diff --git a/figures/beacon/auger/1512.02216.figure2.beacon_beat.png b/figures/beacon/auger/1512.02216.figure2.beacon_beat.png new file mode 100644 index 0000000..2c5afa9 Binary files /dev/null and b/figures/beacon/auger/1512.02216.figure2.beacon_beat.png differ diff --git a/figures/beacon/auger/1512.02216.figure4.ads-b.png b/figures/beacon/auger/1512.02216.figure4.ads-b.png new file mode 100644 index 0000000..3ec0a10 Binary files /dev/null and b/figures/beacon/auger/1512.02216.figure4.ads-b.png differ diff --git a/figures/fourier/02-fourier_phase-f_max_showcase.pdf b/figures/fourier/02-fourier_phase-f_max_showcase.pdf new file mode 100644 index 0000000..d9e6833 Binary files /dev/null and b/figures/fourier/02-fourier_phase-f_max_showcase.pdf differ diff --git a/figures/fourier/02-fourier_phase-phase_reconstruction-unfolded.pdf b/figures/fourier/02-fourier_phase-phase_reconstruction-unfolded.pdf new file mode 100644 index 0000000..1eaa1aa Binary files /dev/null and b/figures/fourier/02-fourier_phase-phase_reconstruction-unfolded.pdf differ diff --git a/figures/fourier/02-fourier_phase-phi_f_vs_phi_t.pdf b/figures/fourier/02-fourier_phase-phi_f_vs_phi_t.pdf index c1df6c0..c782f82 100644 Binary files a/figures/fourier/02-fourier_phase-phi_f_vs_phi_t.pdf and b/figures/fourier/02-fourier_phase-phi_f_vs_phi_t.pdf differ diff --git a/figures/fourier/02-fourier_phase-relative_amplitudes_vs_N_samples.pdf b/figures/fourier/02-fourier_phase-relative_amplitudes_vs_N_samples.pdf index 4183432..ff597dd 100644 Binary files a/figures/fourier/02-fourier_phase-relative_amplitudes_vs_N_samples.pdf and b/figures/fourier/02-fourier_phase-relative_amplitudes_vs_N_samples.pdf differ diff --git a/presentations/2022-02-03_group_meeting/2022-02-03_group_meeting.tex b/presentations/2022-02-03_group_meeting/2022-02-03_group_meeting.tex index 1906da0..3f36250 100644 --- a/presentations/2022-02-03_group_meeting/2022-02-03_group_meeting.tex +++ b/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}% - \usebeamercolor[fg]{footline}% - \hspace{1em}% - \insertframenumber +%%%%%% +% Disable Captions +%%%%% +\setbeamertemplate{caption}{\raggedright\small\insertcaption\par} + +\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} - \begin{itemize} - \item GNSS (online) - \item Beacon (offline) - \end{itemize} - \end{block} + {Timing Mechanisms} + \begin{itemize} + \item GNSS (online) + \item Beacon (offline) + \end{itemize} + \vspace{2em} + \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 More accurate reference timing needed to characterise/improve current mechanisms. + \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