From ef53add86dba47e66840f38e114e3685bbac0780 Mon Sep 17 00:00:00 2001 From: Eric Teunis de Boone Date: Tue, 4 Jul 2023 16:38:20 +0200 Subject: [PATCH] WuotD: Still Missing Introduction --- .../2023-07-06_final_masters/2023-Masters.tex | 292 +++++++++++++++++- 1 file changed, 279 insertions(+), 13 deletions(-) diff --git a/presentations/2023-07-06_final_masters/2023-Masters.tex b/presentations/2023-07-06_final_masters/2023-Masters.tex index 26e8f3f..12c82de 100644 --- a/presentations/2023-07-06_final_masters/2023-Masters.tex +++ b/presentations/2023-07-06_final_masters/2023-Masters.tex @@ -15,6 +15,7 @@ \usepackage{graphicx} \usepackage{tikz} \usepackage{xurl} +\usepackage{physics} \graphicspath{{.}{./figures/}{../../figures/}} \usepackage{todo} @@ -26,6 +27,7 @@ {\usebibmacro{citeindex}% \usebibmacro{cite} \newunit + \clearfield{eprintclass} \usebibmacro{eprint}} {\multicitedelim} {\usebibmacro{postnote}} @@ -95,25 +97,50 @@ \def\thesissubtitle{} \def\thesisauthorfirst{E.T.} \def\thesisauthorsecond{de Boone} -\def\thesisauthoremail{} +\def\thesisauthoremailraw{ericteunis@deboone.nl} +\def\thesisauthoremail{\href{mailto:\thesisauthoremailraw}{\thesisauthoremailraw}} \def\thesissupervisorfirst{dr. Harm} \def\thesissupervisorsecond{Schoorlemmer} -\def\thesissupervisoremail{} +\def\thesissupervisoremailraw{} +\def\thesissupervisoremail{\href{mailto:\thesissupervisoremailraw}{\thesissupervisoremailraw}} -\title[]{Enhancing Timing Accuracy in Air Shower Radio Detectors} +\title[\thesistitle]{\thesistitle} \date{July, 2023} \author[\thesisauthorfirst\space\thesisauthorsecond]{% - \thesisauthorfirst\space\thesisauthorsecond\thanks{\thesisauthoremail}\\ - \vspace*{2em} - {Supervisor: \thesissupervisorfirst\space\thesissupervisorsecond\thanks{\thesissupervisoremail} } + \texorpdfstring{\thesisauthorfirst\space\thesisauthorsecond\thanks{e-mail: \thesisauthoremail}\\ + \vspace*{0.5em} + {Supervisor: \thesissupervisorfirst\space\thesissupervisorsecond } + }{\thesisauthorfirst\space\thesisauthorsecond<\thesisauthoremailraw>} } % >>> Meta data +\newcommand{\tclock}{\ensuremath{t_\mathrm{clock}}} +\newcommand{\ns}{\ensuremath{\mathrm{ns}}} + +\newcommand{\pTrue}{\phi} +\newcommand{\PTrue}{\Phi} +\newcommand{\pMeas}{\varphi} + +\newcommand{\pTrueEmit}{\pTrue_0} +\newcommand{\pTrueArriv}{\pTrueArriv'} +\newcommand{\pMeasArriv}{\pMeas_0} +\newcommand{\pProp}{\pTrue_d} +\newcommand{\pClock}{\pTrue_c} + \begin{document} { % Titlepage <<< +\setbeamertemplate{background} +{% + \parbox[c][\paperheight][c]{\paperwidth}{% + \centering% + \vfill% + \includegraphics[width=\textwidth]{beacon/array_setup_gps_transmitter_cows.png}% + \vspace*{2em} + }% +} \setbeamertemplate{footline}{} % no page number here \frame{ \titlepage } } % >>> @@ -121,18 +148,72 @@ %%%%%%%%%%%%%%% % Start of slides <<< %%%%%%%%%%%%%%% -\section{Cosmic Particles}% <<<< +\section{Cosmic Particle Detection}% <<<< % Sources, Types, Propagation, Observables % Flux -> Large instrumentation area % Detection methods of Auger % - FD, SD % AERA / AugerPrime RD or GRAND -\begin{frame} +\begin{frame}{Ultra High Energy particles} \end{frame} +\begin{frame}{Air Showers} +% Observables +\end{frame} + +\begin{frame}{UHE particle flux} +\end{frame} + +\begin{frame}{Detection methods} +\end{frame} + +\begin{frame}{Radio Emission} +\end{frame} + + % >>>> \section{Radio Interferometry}% <<<< -\begin{frame} +\begin{frame}{Radio Interferometry: Concept} + Interferometry: Amplitude + Timing information of the $\vec{E}$-field\\ + \vspace*{ 0.8em } + \begin{columns} + \begin{column}{0.4\textwidth} + \begin{figure} + \includegraphics<1>[width=\textwidth]{radio_interferometry/rit_schematic_base.pdf}% + \includegraphics<2>[width=\textwidth]{radio_interferometry/rit_schematic_far.pdf}% + \includegraphics<3>[width=\textwidth]{radio_interferometry/rit_schematic_close.pdf}% + \includegraphics<4>[width=\textwidth]{radio_interferometry/rit_schematic_true.pdf}% + \end{figure} + \end{column} + \begin{column}{0.6\textwidth} + \vspace*{\fill} + \begin{itemize} + \item<1-> Measure signal $S_i(t)$ at antenna $\vec{a_i}$ + + \item<2-> Calculate light travel time \\[5pt] + \quad $\Delta_i(\vec{x}) = \frac{ \left| \vec{x} - \vec{a_i} \right| }{c} n_{eff}$ + + \item<2-> Sum waveforms accounting \\ + for time delay \\[5pt] + \quad $S(\vec{x}, t) = \sum S_i( t + \Delta_i(\vec{x}) )$ + \end{itemize} + \vspace*{\fill} + \begin{figure}% Spatially + \includegraphics<1>[width=0.8\textwidth]{radio_interferometry/single_trace.png}% + \includegraphics<2>[width=0.8\textwidth]{radio_interferometry/trace_overlap_bad.png}% + \includegraphics<3>[width=0.8\textwidth]{radio_interferometry/trace_overlap_medium.png}% + \includegraphics<4>[width=0.8\textwidth]{radio_interferometry/trace_overlap_best.png}% + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Radio Interferometry: Image} + \begin{figure} + \centering + \includegraphics[width=0.7\textwidth]{2006.10348/fig01.png}% + \imagecite{Schoorlemmer:2020low} + \end{figure} \end{frame} % >>>> @@ -140,7 +221,32 @@ % GNSS % reference system: White Rabbit, AERA beacon, (ADS-B?) % GRAND setup and measurements -\begin{frame} +\begin{frame}{Timing in Radio Detectors: GNSS} +% Geometry + Default Timing mechanism: Global Navigation Satellite Systems\\ + \begin{columns} + \begin{column}{0.5\textwidth} + \vfill + \begin{figure} + \begin{tikzpicture}[scale=1] + \clip (2.5 , 0) rectangle ( 6, 2.5); + \node[anchor=south west, inner sep=0] (image) at (0,0) {\includegraphics[width=\textwidth]{beacon/array_setup_gps_transmitter_cows.png}}; + %\draw[help lines,xstep=1,ystep=1] (0,0) grid (11,5); + \end{tikzpicture} + \imagecredit{H. Schoorlemmer} + \end{figure} + \end{column} + \hfill + \begin{column}{0.45\textwidth} + In AERA, $ \Delta \tclock \gtrsim 10\ns$ + \\ + \begin{figure} + \centering + \includegraphics[width=\textwidth]{gnss/auger/1512.02216.figure3.gnss-time-differences.png} + \imagecite{PierreAuger:2015aqe} + \end{figure} + \end{column} + \end{columns} \end{frame} % >>>> @@ -148,13 +254,173 @@ % Geometry % Pulse method + SNR % Sine method + SNR -\begin{frame} +\begin{frame}{Beacon Synchronisation} +% Geometry + \vspace*{0em} + { + { \color{red} GNSS } + + + Extra Timing mechanism: {\color{blue} Beacon}%, {\color{green} ADS-B} + } + \\ + \vspace*{2em} + \begin{figure} + \hspace*{-2em} + \begin{tikzpicture} + [circle/.style={circle, ultra thick, radius=8mm}] + \node[anchor=south west, inner sep=0] (image) at (0,0) {\includegraphics[width=\textwidth]{beacon/array_setup_gps_transmitter_cows.png}}; + \begin{scope}[x={(image.south east)}, y={(image.north west)}] + %\draw[help lines,xstep=.1,ystep=.1] (0,0) grid (1,1); + %\foreach \x in {0,1,...,9} { \node [anchor=north] at (\x/10,0) {0.\x}; } + %\foreach \y in {0,1,...,9} { \node [anchor=east] at (0,\y/10) {0.\y}; } + \node (transmitter) at (0.23, 0.32) {}; + \node (gnss) at (0.85, 0.87) {}; + %\node (aeroplane) at (0.3, 0.67) {\includegraphics[width=1.5cm]{templates/aeroplane.png}}; + %\draw[green, ultra thick, visible on=<{1-}>] (aeroplane.center) circle[radius=8mm]; + \draw[red, ultra thick, visible on=<{1-}>] (gnss.center) circle[radius=8mm]; + \draw[blue, ultra thick, visible on=<{1-}>] (transmitter.center) circle[radius=8mm]; + \end{scope} + \end{tikzpicture} + \imagecredit{H. Schoorlemmer} + \end{figure} +\end{frame} + +\subsection{Pulse Beacon} +\begin{frame}{Pulse Beacon} + \begin{figure} + \includegraphics[width=\textwidth]{pulse/antenna_signals_tdt0.2_zoom.pdf} + \end{figure} + \vfill +\end{frame} +\begin{frame}{Pulse Beacon} + Correlation: similarity between two signals.\\ + \begin{figure} + \includegraphics[width=\textwidth]{pulse/correlation_tdt0.2_zoom.pdf} + \end{figure} +\end{frame} +\begin{frame}{Pulse Beacon Timing} + \begin{figure} + \includegraphics[width=0.8\textwidth]{pulse/time_res_vs_snr_multiple_dt_small.pdf} + \end{figure} +\end{frame} + +\subsection{Sine Beacon} +\begin{frame}{(Multi)Sine Beacon} + \begin{equation*} + \Delta \tclock = \left[ \frac{\varphi}{2\pi} \; + \; k \right] T + \end{equation*} + \begin{figure} + \includegraphics[width=.45\textwidth]{methods/fourier/waveform.pdf} + \hfill + \includegraphics[width=.45\textwidth]{methods/fourier/noisy_spectrum.pdf} + \end{figure} +\end{frame} +\begin{frame}{(Multi)Sine Beacon Timing} + \begin{figure} + \includegraphics[width=0.8\textwidth]{beacon/time_res_vs_snr.pdf} + \end{figure} + \begin{columns} + \begin{column}{0.3\textwidth} + \end{column} + \begin{column}{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*} + + \tiny{Random Phasor Sum: ``Statistical Optics'', J. Goodman} + \end{column} + \end{columns} + \end{frame} % >>>> \section{Single Sine Synchronisation}% <<<< % Sine method + Radio Interferometry -\begin{frame} +\begin{frame}{Single Sine Synchronisation} + \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} +\end{frame} + +\begin{frame}{Single Sine Synchronisation Simulation} + Air Shower detected on a grid of 100x100 antennas. + + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item Add beacon to antenna + \item Randomise clocks + \item Measure phase + \item Repair clocks for small offsets + \item Iteratively find best $k_{ij}$ + \end{itemize} + \end{column} + \hfill + \begin{column}{0.4\textwidth} + \begin{figure} + \includegraphics<1>[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.pdf}% + \includegraphics<2>[width=\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.masked.pdf}% + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Simulation: Period $k_i$} + \small{ + Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$ + \\ + Iterative process: \\ + \; Scan positions finding the best $\{k_i\}$ set, then zoom in on strongest. + } + + \only<1-4>{\begin{figure} + \includegraphics<1>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i5.loc8.0-2795.4-7816.0.pdf} + \includegraphics<2>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i99.loc8.0-2795.4-7816.0.pdf} + \includegraphics<3>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf} + \includegraphics<4>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf} + \end{figure}} + \only<5>{\begin{figure} + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf} + \vspace{0.5cm} + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run1.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run1.power.pdf} + \end{figure}} +\end{frame} + + +\begin{frame}{Time resolving short period beacon: phase vs full} + \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_all.scale4d.pdf}% + \end{column} + \end{columns} \end{frame} % >>>> @@ -163,7 +429,7 @@ % Outlook: Parasitic/Active vs Pulse/Sine table % Parasitic Single Sine: 67MHz Auger % Implementation for GRAND? -\begin{frame} +\begin{frame}{Conclusion and Outlook} \end{frame} % >>>>