Old CRHEP presentation from 2022-12-15

presentations/2022-12-15_group_meeting/2022-12-15_CRHEP.tex

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+\documentclass[showdate=false]{beamer}
+
+\usepackage[british]{babel}
+\usepackage{amsmath}
+\usepackage{hyperref}
+\usepackage[backend=bibtex,style=trad-plain]{biblatex}
+\usepackage{graphicx}
+\graphicspath{{.}{../../figures/}}
+\usepackage{todo}
+
+\addbibresource{../../../bibliotheca/bibliography.bib}
+
+% Disable Captions
+\setbeamertemplate{caption}{\raggedright\small\insertcaption\par}
+
+% Show Section overview at beginning of section
+%\AtBeginSection[]
+%{
+%	\begin{frame}<beamer>{Table of Contents}
+%		\tableofcontents[currentsection, currentsubsection, sectionstyle=show/shaded, subsectionstyle=hide]
+%	\end{frame}
+%}
+
+% no to navigation, yes to frame numbering
+\beamertemplatenavigationsymbolsempty
+\setbeamerfont{page number in head/foot}{size=\normalsize}
+\setbeamertemplate{footline}[frame number]
+
+\title[Beacon Timing]{Enhancing Timing Accuracy using Beacons}
+\date{Dec 15, 2022}
+\author{E.T. de Boone}
+
+\begin{document}
+\frame{\titlepage}
+
+\begin{frame}{Enhancing time accuracy}
+	\begin{block}{}
+		Goal: $\sigma_{ij} < 1\mathrm{ns}$
+		(enabling Radio Interferometry)
+	\end{block}
+
+	\begin{block}{Strategy}
+	\begin{itemize}
+		\item Simulating beacons (both pulse and sine)
+		\item Characterising GNSS (GRAND)
+	\end{itemize}
+	\end{block}
+\end{frame}
+
+% Antenna Setup
+\section{Beacon}
+
+\begin{frame}{Antenna Setup}
+	\begin{block}{}
+		Local time $t_i$ due to time delay $t_{\mathrm{d}i}$ and clock skew $\sigma_i$\\
+	\end{block}
+	\begin{figure}
+		\includegraphics[width=0.8\textwidth]{beacon/antenna_setup_two.pdf}
+	\end{figure}
+	\vskip -2em
+	\begin{equation*}
+		\Delta t'_{12} = t'_1 - t'_2 = \Delta t_{\mathrm{d}12} + \sigma_{12} + (t_0 - t_0)
+	\end{equation*}
+\end{frame}
+
+\begin{frame}{Beacon: Sine: Two traces}
+	\begin{equation*}
+		t'_i = (\frac{\varphi'_i}{2\pi} + n_i)T = A_i + B_i
+	\end{equation*}
+	\begin{figure}
+		\includegraphics[width=1\textwidth]{beacon/08_beacon_sync_timing_outline.pdf}
+	\end{figure}
+	\begin{align*}
+		\Delta t_{ij} &= (A_j + B_j) - (A_i + B_i) + \Delta t_\varphi \\
+		 &= \Delta A_{ij} + \Delta t_\varphi + k_{ij}T\\
+	\end{align*}
+\end{frame}
+
+\begin{frame}{Beacon: Sine: Two traces: Discrete solutions}
+	\begin{figure}
+		\includegraphics<1>[width=1\textwidth]{beacon/08_beacon_sync_timing_outline.pdf}
+		%\includegraphics<2>[width=1\textwidth]{beacon/08_beacon_sync_synchronised_period_alignment.pdf}
+	\end{figure}
+		\begin{figure}
+			\includegraphics[width=1\textwidth]{beacon/08_beacon_sync_coherent_sum.pdf}
+		\end{figure}
+\end{frame}
+
+\begin{frame}{Simulation}
+	\begin{block}{}
+		Apply same steps to an airshower simulation:
+		\begin{itemize}
+			\item Add (sine) beacon to each antenna
+			\item Shift clocks
+			\item Measure phase
+			\item Repair clocks for small offset
+			\item Approximate
+		\end{itemize}
+	\end{block}
+\end{frame}
+\begin{frame}{}
+	\begin{figure}
+		\includegraphics<1>[width=1\textwidth]{figs/orig_antenna_geometry.pdf}
+	\end{figure}
+\end{frame}
+
+\begin{frame}{Simulation: Phase: Local }
+	\begin{block}{}
+		@Antenna $i$: measure phase $\varphi_i$ , get $\varphi(\sigma_i) = \varphi_i - \varphi(t_0) - \varphi(t_{\mathrm{d}i})$
+	\end{block}
+	\begin{figure}
+		\includegraphics<1>[width=1\textwidth]{figs/ba_measure_beacon_phase.py.A63.pdf}
+		\includegraphics<2>[width=1\textwidth]{figs/ba_measure_beacon_phase.py.A63.zoomed.pdf}
+		\includegraphics<3>[width=1\textwidth]{figs/bb_measure_true_phase.py.F0.05153.pdf}
+	\end{figure}
+\end{frame}
+
+\begin{frame}{Simulation: Phase: Baseline}
+	\begin{block}{}
+		@Baseline $i,j$: $\Delta \varphi_{ij} = \varphi(\sigma_i) - \varphi(\sigma_j)$ \\
+
+		Minimise matrix: 
+		$\left(\begin{matrix}
+			\Delta_{11} & \Delta_{12} & \Delta_{13} & \\
+			\Delta_{21} & \Delta_{22} & \Delta_{23} & \\
+			\Delta_{31} & \Delta_{32} & \Delta_{33} & \\
+		\end{matrix}\right)$
+	\end{block}
+	\begin{figure}
+		\includegraphics<1>[width=1\textwidth]{figs/bc_baseline_phase_deltas.py.0ns.1.F0.05153.pdf}
+		\includegraphics<2>[width=1\textwidth]{figs/bc_baseline_phase_deltas.py.5ns_gauss1.F0.05153.pdf}
+	\end{figure}
+\end{frame}
+
+\begin{frame}{Simulation: Period $k$}
+	\begin{block}{}
+		Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$
+	\end{block}
+
+	\begin{figure}
+	\includegraphics<1>[width=1\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.pdf}
+	\includegraphics<2>[width=1\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.peak.pdf}
+	\includegraphics<3>[width=1\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.beacon.pdf}
+	\includegraphics<4>[width=1\textwidth]{figs/bc_period_from_shower.py.maxima.run0.0ns.pdf}
+	\end{figure}
+\end{frame}
+
+\begin{frame}{Interferometry}
+	\begin{figure}
+		\includegraphics<1>[width=1\textwidth]{figs/reconstruct_5ns.pdf}
+		\includegraphics<2>[width=1\textwidth]{figs/reconstruct_15ns.pdf}
+	\end{figure}
+\end{frame}
+\end{document}

presentations/2022-12-15_group_meeting/README.md

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+# Short Presentation on current status (Beacon)
+
+Mostly to show what I've been doing uptil now.