97 lines
2.2 KiB
TeX
97 lines
2.2 KiB
TeX
\documentclass[../thesis.tex]{subfiles}
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\graphicspath{
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{.}
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{../../figures/}
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{../../../figures/}
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}
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\begin{document}
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\chapter{Introduction}
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\label{sec:introduction}
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\section{Cosmic Rays}
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\label{sec:crs}
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\subsection{Airshowers}
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\label{sec:airshowers}
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\subsection{Detectors}
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\label{sec:detectors}
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Standalone devices,
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\gls*{PA},
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\gls*{GRAND}
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\section{Time Synchronisation}
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\label{sec:timesynchro}
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The main method of synchronising multiple stations is by employing a \gls{GNSS}.
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This system should deliver timing with an accuracy in the order of $10\ns$ \cite{} (see Section~\ref{sec:grand:gnss}).
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\\
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Need reference system with better accuracy to constrain current mechanism (Figure~\ref{fig:reference-clock}).
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\begin{figure}
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\centering
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\includegraphics[width=0.5\textwidth]{clocks/reference-clock.pdf}
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\caption{
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Using a reference clock to compare two other clocks.
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}
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\label{fig:reference-clock}
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\todo{
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redo figure with less margins,
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remove spines,
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rotate labels
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}
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\end{figure}
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\section{Interferometry}
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\label{sec:interferometry}
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Rough outline of Interferometry?
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\\
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Requires $\sigma_t \lesssim 1\ns$ \cite{Schoorlemmer:2020low}
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\begin{figure}
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\includegraphics[width=0.5\textwidth]{radio_interferometry/Schematic_RIT_extracted.png}
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\caption{From H. Schoorlemmer}
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\end{figure}
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\begin{equation}
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\label{eq:propagation_delay}
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\Delta_i = \frac{ \left|{ \vec{x} - \vec{a_i} }\right| }{c} n_{eff}
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\end{equation}
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\begin{equation}
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\label{eq:interferometric_sum}
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S(\vec{x}, t) = \sum_i S_i(t + \Delta_i(\vec{x}))
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\end{equation}
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\begin{equation}
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\label{eq:coherence_condition}
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\Delta t \leq \frac{1}{f}
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\end{equation}
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\begin{figure}
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\begin{subfigure}[t]{0.3\textwidth}
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\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_bad.png}
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\label{fig:trace_overlap:bad}
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\end{subfigure}
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\hfill
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\begin{subfigure}[t]{0.3\textwidth}
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\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_medium.png}
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\label{fig:trace_overlap:medium}
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\end{subfigure}
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\hfill
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\begin{subfigure}[t]{0.3\textwidth}
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\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_best.png}
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\label{fig:trace_overlap:best}
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\end{subfigure}
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\caption{Trace overlap due to wrong positions}
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\label{fig:trace_overlap}
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\end{figure}
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\end{document}
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