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Waiting for reruns of vary-fixes script
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figures/ZH_simulation/array_geometry_beacon_amplitude.png
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figures/ZH_simulation/array_geometry_beacon_amplitude.png
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figures/ZH_simulation/array_geometry_shower_amplitude.png
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figures/ZH_simulation/ba_measure_beacon_phase.py.A74.masked.pdf
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figures/ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.pdf
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figures/ZH_simulation/tx_array_geometry.png
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@ -74,7 +74,7 @@
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Local antenna time $t'_i$ due to time delay $t_{\mathrm{d}i}$ and clock skew $\sigma_i$
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\\
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\begin{figure}
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\includegraphics[width=0.4\textwidth]{beacon/antenna_setup_two.pdf}
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\includegraphics[width=0.6\textwidth]{beacon/antenna_setup_two.pdf}
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\end{figure}
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\vskip -2em
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\begin{equation*}
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@ -106,40 +106,65 @@
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\includegraphics<-2>[width=1\textwidth]{beacon/08_beacon_sync_coherent_sum.pdf}
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\end{figure}
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\only<3>{\begin{equation*}\Delta t'_{ij} = \Delta A_{ij} + \cancel{\Delta t'_\varphi} + \cancel{k_{ij}T} \end{equation*}}
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\only<3>\vfill
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\end{frame}
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\section{Simulations}
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\begin{frame}{Simulation}
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\begin{block}{}
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\begin{frame}{Simulation: Sine}
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Apply previous steps to an airshower simulation (which provides the pulse):
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\begin{block}{}
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\begin{itemize}
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\item Add (sine) beacon to each antenna
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\item Shift clocks
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\item Measure phase
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\item Repair clocks for small offset $\Delta A_{ij}$
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\item Repair clocks for small offset $\Delta t'_{ij}$
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\item Iteratively find best $k_{ij}$
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\end{itemize}
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\end{block}
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\end{frame}
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\begin{frame}{Simulation: Antenna Setup}
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\begin{figure}
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\includegraphics[width=0.5\textwidth]{path_leading_to_array_setup_with_inset_tx_array}
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\end{figure}
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\begin{columns}
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\begin{column}{0.5\textwidth}
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\begin{figure}
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\includegraphics[width=\textwidth]{ZH_simulation/tx_array_geometry.png}
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\end{figure}
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\end{column}
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\hfill
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\begin{column}{0.45\textwidth}
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\begin{figure}
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\includegraphics[width=\textwidth]{ZH_simulation/array_geometry_beacon_amplitude.png}
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\end{figure}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}{Simulation: Local Phase}
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\begin{frame}{Simulation: Measure Local Phase}
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\begin{block}{}
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@Antenna $i$: measure phase $\varphi_i$ using DTFT, get $\varphi(\sigma_i) = \varphi_i - \varphi(t_0) - \varphi(t_{\mathrm{d}i})$
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\end{block}
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\begin{figure}
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\includegraphics<1>[width=1\textwidth]{ba_measure_beacon_phase.py.A63.pdf}
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\includegraphics<2>[width=1\textwidth]{ba_measure_beacon_phase.py.A63.zoomed.pdf}
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\includegraphics<3>[width=1\textwidth]{bb_measure_true_phase.py.F0.05153.pdf}
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\includegraphics<1>[width=0.8\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.pdf}
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\includegraphics<2>[width=0.8\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.masked.pdf}
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\end{figure}
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\end{frame}
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\begin{frame}{Sine: Signal to Noise}
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\begin{frame}{Simulation: Phase measurement}
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Beacon frequency: $51.53~\mathrm{MHz}$
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\begin{figure}
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\includegraphics<1>[width=0.8\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e1.pdf}
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\includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e1.pdf}
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\hfill
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\includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e3.pdf}
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\\
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\vspace{0.5cm}
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\includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e4.pdf}
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\hfill
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\includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e5.pdf}
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\end{figure}
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\end{frame}
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\begin{frame}{Simulation: Signal to Noise}
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\begin{figure}
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\includegraphics[width=0.8\textwidth]{beacon/time_res_vs_snr.pdf}
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\end{figure}
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@ -159,49 +184,93 @@
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\right)}{2}
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\cos{\pTrue}
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\end{equation*}
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\tiny{Random Phasor Sum: ``Statistical Optics'', J. Goodman}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}{Simulation: Phase: Baseline}
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Previously, matrix minimisation
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\begin{block}{}
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\begin{block}{Correction to previous talk: modifies global phase only}
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@Baseline $i,j$: $\Delta \varphi_{ij} = \varphi(\sigma_i) - \varphi(\sigma_j)$ \\
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Minimise matrix:
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$\left(\begin{matrix}
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\tiny$\left(\begin{matrix}
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\Delta_{11} & \Delta_{12} & \Delta_{13} & \\
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\Delta_{21} & \Delta_{22} & \Delta_{23} & \\
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\Delta_{31} & \Delta_{32} & \Delta_{33} & \\
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\end{matrix}\right)$
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\end{block}
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\begin{figure}
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\includegraphics<1>[width=1\textwidth]{bc_baseline_phase_deltas.py.0ns.1.F0.05153.pdf}
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\includegraphics<2>[width=1\textwidth]{bc_baseline_phase_deltas.py.5ns_gauss1.F0.05153.pdf}
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\includegraphics<1>[width=0.8\textwidth]{ZH_simulation/bc_baseline_phase_deltas.py.residuals.c5_b_N4096_noise1e3.pdf}
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\end{figure}
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\end{frame}
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\begin{frame}{Simulation: Period $k$}
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\begin{block}{}
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Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$
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\end{block}
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\begin{frame}{Simulation: Period $k_i$}
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\small{
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Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$
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\\
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Iterative process: \\
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\; Scan positions finding the best $\{k_i\}$ set, then zoom in on strongest.
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}
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\only<1-4>{\begin{figure}
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\includegraphics<1>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i5.loc8.0-2795.4-7816.0.pdf}
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\includegraphics<2>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i99.loc8.0-2795.4-7816.0.pdf}
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\includegraphics<3>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf}
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\includegraphics<4>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf}
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\end{figure}}
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\only<5>{\begin{figure}
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\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf}
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\hfill
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\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf}
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\vspace{0.5cm}
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\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run1.pdf}
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\hfill
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\includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run1.power.pdf}
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\end{figure}}
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\end{frame}
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\begin{frame}{Simulation: Effects of Corrections}
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Found both phase and period differences
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\visible<2->{\begin{figure}
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\includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_none.scale4d.pdf}
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\hfill
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\includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf}
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\vspace{0.5cm}
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\includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf}
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\hfill
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\includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.no_offset.scale4d.pdf}
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\end{figure}}
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\end{frame}
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\begin{frame}{Simulation Conclusions}
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\begin{columns}
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\begin{column}{0.5\textwidth}
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\begin{itemize}
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\item (Single) Sine beacon:\\
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$\sigma < 1\mathrm{ns}$ from $\mathrm{SNR} > 3$.
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\vspace{1cm}
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\item Pulsed beacon:\\
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(small) ongoing work\\
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while writing thesis.
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\end{itemize}
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\end{column}
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\begin{column}{0.5\textwidth}
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\begin{figure}
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\includegraphics[width=1.1\textwidth]{beacon/time_res_vs_snr.pdf}
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\end{figure}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}{Simulation: Effects of Corrections (fullsize)}
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\begin{figure}
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\includegraphics<1>[width=0.8\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.pdf}
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\includegraphics<2>[width=0.8\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.peak.pdf}
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\includegraphics<3>[width=0.8\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.beacon.pdf}
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\includegraphics<4>[width=0.8\textwidth]{figs/bc_period_from_shower.py.maxima.run0.0ns.pdf}
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\includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_none.scale4d.pdf}
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\includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf}
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\includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf}
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\includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.no_offset.scale4d.pdf}
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\end{figure}
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\end{frame}
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%
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%\begin{frame}{Interferometry}
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% \begin{figure}
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% \includegraphics<1>[width=1\textwidth]{figs/reconstruct_5ns.pdf}
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% \includegraphics<2>[width=1\textwidth]{figs/reconstruct_15ns.pdf}
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% \end{figure}
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%\end{frame}
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\end{document}
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