WuotD: Still Missing Introduction

This commit is contained in:
Eric Teunis de Boone 2023-07-04 16:38:20 +02:00
parent 10ecbd7d75
commit ef53add86d

View file

@ -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}
% >>>>