935 lines
30 KiB
TeX
935 lines
30 KiB
TeX
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%% From https://tex.stackexchange.com/a/55849
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% Keys to support piece-wise uncovering of elements in TikZ pictures:
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% \node[visible on=<2->](foo){Foo}
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%
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% output driver does not support transparencies (e.g., PS)
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%
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\tikzset{
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invisible/.style={opacity=0},
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visible on/.style={alt={#1{}{invisible}}},
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alt/.code args={<#1>#2#3}{%
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\alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}} % \pgfkeysalso doesn't change the path
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},
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}
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\hypersetup{pdfpagemode=UseNone} % don't show bookmarks on initial view
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% >>> Preamble
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%%%%%%%%%%%%%%%
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% Meta data <<<
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%%%%%%%%%%%%%%%
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\def\thesistitle{Enhancing Timing Accuracy\texorpdfstring{\\[0.3cm]}{ }in Air Shower Radio Detectors}
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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\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\thesissupervisoremailraw{}
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\def\thesissupervisoremail{\href{mailto:\thesissupervisoremailraw}{\thesissupervisoremailraw}}
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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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\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{\tClock}{\tclock}
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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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%%%%%%%%%%%%%%%
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% Start of slides <<<
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%%%%%%%%%%%%%%%
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\section{Cosmic Particles 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}{Ultra High Energy particles}
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\begin{figure}
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\centering
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\includegraphics[width=0.9\textwidth]{astroparticle/bk978-0-7503-2344-4ch1f2_hr.jpg}%
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\imagecredit{Juan Antonio Aguilar and Jamie Yang. IceCube/WIPAC}
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\end{figure}
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\end{frame}
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\begin{frame}{Ultra High Energy particle flux}
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\begin{columns}
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\begin{column}{0.6\textwidth}
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\begin{figure}
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\centering
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%\includegraphics[width=0.7\textwidth]{astroparticle/cr_flux_PDG_2023.pdf}%
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\includegraphics[width=\textwidth]{astroparticle/spectrum.png}%
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\imagecredit{\nocite{PDG2022}Particle Data Group}
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\end{figure}
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\end{column}
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\begin{column}{0.5\textwidth}
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Large Area Experiments:\\
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%\begin{multicols}{2}
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\begin{itemize}
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\item Pierre Auger Observatory
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\item Giant Radio Array for Neutrino Detection
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\end{itemize}
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\vfill
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\begin{figure}
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\includegraphics[width=\textwidth]{images/A-schematic-of-the-Pierre-Auger-Observatory-where-each-black-dot-is-a-water-Cherenkov.png}
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\imagecredit{\href{https://www.researchgate.net/figure/A-schematic-of-the-Pierre-Auger-Observatory-where-each-black-dot-is-a-water-Cherenkov_fig1_319524774}{Hans O. Klages}}
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\end{figure}
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%\end{multicols}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}{Air Showers}
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% Observables
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% \begin{columns}
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% \begin{column}{0.45\textwidth}
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% \begin{figure}
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% \includegraphics[width=\textwidth]{airshower/shower_development_depth_iron_proton_photon_with_muons.pdf}
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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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% \end{column}
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% \end{columns}
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\begin{figure}
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\hspace*{-2em}
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\centering
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\includegraphics[width=1.13\textwidth]{airshower/Auger_ScreenShot_GoldenHybrid1_shower_SD_FD.png}
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\imagesource{From:~\url{https://opendata.auger.org/display.php?evid=172657447200}}
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\end{figure}
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\end{frame}
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\begin{frame}{Air Shower Radio Emission}
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\begin{columns}
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\begin{column}{0.45\textwidth}
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\begin{figure}
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\includegraphics[width=\textwidth]{airshower/shower_development_depth_iron_proton_photon.pdf}
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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}{0.545\textwidth}
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\begin{figure}
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\centering
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Charge excess
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\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_askaryan.png}\\%
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\vspace*{2em}
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Geomagnetic
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\includegraphics[width=\textwidth]{airshower/airshower_radio_polarisation_geomagnetic.png}%
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\imagesource{\arxivcite{Huege:2017bqv}}
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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{Radio Interferometry}% <<<<
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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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\imagesource{\arxivcite{Schoorlemmer:2020low}}
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\end{figure}
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\end{frame}
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% >>>>
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\section{Timing in Air Shower Radio Detectors}% <<<<
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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}{Timing in Air Shower Radio Detectors}
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% Geometry
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Relative timing is important for Radio Interferometry. {\small ($ 1\ns\, @ c \sim 30\mathrm{cm}$)}\\
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\vspace*{1em}
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Large inter-detector spacing ($\sim 1\mathrm{km}$)\\
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$\mapsto$ Default timing mechanism: Global Navigation Satellite Systems\\
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\vspace*{1em}
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What is the accuracy of such systems?\\
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\visible<2>{
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\quad @Auger: $\sigma_t \gtrsim 10\ns$
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}
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\vfill
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\begin{columns}
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\begin{column}{0.45\textwidth}
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\begin{figure}
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\visible<2>{
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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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\vspace*{-1em}
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\imagesource{\arxivcite{PierreAuger:2015aqe}}
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}
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\end{figure}
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\end{column}
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\hfill
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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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\end{columns}
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\end{frame}
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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}[t]{Timing in Radio Detectors: Beacon Synchronisation}
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% Geometry
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Relative timing is important for Radio Interferometry.\\
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\vspace*{1em}
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Default Timing mechanism: {\color<1>{red} Global Navigation Satellite Systems}\\
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\visible<1->{
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+Extra Timing mechanism: {\color<1>{blue} Beacon} (Pulse, Sine)%, {\color{green} ADS-B}
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}
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\vfill
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\begin{figure}
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\hspace*{-2em}
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\begin{tikzpicture}
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\node[anchor=south west, inner sep=0] (image) at (0,0) {\includegraphics[width=0.8\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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%% Aeroplane
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%\node[ visible on=<{2-}>] (aeroplane) at (0.5, 0.67) {\scalebox{-1}[1]{\includegraphics[width=1.5cm]{templates/aeroplane.png}}};
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%\draw[green, ultra thick, visible on=<{2-}>] (aeroplane.center) circle[radius=8mm];
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%% Circles
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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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%% Mask Transmitter
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\fill[white, visible on=<0>] (0,0) rectangle (0.45,1) ;
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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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\section{Beacon Synchronisation}
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\begin{frame}[t]{Beacon Synchronisation: Geometry}
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Local antenna time $t'_i$ due to time~delay~$t_{\mathrm{d}i}$, clock~skew~$\sigma_i$\\
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and transmitter~time~$t_\mathrm{tx}$
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\begin{equation*}
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t'_i = t_{tx} + t_{\mathrm{d}i} + \sigma_i
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\end{equation*}
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\vfill
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\begin{figure}
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\begin{tikzpicture}
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[inner sep=2mm,
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place/.style={circle,draw=black!50,fill=white,thick}
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]
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\clip (0 , 0) rectangle (9, 2.5);
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\node[anchor=south west, inner sep=0] (image) at (0,0) {\includegraphics[width=0.8\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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%\fill[white] (0.4,0) rectangle (0.6,0.4);
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\node (transmitter) at (0.23, 0.32) {};
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\node (ant1) at (0.51, 0.32) [place] {1};
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%\node (ant1) at (0.72, 0.25) [place] {1};
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\node (ant2) at (0.65, 0.50) [place] {2};
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%
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\draw (transmitter.center) to node [below] {$t_{\mathrm{d}1}$} (ant1) ;
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\draw (transmitter.center) to node [above] {$t_{\mathrm{d}2}$} (ant2) ;
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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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\vfill
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Measured time difference:\\
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\vspace{-0.5em}
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\begin{equation*}
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\Delta t'_{12} = t'_1 - t'_2 = \Delta t_{\mathrm{d}12} + \sigma_{12} + (t_\mathrm{tx} - t_\mathrm{tx})
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\end{equation*}
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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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\centering
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\includegraphics[width=0.8\textwidth]{pulse/time_res_vs_snr_multiple_dt.pdf}
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|
\end{figure}
|
|
\end{frame}
|
|
|
|
\subsection{Sine Beacon}
|
|
\begin{frame}{(Multi)Sine Beacon}
|
|
Phase measurement $\varphi'_i$ using Fourier Transform, $k$~unknown:
|
|
\begin{equation*}
|
|
t'_i = \left[ \frac{\varphi'_i}{2\pi} \; + \; k \right] T
|
|
\end{equation*}
|
|
\begin{figure}
|
|
\includegraphics[width=.45\textwidth]{methods/fourier/waveform.pdf}
|
|
\hfill
|
|
\includegraphics<1>[width=.45\textwidth]{methods/fourier/noisy_spectrum.pdf}
|
|
\end{figure}
|
|
\end{frame}
|
|
\begin{frame}{(Multi)Sine Beacon Timing}
|
|
\vspace*{1em}
|
|
\begin{figure}
|
|
\centering
|
|
\includegraphics[width=0.8\textwidth]{beacon/time_res_vs_snr_large.pdf}
|
|
\end{figure}
|
|
\vspace*{-1em}
|
|
\begin{columns}
|
|
\begin{column}[b]{0.4\textwidth}
|
|
\centering
|
|
\tiny
|
|
Random~Phasor~Sum:
|
|
\autocite{goodman1985:2.9}~
|
|
``Statistical~Optics'',
|
|
J.~Goodman
|
|
\end{column}
|
|
\begin{column}[b]{0.7\textwidth}
|
|
\tiny\begin{equation*}
|
|
p_\PTrue(\pTrue; s, \sigma) =
|
|
\frac{ e^{-\left(\frac{s^2}{2\sigma^2}\right)} }{ 2 \pi }
|
|
+
|
|
\sqrt{\frac{1}{2\pi}}
|
|
\frac{s}{\sigma}
|
|
e^{-\left( \frac{s^2}{2\sigma^2}\sin^2{\pTrue} \right)}
|
|
\frac{\left(
|
|
1 + \erf{ \frac{s \cos{\pTrue}}{\sqrt{2} \sigma }}
|
|
\right)}{2}
|
|
\cos{\pTrue}
|
|
\end{equation*}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Beacon Synchronisation: Conclusion}
|
|
\vspace*{2em}
|
|
\begin{columns}[T]
|
|
\begin{column}{0.49\textwidth}
|
|
\begin{center}\bfseries Pulse \end{center}
|
|
\vspace*{-1em}
|
|
\begin{itemize}
|
|
\item discrete
|
|
\item requires template
|
|
\end{itemize}
|
|
\end{column}
|
|
\hfill
|
|
\begin{column}{0.49\textwidth}
|
|
\begin{center}\bfseries Sine \end{center}
|
|
\vspace*{-1em}
|
|
\begin{itemize}
|
|
\item continuous
|
|
\item longer trace\\ $\mapsto$ better SNR
|
|
\item $k$ period unknown
|
|
\end{itemize}
|
|
\end{column}
|
|
\end{columns}
|
|
\vfill
|
|
\begin{columns}
|
|
\begin{column}{0.49\textwidth}
|
|
\includegraphics[width=1\textwidth]{pulse/time_res_vs_snr_multiple_dt_small.pdf}
|
|
\end{column}
|
|
\hfill
|
|
\begin{column}{0.49\textwidth}
|
|
\includegraphics[width=1\textwidth]{beacon/time_res_vs_snr_small.pdf}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
% >>>>
|
|
\section{Single Sine Synchronisation}% <<<<
|
|
% Sine method + Radio Interferometry
|
|
\begin{frame}{Single Sine Synchronisation}
|
|
$k$ is discrete, lift the period degeneracy using the air~shower radiosignal
|
|
\begin{equation*}
|
|
t'_i = (\frac{\varphi'_i}{2\pi} + n_i)T = A_i + B_i
|
|
\end{equation*}
|
|
\vspace*{-2em}
|
|
\begin{figure}
|
|
%\centering
|
|
\hspace*{-5em}
|
|
\includegraphics<1>[width=1.3\textwidth]{beacon/08_beacon_sync_timing_outline.pdf}%
|
|
\includegraphics<2>[width=1.3\textwidth]{beacon/08_beacon_sync_synchronised_outline.pdf}%
|
|
\includegraphics<3>[width=1.3\textwidth]{beacon/08_beacon_sync_synchronised_period_alignment.pdf}%
|
|
\end{figure}
|
|
\begin{align*}
|
|
\Delta t'_{ij} &= (A_j + B_j) - (A_i + B_i) + \Delta t'_\varphi \\
|
|
&= \Delta A_{ij} + \only<1>{\Delta t'_\varphi}\only<2->{\cancel{\Delta t'_\varphi}} + k_{ij}T\\
|
|
\end{align*}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Single Sine Synchronisation Simulation}
|
|
Air Shower simulation on a grid of 100x100 antennas.
|
|
\\
|
|
\begin{columns}
|
|
\begin{column}{0.45\textwidth}
|
|
\begin{itemize}
|
|
\item<2-> Add beacon ($T\sim20\ns$) to antenna
|
|
\item<2-> Randomise clocks ($\sigma=30\ns$)
|
|
\item<3-> Measure phase with DTFT
|
|
\item<3-> Repair clocks for small offsets
|
|
\item<3-> Iteratively find best $k_{ij}$
|
|
\end{itemize}
|
|
\end{column}
|
|
\hfill
|
|
\begin{column}{0.5\textwidth}
|
|
\begin{figure}
|
|
\hspace*{-2em}
|
|
\includegraphics<1>[width=1.2\textwidth]{ZH_simulation/array_geometry_shower_amplitude.png}
|
|
\includegraphics<2>[width=1.2\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.pdf}%
|
|
\includegraphics<3>[width=1.2\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.masked.pdf}%
|
|
\end{figure}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Single Sine Synchronisation: Iterative $k_{0i}$-finding}
|
|
\small{
|
|
``Interferometry'' while allowing to shift by $T = 1/f_\mathrm{beacon}$
|
|
\\[5pt]
|
|
Iterative process optimizing signal power: \\
|
|
\; Scan positions finding the best $\{k_{0i}\}$ set,\\
|
|
\; then evaluate on a grid near shower axis and zoom in.
|
|
}
|
|
|
|
\only<1-3>{\begin{figure}
|
|
\includegraphics<1>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i1.zoomed.beacon.pdf}
|
|
\includegraphics<2>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf}
|
|
\includegraphics<3>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf}
|
|
\end{figure}}
|
|
\only<4>{\begin{figure}
|
|
\includegraphics[width=0.4\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run1.pdf}
|
|
\hfill
|
|
\includegraphics[width=0.4\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run1.power.pdf}
|
|
\vspace{0.5cm}
|
|
\includegraphics[width=0.4\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run2.pdf}
|
|
\hfill
|
|
\includegraphics[width=0.4\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run2.power.pdf}
|
|
\end{figure}}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Single Sine Synchronisation: Timing Reparation}
|
|
\begin{columns}
|
|
\begin{column}{0.45\textwidth}
|
|
{ Phase reparation }
|
|
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_phases.axis.trace_overlap.repair_phases.pdf}%
|
|
\vfill
|
|
\includegraphics[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf}%
|
|
\label{fig:sine:repairments}
|
|
\end{column}
|
|
\hfill
|
|
\begin{column}{0.45\textwidth}
|
|
{ Phase + Period reparation }
|
|
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_full.axis.trace_overlap.repair_full.pdf}%
|
|
\vfill
|
|
\includegraphics[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_full.scale4d.pdf}%
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Single Sine Synchronisation: Comparison}
|
|
\begin{columns}
|
|
\begin{column}{0.45\textwidth}
|
|
{ True clock }
|
|
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.no_offset.axis.trace_overlap.no_offset.pdf}%
|
|
\vfill
|
|
\includegraphics[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.no_offset.scale4d.pdf}%
|
|
\end{column}
|
|
\hfill
|
|
\begin{column}{0.45\textwidth}
|
|
{ Phase + Period reparation }
|
|
\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap/on-axis/dc_grid_power_time_fixes.py.repair_full.axis.trace_overlap.repair_full.pdf}%
|
|
\vfill
|
|
\includegraphics[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_full.scale4d.pdf}%
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
% >>>>
|
|
\section{Conclusion}% <<<<
|
|
% Single Sine + Air Shower
|
|
% Outlook: Parasitic/Active vs Pulse/Sine table
|
|
% Parasitic Single Sine: 67MHz Auger
|
|
% Implementation for GRAND?
|
|
\begin{frame}{Conclusion and Outlook}
|
|
\begin{itemize}
|
|
\item Cosmic Particles induce Extensive Air Showers\\[10pt]
|
|
\item Relative Timing is crucial to Radio Interferometry\\[10pt]
|
|
\item Pulse and Sine beacons can synchronise effectively\\[10pt]
|
|
\item Single Sine + Air Shower works
|
|
\end{itemize}
|
|
\vspace*{2em}
|
|
|
|
\visible<2>{
|
|
Outlook:
|
|
\begin{itemize}
|
|
\item Parasitic setups, i.e.~the $67\mathrm{MHz}$ in Auger,\\[10pt]
|
|
\item Self-calibration using pulsed beacon
|
|
\end{itemize}
|
|
}
|
|
\vfill
|
|
\end{frame}
|
|
|
|
% >>>>
|
|
% >>> End of Slides
|
|
%%%%%%%%%%%%%%%
|
|
% Backup slides <<<
|
|
%%%%%%%%%%%%%%%
|
|
\appendix
|
|
\begin{frame}[c]
|
|
\centering
|
|
\Large {
|
|
\textcolor{blue} {
|
|
Supplemental material
|
|
}
|
|
}
|
|
\end{frame}
|
|
|
|
\section*{Table of Contents}
|
|
\begin{frame}{Table of Contents}
|
|
\tableofcontents
|
|
\end{frame}
|
|
|
|
\begin{frame}{Single Sine Timing Result}
|
|
\centering
|
|
\includegraphics<1>[width=\textwidth]{ZH_simulation/cb_report_measured_antenna_time_offsets.py.time-amplitudes.comparison.pdf}
|
|
\includegraphics<2>[width=\textwidth]{ZH_simulation/cb_report_measured_antenna_time_offsets.py.time-amplitudes.residuals.pdf}
|
|
\end{frame}
|
|
|
|
\section{Airshower}
|
|
\begin{frame}{Airshower development}
|
|
\begin{figure}
|
|
\includegraphics[width=\textwidth]{1607.08781/fig02a_airshower+detectors.png}
|
|
\imagesource{\arxivcite{Schroder:2016hrv}}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Radio footprint; GRAND}
|
|
\begin{figure}
|
|
\includegraphics[width=0.9\textwidth]{grand/GRAND-detection-principle-1.png}
|
|
\imagecredit{\arxivcite{GRAND:2018iaj}}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
\section{Radio Interferometry}
|
|
\begin{frame}{Radio Interferometry: Xmax Resolution vs Timing Resolution}
|
|
\begin{figure}
|
|
\centering
|
|
\includegraphics[width=0.7\textwidth]{2006.10348/fig03_b.png}%
|
|
\imagecredit{\arxivcite{Schoorlemmer:2020low}}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
\section{Beacon contamination}
|
|
\begin{frame}{Sine: Air Shower - Beacon}
|
|
\centering
|
|
\includegraphics[width=\textwidth]{ZH_simulation/da_reconstruction.py.traces.A74.zoomed.peak.Ex.pdf}
|
|
\end{frame}
|
|
|
|
\section{Beacon Pulse}
|
|
\begin{frame}{Filter Response and Sampling}
|
|
\centering
|
|
\includegraphics[width=\textwidth]{pulse/interpolation_deltapeak+antenna.pdf}
|
|
\end{frame}
|
|
%\begin{frame}{Hilbert Timing}
|
|
% \centering
|
|
% \includegraphics[width=\textwidth]{pulse/hilbert_timing_zoom.pdf}
|
|
%\end{frame}
|
|
|
|
\section{Beacon without TX}
|
|
\subsection{Pulse}
|
|
\begin{frame}{Beacon: Pulse (single baseline)}
|
|
\begin{figure}
|
|
\includegraphics<1>[width=\textwidth]{beacon/field/field_single_center_time.pdf}
|
|
\includegraphics<2>[width=\textwidth]{beacon/field/field_single_left_time.pdf}
|
|
\end{figure}
|
|
\end{frame}
|
|
\begin{frame}{Beacon: Pulse (3 baselines)}
|
|
\begin{figure}
|
|
\includegraphics<1>[width=\textwidth]{beacon/field/field_three_center_time.pdf}
|
|
\includegraphics<2>[width=\textwidth]{beacon/field/field_three_left_time.pdf}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Beacon: Pulse (multi baseline)}
|
|
\begin{figure}
|
|
\includegraphics<1>[width=\textwidth]{beacon/field/field_square_ref0_time.pdf}
|
|
\includegraphics<2>[width=\textwidth]{beacon/field/field_square_all_time.pdf}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
\subsection{Sine}
|
|
\begin{frame}{Beacon: Sine (single baseline)}
|
|
\begin{figure}
|
|
\includegraphics<1>[width=\textwidth]{beacon/field/field_single_center_phase.pdf}
|
|
\includegraphics<2>[width=\textwidth]{beacon/field/field_single_left_phase.pdf}
|
|
\end{figure}
|
|
\end{frame}
|
|
\begin{frame}{Beacon: Sine (3 baseline)}
|
|
\begin{figure}
|
|
\includegraphics<1>[width=\textwidth]{beacon/field/field_three_center_phase.pdf}
|
|
\includegraphics<2>[width=\textwidth]{beacon/field/field_three_left_phase.pdf}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
\begin{frame}{Beacon: Sine (multi baseline reference antenna)}
|
|
\begin{figure}
|
|
\includegraphics<1>[width=\textwidth]{beacon/field/field_square_ref0_phase.pdf}
|
|
%\includegraphics<2>[width=\textwidth]{beacon/field/field_square_ref0_phase_zoomtx.pdf}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
\begin{frame}{Beacon: Sine (all baselines)}
|
|
\begin{figure}
|
|
\includegraphics<1>[width=\textwidth]{beacon/field/field_square_all_phase.pdf}
|
|
%\includegraphics<2>[width=\textwidth]{beacon/field/field_square_all_phase_zoomtx.pdf}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
\section{Fourier}
|
|
\begin{frame}{DTFT vs DFT}
|
|
\centering
|
|
\includegraphics[width=\textwidth]{methods/fourier/noisy_spectrum.pdf}
|
|
\end{frame}
|
|
\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*}
|
|
\includegraphics[width=\textwidth]{fourier/02-fourier_phase-f_max_showcase.pdf}
|
|
\end{frame}
|
|
\begin{frame}{Phase reconstruction?}
|
|
\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}
|
|
|
|
|
|
|
|
|
|
%%%%%%%%%%
|
|
\section{GNSS clock stability}
|
|
\begin{frame}{GNSS clock stability I}
|
|
\begin{columns}
|
|
\begin{column}{0.4\textwidth}
|
|
\begin{figure}
|
|
\centering
|
|
\includegraphics[width=0.8\textwidth]{grand/setup/antenna-to-adc.pdf}
|
|
\caption{
|
|
GRAND Digitizer Unit's ADC to antennae
|
|
}
|
|
\end{figure}
|
|
\end{column}
|
|
\hfill
|
|
\begin{column}{0.5\textwidth}
|
|
\begin{figure}
|
|
\includegraphics[width=\textwidth]{grand/setup/channel-delay-setup.pdf}%
|
|
\caption{
|
|
Channel filterchain delay experiment
|
|
}
|
|
\end{figure}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}{GNSS filterchain delay experiment}
|
|
\begin{columns}
|
|
\begin{column}{0.5\textwidth}
|
|
\centering
|
|
Pulse
|
|
\includegraphics[width=\textwidth]{grand/split-cable/split-cable-delays-ch1ch4.pdf}
|
|
\end{column}
|
|
\begin{column}{0.5\textwidth}
|
|
\centering
|
|
50MHz Sinewave delay(ch1, ch2) = $46\mathrm{ps} \pm 10$
|
|
\includegraphics[width=\textwidth]{grand/split-cable/split-cable-delay-ch1ch2-50mhz-200mVpp.pdf}
|
|
%\includegraphics[width=\textwidth]{fourier/04_signal_to_noise_fig04.png}
|
|
\end{column}
|
|
\end{columns}
|
|
|
|
\end{frame}
|
|
|
|
\begin{frame}{GNSS clock stability II}
|
|
\begin{figure}
|
|
\centering
|
|
\includegraphics[width=0.7\textwidth]{grand/setup/grand-gps-setup.pdf}
|
|
\caption{
|
|
GNSS stability experiment
|
|
}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
\subsection{In the field}
|
|
\begin{frame}{}
|
|
\centering
|
|
\includegraphics[width=0.5\textwidth]{images/IMG_20220712_164912_grand_DU.jpg}%
|
|
\includegraphics[width=0.5\textwidth]{images/IMG_20220712_164904_checking_gnss.jpg}%
|
|
\vfill
|
|
\includegraphics[width=0.5\textwidth]{images/IMG_20220819_152900.jpg}% Outside box Inside Cabling
|
|
\includegraphics[width=0.5\textwidth]{images/flir_20220812T114019.jpg}% Heat Inside
|
|
\end{frame}
|
|
|
|
\begin{frame}{GNSS clock stability III}
|
|
\begin{columns}
|
|
\begin{column}{0.5\textwidth}
|
|
\includegraphics[width=\textwidth]{images/IMG_20220819_154801.jpg}% Closed box outside
|
|
\end{column}
|
|
\begin{column}{0.5\textwidth}
|
|
\includegraphics[width=\textwidth]{images/IMG_20220815_161244.jpg}% Open box outside
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\section{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{
|
|
\cite{WRPTP}
|
|
Precision Time Protocol messages.
|
|
}
|
|
\end{figure}
|
|
\end{frame}
|
|
\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}}
|
|
\imagecredit{\autocite{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}}
|
|
\imagecredit{\autocite{WRPTP}}
|
|
\end{figure}
|
|
\end{column}
|
|
\end{columns}
|
|
\end{frame}
|
|
|
|
\begin{frame}{White Rabbit Clock Reference}
|
|
\begin{figure}
|
|
\centering
|
|
\hspace*{-5em}
|
|
\includegraphics[width=1.35\textwidth]{clocks/wr-clocks.pdf}
|
|
\end{figure}
|
|
\end{frame}%>>>
|
|
% >>> End of Backup Slides
|
|
%%%%%%%%%%%%%%
|
|
% Bibliography <<<
|
|
%%%%%%%%%%%%%%
|
|
\section*{References}
|
|
\begin{frame}[allowframebreaks]
|
|
\frametitle{References}
|
|
\printbibliography
|
|
\end{frame}
|
|
% >>> Bibliography
|
|
\end{document}
|
|
|