From 2b3b407481b5440fd236351d9bd519752c15024e Mon Sep 17 00:00:00 2001 From: Eric Teunis de Boone Date: Tue, 11 Apr 2023 10:23:42 +0200 Subject: [PATCH] Old CRHEP presentation from 2022-12-15 --- .../2022-12-15_CRHEP.tex | 154 ++++++++++++++++++ .../2022-12-15_group_meeting/README.md | 3 + .../figs/ba_measure_beacon_phase.py.A63.pdf | Bin 0 -> 137868 bytes .../ba_measure_beacon_phase.py.A63.zoomed.pdf | Bin 0 -> 20169 bytes .../bb_measure_true_phase.py.F0.05153.pdf | Bin 0 -> 19301 bytes ...aseline_phase_deltas.py.0ns.1.F0.05153.pdf | Bin 0 -> 27311 bytes ...ne_phase_deltas.py.5ns_gauss1.F0.05153.pdf | Bin 0 -> 31122 bytes ..._period_from_shower.py.maxima.run0.0ns.pdf | Bin 0 -> 13203 bytes ...hower.py.loc12.0-2894.2-7780.1.i5.run2.pdf | Bin 0 -> 146121 bytes ....0-2894.2-7780.1.i5.run2.zoomed.beacon.pdf | Bin 0 -> 18857 bytes ...12.0-2894.2-7780.1.i5.run2.zoomed.peak.pdf | Bin 0 -> 15768 bytes .../figs/orig_antenna_Efields.pdf | Bin 0 -> 24816 bytes .../figs/orig_antenna_geometry.pdf 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presentations/2022-12-15_group_meeting/figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.pdf create mode 100644 presentations/2022-12-15_group_meeting/figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.beacon.pdf create mode 100644 presentations/2022-12-15_group_meeting/figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.peak.pdf create mode 100644 presentations/2022-12-15_group_meeting/figs/orig_antenna_Efields.pdf create mode 100644 presentations/2022-12-15_group_meeting/figs/orig_antenna_geometry.pdf create mode 100644 presentations/2022-12-15_group_meeting/figs/reconstruct_15ns.pdf create mode 100644 presentations/2022-12-15_group_meeting/figs/reconstruct_5ns.pdf diff --git a/presentations/2022-12-15_group_meeting/2022-12-15_CRHEP.tex b/presentations/2022-12-15_group_meeting/2022-12-15_CRHEP.tex new file mode 100644 index 0000000..3b0af7f --- /dev/null +++ b/presentations/2022-12-15_group_meeting/2022-12-15_CRHEP.tex @@ -0,0 +1,154 @@ +\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}{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} diff --git 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