdf}
	\end{figure}
\end{frame}


%%%%%%%%%%
\subsection{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 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}

\subsubsection{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}

\subsubsection{White Rabbit}
\begin{frame}{White Rabbit: GNSS}
	\begin{figure}
		\includegraphics<1>[width=\textwidth]{gnss/phase-delocked-gps-white-rabbit-setup-colored.pdf}
		\includegraphics<2>[width=\textwidth]{gnss/phase-delocked-gps-white-rabbit-setup-colored.pdf}
	\end{figure}
\end{frame}
\begin{frame}{White Rabbit: Precision Time Protocol}
	\begin{figure}
		\includegraphics[height=\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}