Thesis: Radio Interferometry: separate chapter

documents/thesis/chapters/introduction.tex

@@ -10,7 +10,7 @@
 \begin{document}
 \chapter{Introduction}
 \label{sec:introduction}
-
+%<<<
 % Intro Cosmic Ray
 In the beginning of the $\mathrm{20^{th}}$~century, various types of radiation were discovered.
 With the balloonflight of Victor Hess \Todo{ref} in \Todo{year}, one type was determined to come from beyond the atmosphere and named ``Cosmic Rays''.
@@ -29,16 +29,16 @@ However, advanced analyses require an even higher accuracy.
 \\
 In this thesis, methods (and their limits) to obtain this accuracy for radio arrays are investigated.
 
-
+% >>>
 \section{Cosmic Particles}%<<<<<<
 %<<<
 \label{sec:crs}
-Particles from outer space,
-Particle type,
-Energy,
-magnetic fields -- origin,
-
-\hrule
+%Particles from outer space,
+%Particle type,
+%Energy,
+%magnetic fields -- origin,
+%
+%\hrule
 
 % Cosmic Particles = CR + Photon + Neutrino
 There is a variety of extra terrestrial particles with which the Earth is bombarded.\Todo{rephrase}
@@ -69,7 +69,7 @@ Note that cosmic rays are deemed\Todo{rephrase} to be charged nuclei.
 
 
 % Energy
-Cosmic rays span a large range of energy as illustrated in Figure~\ref{fig:cr_flux}.
+Cosmic rays span a large range of energy and flux as illustrated in Figure~\ref{fig:cr_flux}.
 The acceleration of cosmic rays is thought to occur in highly energetic regions\Todo{expand}
 \\
 
@@ -88,11 +88,11 @@ Likewise, with an rapidly increasing flux for lower energies, one component can
 %>>>
 \subsection{Air Showers}%<<<
 \label{sec:airshowers}
-Particle cascades,
-Xmax?,
-Radio emission,
-
-\hrule
+%Particle cascades,
+%Xmax?,
+%Radio emission,
+%
+%\hrule
 When a particle with an energy above $1\;\TeV$ comes into contact with the atmosphere, secondary particles are generated, forming an air shower.
 This air shower consists of a cascade of interactions producing more particles that subsequently undergo further interactions.
 Thus, the number of particles rapidly increases further down the air shower.
@@ -200,103 +200,9 @@ This will be used later on and gives an insight into the timing accuracy require
 \\
 Chapter~\ref{sec:waveform} reviews typical techniques to analyse waveforms to obtain timing information.
 \\
-Chapter~\ref{sec:disciplining} introduces the concept of a beacon transmitter to synchronise an array of radio antennas using techniques from the preceding chapter to constrain the achievable timing accuracy.
+Chapter~\ref{sec:disciplining} introduces the concept of a beacon transmitter to synchronise an array of radio antennas and constrains the achievable timing accuracy using the techniques described in the preceding chapter.
 \\
 Chapter~\ref{sec:single_sine_sync} shows\Todo{word} how a sine wave beacon can synchronise an array while using the radio interferometric approach to resolve\Todo{word} an airshower.
 \\
-Finally, Chapter~\ref{sec:gnss_accuracy} investigates the limitations of the current hardware in \gls{GRAND} and its ability to record and reconstruct a beacon signal.
-
-
-
-
-
-
-\cleardoublepage
-\chapter{Air Shower Radio Interferometry}
-\label{sec:interferometry}
-The radio signals emitted by the air shower (see Section~\ref{sec:airshowers}) can be recorded by radio antennas.
-An array of radio antennas can be used as an interferometer.
-Therefore, air showers can be analysed using radio interferometry.
-\\
-%
-Unlike, astronomical interferometry, the source of the signal is closeby.
-
-
-
-\begin{figure}
-	\centering
-	\includegraphics[width=0.5\textwidth]{radio_interferometry/rit_schematic_true.pdf}%
-%	\includegraphics[width=0.5\textwidth]{radio_interferometry/Schematic_RIT_extracted.png}
-%	\caption{From H. Schoorlemmer}
-\end{figure}
-
-\begin{equation}\label{eq:propagation_delay}%<<<
-	\Delta_i(\vec{x}) = \frac{ \left|{ \vec{x} - \vec{a_i} }\right| }{c} n_{eff}
-\end{equation}%>>>
-
-
-\begin{equation}\label{eq:interferometric_sum}%<<<
-	S(\vec{x}, t) = \sum_i S_i(t + \Delta_i(\vec{x}))
-\end{equation}%>>>
-
-
-\begin{figure}
-	\centering
-	\begin{subfigure}[t]{0.3\textwidth}
-		\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_bad.png}
-		\label{fig:trace_overlap:bad}
-	\end{subfigure}
-	\hfill
-	\begin{subfigure}[t]{0.3\textwidth}
-		\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_medium.png}
-		\label{fig:trace_overlap:medium}
-	\end{subfigure}
-	\hfill
-	\begin{subfigure}[t]{0.3\textwidth}
-		\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_best.png}
-		\label{fig:trace_overlap:best}
-	\end{subfigure}
-	\caption{
-		Trace overlap due to wrong positions
-	}
-	\label{fig:trace_overlap}
-\end{figure}
-
-
-
-\begin{figure}
-	\centering
-	\includegraphics[width=0.7\textwidth]{2006.10348/fig03_b.png}%
-	\caption{
-		From \protect \cite{Schoorlemmer:2020low}.
-		$\Xmax$ resolution as a function of detector-to-detector synchronisation.
-	}
-	\label{fig:xmax_synchronise}
-\end{figure}
-
-\section{Time Synchronisation}
-\label{sec:timesynchro}
-The main method of synchronising multiple stations is by employing a \gls{GNSS}.
-This system should deliver timing with an accuracy in the order of $10\ns$ \cite{} (see Section~\ref{sec:grand:gnss}).
-\\
-
-Need reference system with better accuracy to constrain current mechanism (Figure~\ref{fig:reference-clock}).
-
-%\begin{figure}
-%	\centering
-%	\includegraphics[width=0.5\textwidth]{clocks/reference-clock.pdf}
-%	\caption{
-%		Using a reference clock to compare two other clocks.
-%		\protect \todo{
-%			redo figure with less margins,
-%			remove spines,
-%			rotate labels
-%		}
-%	}
-%	\label{fig:reference-clock}
-%\end{figure}
-
-
-
-
+Finally, Chapter~\ref{sec:gnss_accuracy} investigates the limitations of the current hardware of \gls{GRAND} and its ability to record and reconstruct a beacon signal.
 \end{document}

documents/thesis/chapters/radio_interferometry.tex

@@ -0,0 +1,94 @@
+% vim: fdm=marker fmr=<<<,>>>
+\documentclass[../thesis.tex]{subfiles}
+
+\graphicspath{
+	{.}
+	{../../figures/}
+	{../../../figures/}
+}
+
+\begin{document}
+\chapter{Air Shower Radio Interferometry}
+\label{sec:interferometry}
+The radio signals emitted by the air shower (see Section~\ref{sec:airshowers}) can be recorded by radio antennas.
+An array of radio antennas can be used as an interferometer.
+Therefore, air showers can be analysed using radio interferometry.
+\\
+%
+Unlike, astronomical interferometry, the source of the signal is closeby.
+
+
+
+\begin{figure}
+	\centering
+	\includegraphics[width=0.5\textwidth]{radio_interferometry/rit_schematic_true.pdf}%
+%	\includegraphics[width=0.5\textwidth]{radio_interferometry/Schematic_RIT_extracted.png}
+%	\caption{From H. Schoorlemmer}
+\end{figure}
+
+\begin{equation}\label{eq:propagation_delay}%<<<
+	\Delta_i(\vec{x}) = \frac{ \left|{ \vec{x} - \vec{a_i} }\right| }{c} n_{eff}
+\end{equation}%>>>
+
+
+\begin{equation}\label{eq:interferometric_sum}%<<<
+	S(\vec{x}, t) = \sum_i S_i(t + \Delta_i(\vec{x}))
+\end{equation}%>>>
+
+
+\begin{figure}
+	\centering
+	\begin{subfigure}[t]{0.3\textwidth}
+		\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_bad.png}
+		\label{fig:trace_overlap:bad}
+	\end{subfigure}
+	\hfill
+	\begin{subfigure}[t]{0.3\textwidth}
+		\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_medium.png}
+		\label{fig:trace_overlap:medium}
+	\end{subfigure}
+	\hfill
+	\begin{subfigure}[t]{0.3\textwidth}
+		\includegraphics[width=\textwidth]{radio_interferometry/trace_overlap_best.png}
+		\label{fig:trace_overlap:best}
+	\end{subfigure}
+	\caption{
+		Trace overlap due to wrong positions
+	}
+	\label{fig:trace_overlap}
+\end{figure}
+
+
+
+\begin{figure}
+	\centering
+	\includegraphics[width=0.7\textwidth]{2006.10348/fig03_b.png}%
+	\caption{
+		From \protect \cite{Schoorlemmer:2020low}.
+		$\Xmax$ resolution as a function of detector-to-detector synchronisation.
+	}
+	\label{fig:xmax_synchronise}
+\end{figure}
+
+\section{Time Synchronisation}
+\label{sec:timesynchro}
+The main method of synchronising multiple stations is by employing a \gls{GNSS}.
+This system should deliver timing with an accuracy in the order of $10\ns$ \cite{} (see Section~\ref{sec:grand:gnss}).
+\\
+
+Need reference system with better accuracy to constrain current mechanism (Figure~\ref{fig:reference-clock}).
+
+%\begin{figure}
+%	\centering
+%	\includegraphics[width=0.5\textwidth]{clocks/reference-clock.pdf}
+%	\caption{
+%		Using a reference clock to compare two other clocks.
+%		\protect \todo{
+%			redo figure with less margins,
+%			remove spines,
+%			rotate labels
+%		}
+%	}
+%	\label{fig:reference-clock}
+%\end{figure}
+\end{document}

documents/thesis/thesis.tex

@@ -53,6 +53,9 @@
 %%	Introduction
 \subfile{chapters/introduction.tex}
 
+%%  Radio Interferometry
+\subfile{chapters/radio_interferometry.tex}
+
 %%  Electric field from airshower to waveform analysis
 \subfile{chapters/radio_measurement.tex}