\documentclass[showdate=false]{beamer}

\usepackage[british]{babel}
\usepackage{amsmath}
\usepackage{hyperref}
\usepackage[backend=bibtex,style=trad-plain]{biblatex}
\usepackage{appendixnumberbeamer}
\usepackage{graphicx}
\graphicspath{{.}{./figures/}{../../figures/}}
\usepackage{todo}

\addbibresource{../../../bibliotheca/bibliography.bib}

% Disable Captions
\setbeamertemplate{caption}{\raggedright\small\insertcaption\par}

% no to navigation, yes to frame numbering
\beamertemplatenavigationsymbolsempty
\setbeamerfont{page number in head/foot}{size=\normalsize}
\setbeamertemplate{footline}[frame number]

\title[]{Early contest STEP-UP}
\date{March $13^{\text{\tiny{th}}}$, 2023}
\author{E.T. de Boone}

\begin{document}
\frame{\titlepage}

% Context
%%%%%%%%%
\begin{frame}{Airshowers from Ultra High Energy particles}
	academic curriculum?

	\begin{figure}
		\includegraphics[width=\textwidth]{grand/astroparticletypes_grand.jpg}
	\end{figure}
\end{frame}

\begin{frame}{Radio signals and Airshowers}
	\begin{columns}
		\begin{column}{0.4\textwidth}
			Airshower split into EM, Muon and Hadron
		\end{column}
		\begin{column}{0.5\textwidth}
			\begin{figure}
				\centering
				\includegraphics[width=\textwidth]{1607.08781/fig02a_airshower+detectors.png}
%				\caption{
%					\cite{Schroder:2016hrv}
%				}
			\end{figure}
		\end{column}
	\end{columns}
	\begin{figure}
		\centering
		\includegraphics<2>[width=\textwidth]{airshower/airshower_radio_polarisation.jpg}%
	\end{figure}
\end{frame}

\begin{frame}{Radio Interferometry: Concept}
	\begin{columns}
		\begin{column}{0.4\textwidth}
			\begin{figure}
		   		\includegraphics[width=\textwidth]{radio_interferometry/Schematic_RIT_extracted.png}
			\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]
					$\Delta_i(\vec{x}) = \frac{ \left| \vec{x} - \vec{a_i} \right| }{c} n_{eff}$

				\item<2-> Sum waveforms accounting \\
					for time delay \\[5pt]
					$S(\vec{x}, t) = \sum S_i( t + \Delta_i(\vec{x}) )$
			\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}

% My Internship
%%%%%%%%%%%%%%%
\begin{frame}{Timing Constraint for Radio Interferometry}
	\vspace*{ -2em }
	Required time accuracy $< 1 \mathrm{ns}$ not provided by GNSS $ \gtrsim 5 \mathrm{ns}$.
	\vspace{ 2em }
	\begin{columns}
		\begin{column}{0.4\textwidth}
			Additional synchronisation
			using physics band
			\begin{itemize}
				\item Pulsed beacon
				\item Long period ($\sim 1 \mathrm{\mu s}$)% (AERA)
				\item<3-> Short period ($\lesssim 20 \mathrm{ns}$)
			\end{itemize}
		\end{column}
		\begin{column}{0.6\textwidth}
			\begin{figure}% Clock error fixes
				\includegraphics<1>[width=\textwidth]{radio_interferometry/trace_overlap/dc_grid_power_time_fixes.py.scale4d.best.trace_overlap.zoomed.repair_none.png}%
				\includegraphics<2>[width=\textwidth]{radio_interferometry/trace_overlap/dc_grid_power_time_fixes.py.scale4d.best.trace_overlap.zoomed.no_offset.png}%
				\includegraphics<3>[width=\textwidth]{radio_interferometry/trace_overlap/dc_grid_power_time_fixes.py.scale4d.best.trace_overlap.zoomed.repair_phases.png}%
				\includegraphics<4>[width=\textwidth]{radio_interferometry/trace_overlap/dc_grid_power_time_fixes.py.scale4d.best.trace_overlap.zoomed.repair_all.png}%
			\end{figure}
		\end{column}
	\end{columns}
\end{frame}

% Towards GRAND
%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Advantages of Radio Interferometry}
	\begin{columns}
		\begin{column}{0.4\textwidth}
			\begin{itemize}
				\item Trace longitudinal development of airshower
				\item Lower SNR threshold
			\end{itemize}
		\end{column}
		\begin{column}{0.6\textwidth}
			\begin{figure}
				\includegraphics[width=\textwidth]{2006.10348/fig01.png}
%				\caption{
%					\cite{Schoorlemmer:2020low}
%				}
			\end{figure}
		\end{column}
	\end{columns}
\end{frame}

\begin{frame}{Physics Improvement of Radio Interferometry}
	composition measurement\\
	\vskip 1em

	direction reconstruction improved\\
	relevance for $\nu$s pointing back to sources

%	\visible<2->{
%		\vspace*{\fill}
%		\begin{center}
%		\begin{minipage}{.6\textwidth}
%			\hrule
%			\centering
%			\vspace{10pt}
%			\textit{Thank you!}
%		\end{minipage}
%		\end{center}
%		\vspace{\stretch{2}}
%	}
\end{frame}


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

%%%%%%%%%
\subsection{Single frequency beacon synchronisation}

\begin{frame}{Short period beacon synchronisation}
	\begin{figure}
		\includegraphics<1>[width=\textwidth]{beacon/08_beacon_sync_timing_outline.pdf}%
		\includegraphics<2>[width=\textwidth]{beacon/08_beacon_sync_synchronised_outline.pdf}%
		\includegraphics<3>[width=\textwidth]{beacon/08_beacon_sync_synchronised_period_alignment.pdf}%
	\end{figure}
\end{frame}


\begin{frame}{Time resolving short period beacon}
	\begin{figure}
		\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}

%%%%%%%%%%
\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}




%%%%%%%%%%%%%%
% Bibliography
%%%%%%%%%%%%%%
\section*{References}
\begin{frame}{References}
	\printbibliography
\end{frame}
\end{document}