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Eric Teunis de Boone 2022-02-10 12:19:19 +01:00
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# White Rabbit figures
Probably most of the figures in this directory are directly from the
White Rabbit repository at https://ohwr.org/project/white-rabbit/.
I intend to keep the original filenames.

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presentations/2022-02-03_group_meeting/2022-02-03_group_meeting.tex
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\documentclass[showdate=false]{beamer} \documentclass[showdate=false]{beamer}
\usepackage[british]{babel}
\usepackage{amsmath}
\usepackage{hyperref}
\usepackage[backend=bibtex,style=trad-plain]{biblatex}
\usepackage{graphicx}
\graphicspath{{.}{../../figures/}}
\addtobeamertemplate{navigation symbols}{}{% \addbibresource{../../../bibliotheca/bibliography.bib}
\usebeamerfont{footline}%
\usebeamercolor[fg]{footline}% % Disable Captions
\hspace{1em}% \setbeamertemplate{caption}{\raggedright\small\insertcaption\par}
\insertframenumber
% Show Section overview at beginning of section
\AtBeginSection[]
{
\begin{frame}<beamer>{Table of Contents}
\tableofcontents[currentsection, currentsubsection, sectionstyle=show/shaded, subsectionstyle=hide]
\end{frame}
} }
% no to navigation, yes to frame numbering
\beamertemplatenavigationsymbolsempty
\setbeamerfont{page number in head/foot}{size=\normalsize}
\setbeamertemplate{footline}[frame number]
\title{} \title[Timing Accuracy]{Timing Accuracy in Air Shower Detectors}
\date{February 03, 2022} \date{February 10, 2022}
\author{E.T. de Boone} \author{E.T. de Boone}
\begin{document} \begin{document}
\frame{\titlepage} \frame{\titlepage}
\begin{frame}
\section{Timing Mechanisms in Detectors}
\begin{frame}{Timing Mechanisms}
\begin{block}{Why improve timing accuracy?}
\begin{itemize}
\item Better statistics (narrow down direction of air showers)
\item Interferometry
\end{itemize}
\end{block}
\begin{block}{Strategy}
\begin{itemize}
\item Simulations for synchronisation techniques
\item Characterising current methods
\end{itemize}
\end{block}
\end{frame}
\begin{frame}{Characterising current methods}
\begin{block}{Current Timing Methods}
\begin{itemize}
\item GNSS (online)
\item Beacon (offline)
\end{itemize}
\end{block}
\vspace{2em}
\begin{itemize}
\item GPS Accuracy $\leq 30 \mathrm{ns}$ for $95$\% time (often better)
\item Total time accuracy in the order of 5 -- 10~ns
\item More accurate reference timing needed to characterise/improve current mechanisms.
\end{itemize}
\end{frame} \end{frame}
%%%%%%%%%%%%%
\subsection{Beacon}
\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 and directions
\end{itemize}
\begin{columns}
\begin{column}{.5\textwidth}
\begin{figure}
\includegraphics[width=\textwidth]{beacon/auger/1512.02216.figure2.beacon_beat.png}
\caption{
\cite{PierreAuger:2015aqe}
Four beacon frequencies beating at PA.
}
\end{figure}
\end{column}
\begin{column}{.5\textwidth}
\begin{figure}
\includegraphics[width=\textwidth]{beacon/auger/1512.02216.figure4.ads-b.png}
%\caption{
% \cite{PierreAuger:2015aqe}
% ADS-B and signal intercepts.
%}
\end{figure}
\end{column}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Experimental Setup: White Rabbit}
\subsection[PTP]{Precision Time Protocol}
\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{
\cite{WRPTP}
Precision Time Protocol messages.
}
\end{figure}
\end{frame}
%%%%%%%%%%%%%
\subsection[WR]{White Rabbit}
\begin{frame}{White Rabbit}
\begin{columns}
\begin{column}{.5\textwidth}
White Rabbit:
\begin{itemize}
\item SyncE (common 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=1.1\textwidth]{white-rabbit/protocol/delaymodel.pdf}}
%\caption{\small 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}
\begin{frame}{White Rabbit}
\begin{figure}
\centering
\includegraphics<1>[width=0.8\textwidth]{gnss/phase-delocked-gps-white-rabbit-setup-colored.pdf}
\includegraphics<2>[width=0.8\textwidth]{gnss/phase-locked-gps-white-rabbit-setup-colored.pdf}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Fourier and Phase information}
\begin{frame}{(Discrete) Fourier and Phase}
\begin{equation*}
\hspace{-2em}
u(t) = \exp(i2\pi ft + \phi_t) \xrightarrow{\mathrm{Fourier\; Transform}} f', \phi_f
\end{equation*}
\begin{block}{Discrete Fourier Transform}
\begin{equation*}
N_\mathrm{required} := f_\mathrm{sample\_rate} / f_\mathrm{signal}
\end{equation*}
\begin{equation*}
f_\mathrm{Nyquist} = \frac{1}{2} f_\mathrm{sample\_rate}
\end{equation*}
\end{block}
\includegraphics[width=\textwidth]{fourier/02-fourier_phase-f_max_showcase.pdf}
\end{frame}
%%%%%%%%%%%%%
\subsection{Phase reconstruction}
\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{block}<2->{}
$\rightarrow$ Linear interpolation ({\small $f_\mathrm{signal}$, $f_\mathrm{max}$, $f_\mathrm{submax}$, $\phi_\mathrm{max}$ and $\phi_\mathrm{submax}$})
\end{block}
\vspace{2em}
\begin{figure}
\makebox[\textwidth][c]{
\includegraphics<1-2>[width=1.4\textwidth]{fourier/02-fourier_phase-phi_f_vs_f_max_increasing_N_samples.pdf}
\includegraphics<3>[width=1.3\textwidth]{fourier/02-fourier_phase-phase_reconstruction-unfolded.pdf}
\includegraphics<4>[width=1.3\textwidth]{fourier/02-fourier_phase-phase_reconstruction-unfolded-zoomed.pdf}
}%
\end{figure}
\end{frame}
%%%%%%%%%%%%%
\subsection{Without interpolation?}
\begin{frame}{Without interpolation? (Coming)}
\begin{figure}
\makebox[\textwidth][c]{\includegraphics[width=1.3\textwidth]{fourier/02-fourier_phase-relative_amplitudes_vs_N_samples_absolute.pdf}}\\%
\makebox[\textwidth][c]{\includegraphics[width=1.3\textwidth]{fourier/02-fourier_phase-relative_amplitudes_vs_N_samples_power.pdf}}\\%
\end{figure}
\end{frame}
%%%%%%%%%%%%%
\section*{References}
\begin{frame}{References}
\printbibliography
\end{frame}
\end{document} \end{document}

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presentations/2022-02-03_group_meeting/Makefile
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# vim:ft=make # vim:ft=make
-include config.mk -include config.mk
.PHONY: all clean .PHONY: all clean dist-clean
### Variables ### Variables
MAIN_SRC ?= main.tex MAIN_SRC ?= main.tex
TEXENGINE ?= pdflatex TEXENGINE ?= latexmk --pdf
MAIN_TARGET = $(patsubst %.tex,%.pdf,$(MAIN_SRC))
### Targets ### Targets
MAIN_TARGET=$(patsubst %.tex,%.pdf,$(MAIN_SRC))
all: $(MAIN_TARGET) all: $(MAIN_TARGET)
dist: all clean
$(MAIN_TARGET): $(MAIN_SRC) $(MAIN_TARGET): $(MAIN_SRC)
$(TEXENGINE) $^ $(TEXENGINE) $^
$(TEXENGINE) $^
dist-clean: clean
@rm -vf *.pdf *.eps *.dvi *.ps
clean: clean:
@rm -f *.dat *.log *.out *.aux *.dvi *.ps *.nav *.snm *.toc *.vrb *~ @rm -vf *.dat *.log *.out *.aux *.nav *.snm *.toc *.vrb *~ *.fls *.fdb_latexmk *-blx.bib *.bbl *.blg *.run.xml
@rm -f *.pdf *.eps

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presentations/2022-02-03_group_meeting/README.md
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# Short Presentation on current status # Short Presentation on current status
Mostly to show what I've been doing uptil now. Mostly to show what I've been doing uptil now.
Maybe short description of experimental setup? Add short description of experimental setup?
### Outline
* Timing Mechanisms (GNSS, Beacon)
* White Rabbit as reference timing mechanism
* White Rabbit
* PTP
* Fourier and Phase information
* precise measurement $N_{sample} = N_{required}$
* imprecise measurement $N_{sample} != N_{required}$

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presentations/2022-02-03_group_meeting/config.mk
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MAIN_SRC=2022-02-03_group_meeting.tex MAIN_SRC=2022-02-03_group_meeting.tex
TEXENGINE=pdflatex