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