Wrap up of the Day

presentations/2022-02-03_group_meeting/2022-02-03_group_meeting.tex

@@ -1,17 +1,33 @@
 \documentclass[showdate=false]{beamer}
 
+\usepackage[british]{babel}
 \usepackage{amsmath}
+\usepackage{hyperref}
+\usepackage[backend=bibtex,style=trad-plain]{biblatex}
 \usepackage{graphicx}
 \graphicspath{{.}{../../figures/}}
 
+\addbibresource{../../../bibliotheca/bibliography.bib}
 
-\addtobeamertemplate{navigation symbols}{}{%
+%%%%%%
-    \usebeamerfont{footline}%
+% Disable Captions
-    \usebeamercolor[fg]{footline}%
+%%%%%
-    \hspace{1em}%
+\setbeamertemplate{caption}{\raggedright\small\insertcaption\par}
-    \insertframenumber
+
+\newcommand\blfootnote[1]{%
+  \begingroup
+  \renewcommand\thefootnote{}\footnote{#1}%
+  \addtocounter{footnote}{-1}%
+  \endgroup
 }
 
+%\addtobeamertemplate{navigation symbols}{}{%
+%    \usebeamerfont{footline}%
+%    \usebeamercolor[fg]{footline}%
+%    \hspace{1em}%
+%    \insertframenumber
+%}
+
 %%%%%%%% Outline %%%%%%%%
 %
 % - Timing Mechanisms
@@ -22,7 +38,7 @@
 %
 %
 
-\title{Timing Accuracy in Air Shower Detectors}
+\title[Timing Accuracy]{Timing Accuracy in Air Shower Detectors}
 \date{February 03, 2022}
 \author{E.T. de Boone}
 
@@ -32,31 +48,91 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Timing Mechanisms in Detectors}
 \begin{frame}{Timing Mechanisms}
-	\begin{block}{Timing Mechanisms}
+	{Timing Mechanisms}
 	\begin{itemize}
 		\item GNSS (online)
 		\item Beacon (offline)
 	\end{itemize}
-	\end{block}
+	\vspace{2em}
-	\begin{block}{}
 	\begin{itemize}
 		\item More accurate reference timing needed to characterise/improve current mechanisms.
 	\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%
+\begin{frame}{Timing Mechanisms: GNSS}
+	\begin{block}{}
+		\begin{itemize}
+			\item Accuracy $\sim 5 ns$
+		\end{itemize}
 	\end{block}
 \end{frame}
 
-\begin{frame}{Timing Mechanisms: GNSS}
+%%%%%%%%%%%%%
-\end{frame}
-
 \begin{frame}{Timing Mechanisms: Beacon}
+			\begin{itemize}
+				\item Beating between frequency signals indicate timing
+				\item PA: located in physics band $\mapsto$ offline analysis, \\
+						  corrects for GPS drift.
+				\item different frequency responses for antenna models
+			\end{itemize}
+		\begin{columns}
+		\begin{column}{.5\textwidth}
+			\begin{figure}
+				\includegraphics[width=\textwidth]{beacon/auger/1512.02216.figure2.beacon_beat.png}
+				\caption{Four beacon frequencies create a well-defined beating. From \cite{PierreAuger:2015aqe}}
+			\end{figure}
+		\end{column}
+		\begin{column}{.5\textwidth}
+			\begin{figure}
+				\includegraphics[width=\textwidth]{beacon/auger/1512.02216.figure4.ads-b.png}
+				\caption{Automatic Dependent Surveillance Broadcasts (ADS-B) intercepts. From \cite{PierreAuger:2015aqe}}
+			\end{figure}
+		\end{column}
+	\end{columns}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Experimental Setup: White Rabbit}
-\begin{frame}{White Rabbit}
+\begin{frame}{Precision Time Protocol}
+	\begin{itemize}
+		\item Time synchronisation over (long) distance between (multiple) nodes
+	\end{itemize}
+	\begin{figure}
+		\includegraphics[width=0.4\textwidth]{white-rabbit/protocol/ptpMSGs-color.pdf}
+		\caption{Precision Time Protocol messages. From \cite{WRPTP}}.
+	\end{figure}
 \end{frame}
 
-\begin{frame}{Precision Time Protocol}
+%%%%%%%%%%%%%
+\begin{frame}{White Rabbit}
+	\begin{columns}
+		\begin{column}{.5\textwidth}
+			White Rabbit:
+			\begin{itemize}
+				\item SyncE ($f=125\textrm{MHz}$) (shared oscillator)
+				\item PTP (synchronisation)
+			\end{itemize}
+
+			\vspace{2em}
+
+			Factors:
+			\begin{itemize}
+				\item device ($\Delta_{txm}$, $\Delta_{rxs}$, ...)
+				\item link ($\delta_{ms}$, ...)
+			\end{itemize}
+			\begin{figure}
+				\makebox[\textwidth][c]{\includegraphics[width=1.2\textwidth]{white-rabbit/protocol/delaymodel.pdf}}
+				%\caption{From \cite{WRPTP}}.
+			\end{figure}
+		\end{column}
+		\begin{column}{.5\textwidth}
+			\begin{figure}
+				\makebox[\textwidth][c]{\includegraphics[width=1.1\textwidth]{white-rabbit/protocol/wrptpMSGs_1.pdf}}
+				\caption{From \cite{WRPTP}}.
+			\end{figure}
+		\end{column}
+	\end{columns}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -64,17 +140,57 @@
 \begin{frame}{Discrete Fourier and Phase}
 	\begin{block}{}
 		\begin{equation*}
-			N_{required} = f_{sample\_rate} / f_{signal}
+			u(t) = \exp(2i\pi ft + \phi_t)
+		\end{equation*}
+		\begin{equation*}
+			N_{required} := f_{sample\_rate} / f_{signal}
 		\end{equation*}
 	\end{block}
+	\includegraphics[width=\textwidth]{fourier/02-fourier_phase-f_max_showcase.pdf}
 \end{frame}
 
+
+%%%%%%%%%%%%%
 \begin{frame}{Phase reconstruction??}
+	\begin{block}{}
+		\begin{equation*}
+			u(t) = \exp(2i\pi ft + \phi_t)
+		\end{equation*}
+	\end{block}
 	\begin{figure}
 		\makebox[\textwidth][c]{\includegraphics[width=1.4\textwidth]{fourier/02-fourier_phase-phi_f_vs_phi_t.pdf}}%
 	\end{figure}
+	\begin{block}{}
+		Phase reconstruction is easy if sample rate ``correct''
+	\end{block}
 \end{frame}
+
+%%%%%%%%%%%%%
 \begin{frame}{Phase reconstruction??}
+	\begin{block}{}
+		What if sample rate ``incorrect''?
+	\end{block}
+	\begin{figure}
+		\makebox[\textwidth][c]{\includegraphics[width=1.4\textwidth]{fourier/02-fourier_phase-phi_f_vs_f_max_increasing_N_samples.pdf}}%
+	\end{figure}
+\end{frame}
+
+%%%%%%%%%%%%%
+\begin{frame}{Phase reconstruction??}
+	\begin{block}{}
+		What if sample rate ``incorrect''? \\
+
+		Linear interpolation ({\small $f_\mathrm{max}$, $f_\mathrm{submax}$, $\phi_\mathrm{max}$ and $\phi_\mathrm{submax}$}) 
+	\end{block}
+	\begin{figure}
+		\makebox[\textwidth][c]{
+			\includegraphics[width=\textwidth]{fourier/02-fourier_phase-phase_reconstruction-unfolded.pdf}
+		}
+	\end{figure}
+\end{frame}
+
+%%%%%%%%%%%%%
+\begin{frame}{}
 	\begin{block}{}
 		\begin{equation*}
 			A_1 / A_2