WuotD: Still Missing Introduction
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@ -15,6 +15,7 @@
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\usepackage{graphicx}
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\usepackage{tikz}
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\usepackage{xurl}
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\usepackage{physics}
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\graphicspath{{.}{./figures/}{../../figures/}}
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\usepackage{todo}
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@ -26,6 +27,7 @@
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{\usebibmacro{citeindex}%
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\usebibmacro{cite}
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\newunit
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\clearfield{eprintclass}
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\usebibmacro{eprint}}
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{\multicitedelim}
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{\usebibmacro{postnote}}
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@ -95,25 +97,50 @@
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\def\thesissubtitle{}
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\def\thesisauthorfirst{E.T.}
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\def\thesisauthorsecond{de Boone}
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\def\thesisauthoremail{}
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\def\thesisauthoremailraw{ericteunis@deboone.nl}
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\def\thesisauthoremail{\href{mailto:\thesisauthoremailraw}{\thesisauthoremailraw}}
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\def\thesissupervisorfirst{dr. Harm}
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\def\thesissupervisorsecond{Schoorlemmer}
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\def\thesissupervisoremail{}
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\def\thesissupervisoremailraw{}
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\def\thesissupervisoremail{\href{mailto:\thesissupervisoremailraw}{\thesissupervisoremailraw}}
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\title[]{Enhancing Timing Accuracy in Air Shower Radio Detectors}
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\title[\thesistitle]{\thesistitle}
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\date{July, 2023}
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\author[\thesisauthorfirst\space\thesisauthorsecond]{%
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\thesisauthorfirst\space\thesisauthorsecond\thanks{\thesisauthoremail}\\
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\vspace*{2em}
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{Supervisor: \thesissupervisorfirst\space\thesissupervisorsecond\thanks{\thesissupervisoremail} }
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\texorpdfstring{\thesisauthorfirst\space\thesisauthorsecond\thanks{e-mail: \thesisauthoremail}\\
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\vspace*{0.5em}
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{Supervisor: \thesissupervisorfirst\space\thesissupervisorsecond }
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}{\thesisauthorfirst\space\thesisauthorsecond<\thesisauthoremailraw>}
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}
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% >>> Meta data
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\newcommand{\tclock}{\ensuremath{t_\mathrm{clock}}}
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\newcommand{\ns}{\ensuremath{\mathrm{ns}}}
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\newcommand{\pTrue}{\phi}
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\newcommand{\PTrue}{\Phi}
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\newcommand{\pMeas}{\varphi}
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\newcommand{\pTrueEmit}{\pTrue_0}
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\newcommand{\pTrueArriv}{\pTrueArriv'}
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\newcommand{\pMeasArriv}{\pMeas_0}
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\newcommand{\pProp}{\pTrue_d}
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\newcommand{\pClock}{\pTrue_c}
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\begin{document}
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{ % Titlepage <<<
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\setbeamertemplate{background}
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{%
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\parbox[c][\paperheight][c]{\paperwidth}{%
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\centering%
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\vfill%
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\includegraphics[width=\textwidth]{beacon/array_setup_gps_transmitter_cows.png}%
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\vspace*{2em}
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}%
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}
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\setbeamertemplate{footline}{} % no page number here
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\frame{ \titlepage }
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} % >>>
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@ -121,18 +148,72 @@
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%%%%%%%%%%%%%%%
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% Start of slides <<<
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%%%%%%%%%%%%%%%
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\section{Cosmic Particles}% <<<<
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\section{Cosmic Particle Detection}% <<<<
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% Sources, Types, Propagation, Observables
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% Flux -> Large instrumentation area
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% Detection methods of Auger
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% - FD, SD
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% AERA / AugerPrime RD or GRAND
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\begin{frame}
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\begin{frame}{Ultra High Energy particles}
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\end{frame}
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\begin{frame}{Air Showers}
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% Observables
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\end{frame}
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\begin{frame}{UHE particle flux}
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\end{frame}
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\begin{frame}{Detection methods}
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\end{frame}
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\begin{frame}{Radio Emission}
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\end{frame}
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% >>>>
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\section{Radio Interferometry}% <<<<
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\begin{frame}
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\begin{frame}{Radio Interferometry: Concept}
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Interferometry: Amplitude + Timing information of the $\vec{E}$-field\\
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\vspace*{ 0.8em }
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\begin{columns}
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\begin{column}{0.4\textwidth}
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\begin{figure}
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\includegraphics<1>[width=\textwidth]{radio_interferometry/rit_schematic_base.pdf}%
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\includegraphics<2>[width=\textwidth]{radio_interferometry/rit_schematic_far.pdf}%
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\includegraphics<3>[width=\textwidth]{radio_interferometry/rit_schematic_close.pdf}%
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\includegraphics<4>[width=\textwidth]{radio_interferometry/rit_schematic_true.pdf}%
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\end{figure}
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\end{column}
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\begin{column}{0.6\textwidth}
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\vspace*{\fill}
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\begin{itemize}
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\item<1-> Measure signal $S_i(t)$ at antenna $\vec{a_i}$
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\item<2-> Calculate light travel time \\[5pt]
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\quad $\Delta_i(\vec{x}) = \frac{ \left| \vec{x} - \vec{a_i} \right| }{c} n_{eff}$
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\item<2-> Sum waveforms accounting \\
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for time delay \\[5pt]
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\quad $S(\vec{x}, t) = \sum S_i( t + \Delta_i(\vec{x}) )$
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\end{itemize}
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\vspace*{\fill}
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\begin{figure}% Spatially
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\includegraphics<1>[width=0.8\textwidth]{radio_interferometry/single_trace.png}%
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\includegraphics<2>[width=0.8\textwidth]{radio_interferometry/trace_overlap_bad.png}%
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\includegraphics<3>[width=0.8\textwidth]{radio_interferometry/trace_overlap_medium.png}%
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\includegraphics<4>[width=0.8\textwidth]{radio_interferometry/trace_overlap_best.png}%
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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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\begin{frame}{Radio Interferometry: Image}
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\begin{figure}
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\centering
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\includegraphics[width=0.7\textwidth]{2006.10348/fig01.png}%
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\imagecite{Schoorlemmer:2020low}
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\end{figure}
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\end{frame}
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% >>>>
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@ -140,7 +221,32 @@
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% GNSS
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% reference system: White Rabbit, AERA beacon, (ADS-B?)
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% GRAND setup and measurements
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\begin{frame}
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\begin{frame}{Timing in Radio Detectors: GNSS}
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% Geometry
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Default Timing mechanism: Global Navigation Satellite Systems\\
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\begin{columns}
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\begin{column}{0.5\textwidth}
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\vfill
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\begin{figure}
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\begin{tikzpicture}[scale=1]
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\clip (2.5 , 0) rectangle ( 6, 2.5);
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\node[anchor=south west, inner sep=0] (image) at (0,0) {\includegraphics[width=\textwidth]{beacon/array_setup_gps_transmitter_cows.png}};
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%\draw[help lines,xstep=1,ystep=1] (0,0) grid (11,5);
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\end{tikzpicture}
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\imagecredit{H. Schoorlemmer}
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\end{figure}
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\end{column}
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\hfill
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\begin{column}{0.45\textwidth}
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In AERA, $ \Delta \tclock \gtrsim 10\ns$
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\\
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\begin{figure}
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\centering
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\includegraphics[width=\textwidth]{gnss/auger/1512.02216.figure3.gnss-time-differences.png}
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\imagecite{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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@ -148,13 +254,173 @@
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% Geometry
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% Pulse method + SNR
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% Sine method + SNR
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\begin{frame}
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\begin{frame}{Beacon Synchronisation}
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% Geometry
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\vspace*{0em}
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{
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{ \color{red} GNSS }
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+
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Extra Timing mechanism: {\color{blue} Beacon}%, {\color{green} ADS-B}
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}
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\\
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\vspace*{2em}
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\begin{figure}
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\hspace*{-2em}
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\begin{tikzpicture}
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[circle/.style={circle, ultra thick, radius=8mm}]
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\node[anchor=south west, inner sep=0] (image) at (0,0) {\includegraphics[width=\textwidth]{beacon/array_setup_gps_transmitter_cows.png}};
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\begin{scope}[x={(image.south east)}, y={(image.north west)}]
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%\draw[help lines,xstep=.1,ystep=.1] (0,0) grid (1,1);
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%\foreach \x in {0,1,...,9} { \node [anchor=north] at (\x/10,0) {0.\x}; }
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%\foreach \y in {0,1,...,9} { \node [anchor=east] at (0,\y/10) {0.\y}; }
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\node (transmitter) at (0.23, 0.32) {};
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\node (gnss) at (0.85, 0.87) {};
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%\node (aeroplane) at (0.3, 0.67) {\includegraphics[width=1.5cm]{templates/aeroplane.png}};
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%\draw[green, ultra thick, visible on=<{1-}>] (aeroplane.center) circle[radius=8mm];
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\draw[red, ultra thick, visible on=<{1-}>] (gnss.center) circle[radius=8mm];
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\draw[blue, ultra thick, visible on=<{1-}>] (transmitter.center) circle[radius=8mm];
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\end{scope}
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\end{tikzpicture}
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\imagecredit{H. Schoorlemmer}
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\end{figure}
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\end{frame}
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\subsection{Pulse Beacon}
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\begin{frame}{Pulse Beacon}
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\begin{figure}
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\includegraphics[width=\textwidth]{pulse/antenna_signals_tdt0.2_zoom.pdf}
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\end{figure}
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\vfill
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\end{frame}
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\begin{frame}{Pulse Beacon}
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Correlation: similarity between two signals.\\
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\begin{figure}
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\includegraphics[width=\textwidth]{pulse/correlation_tdt0.2_zoom.pdf}
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\end{figure}
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\end{frame}
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\begin{frame}{Pulse Beacon Timing}
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\begin{figure}
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\includegraphics[width=0.8\textwidth]{pulse/time_res_vs_snr_multiple_dt_small.pdf}
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\end{figure}
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\end{frame}
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\subsection{Sine Beacon}
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\begin{frame}{(Multi)Sine Beacon}
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\begin{equation*}
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\Delta \tclock = \left[ \frac{\varphi}{2\pi} \; + \; k \right] T
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\end{equation*}
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\begin{figure}
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\includegraphics[width=.45\textwidth]{methods/fourier/waveform.pdf}
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\hfill
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\includegraphics[width=.45\textwidth]{methods/fourier/noisy_spectrum.pdf}
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\end{figure}
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\end{frame}
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\begin{frame}{(Multi)Sine Beacon Timing}
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\begin{figure}
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\includegraphics[width=0.8\textwidth]{beacon/time_res_vs_snr.pdf}
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\end{figure}
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\begin{columns}
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\begin{column}{0.3\textwidth}
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\end{column}
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\begin{column}{0.7\textwidth}
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\tiny\begin{equation*}
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p_\PTrue(\pTrue; s, \sigma) =
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\frac{ e^{-\left(\frac{s^2}{2\sigma^2}\right)} }{ 2 \pi }
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+
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\sqrt{\frac{1}{2\pi}}
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\frac{s}{\sigma}
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e^{-\left( \frac{s^2}{2\sigma^2}\sin^2{\pTrue} \right)}
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\frac{\left(
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1 + \erf{ \frac{s \cos{\pTrue}}{\sqrt{2} \sigma }}
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\right)}{2}
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\cos{\pTrue}
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\end{equation*}
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\tiny{Random Phasor Sum: ``Statistical Optics'', J. Goodman}
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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{Single Sine Synchronisation}% <<<<
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% Sine method + Radio Interferometry
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\begin{frame}
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\begin{frame}{Single Sine Synchronisation}
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\begin{figure}
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%\centering
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\hspace*{-5em}
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\includegraphics<1>[width=1.3\textwidth]{beacon/08_beacon_sync_timing_outline.pdf}%
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\includegraphics<2>[width=1.3\textwidth]{beacon/08_beacon_sync_synchronised_outline.pdf}%
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\includegraphics<3>[width=1.3\textwidth]{beacon/08_beacon_sync_synchronised_period_alignment.pdf}%
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\end{figure}
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\end{frame}
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\begin{frame}{Single Sine Synchronisation Simulation}
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Air Shower detected on a grid of 100x100 antennas.
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\begin{columns}
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\begin{column}{0.5\textwidth}
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\begin{itemize}
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\item Add beacon to antenna
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\item Randomise clocks
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\item Measure phase
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\item Repair clocks for small offsets
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\item Iteratively find best $k_{ij}$
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\end{itemize}
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\end{column}
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\hfill
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\begin{column}{0.4\textwidth}
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\begin{figure}
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\includegraphics<1>[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.pdf}%
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\includegraphics<2>[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.masked.pdf}%
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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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\begin{frame}{Simulation: Period $k_i$}
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\small{
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Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$
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\\
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Iterative process: \\
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\; Scan positions finding the best $\{k_i\}$ set, then zoom in on strongest.
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}
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\only<1-4>{\begin{figure}
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\includegraphics<1>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i5.loc8.0-2795.4-7816.0.pdf}
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\includegraphics<2>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i99.loc8.0-2795.4-7816.0.pdf}
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\includegraphics<3>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf}
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\includegraphics<4>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf}
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\end{figure}}
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\only<5>{\begin{figure}
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\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf}
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\hfill
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\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf}
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\vspace{0.5cm}
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\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run1.pdf}
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\hfill
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\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run1.power.pdf}
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\end{figure}}
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\end{frame}
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\begin{frame}{Time resolving short period beacon: phase vs full}
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\begin{columns}
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\begin{column}{0.45\textwidth}
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{ Phase reparation }
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\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_phases.axis.trace_overlap.repair_phases.pdf}%
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\vfill
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\includegraphics[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf}%
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\label{fig:sine:repairments}
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\end{column}
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\hfill
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\begin{column}{0.45\textwidth}
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{ Phase + Period reparation }
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\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_full.axis.trace_overlap.repair_full.pdf}%
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\vfill
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\includegraphics[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf}%
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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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@ -163,7 +429,7 @@
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% Outlook: Parasitic/Active vs Pulse/Sine table
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% Parasitic Single Sine: 67MHz Auger
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% Implementation for GRAND?
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\begin{frame}
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\begin{frame}{Conclusion and Outlook}
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\end{frame}
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% >>>>
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