Wrap up of the Day

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Eric Teunis de Boone 2022-02-01 18:02:24 +01:00
parent 81c3f01eef
commit 51b2dca7e9
7 changed files with 135 additions and 19 deletions

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\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