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b/figures/ZH_simulation/findks/ca_period_from_shower.py.run0.i99.loc8.0-2795.4-7816.0.zoomed.peak.pdf differ diff --git a/figures/ZH_simulation/tx_array_geometry.png b/figures/ZH_simulation/tx_array_geometry.png new file mode 100644 index 0000000..091d336 Binary files /dev/null and b/figures/ZH_simulation/tx_array_geometry.png differ diff --git a/presentations/2023-04-13_group_meeting/2023-04-13_CRHEP.tex b/presentations/2023-04-13_group_meeting/2023-04-13_CRHEP.tex index 7a52bd9..23fe1bc 100644 --- a/presentations/2023-04-13_group_meeting/2023-04-13_CRHEP.tex +++ b/presentations/2023-04-13_group_meeting/2023-04-13_CRHEP.tex @@ -74,7 +74,7 @@ Local antenna time $t'_i$ due to time delay $t_{\mathrm{d}i}$ and clock skew $\sigma_i$ \\ \begin{figure} - \includegraphics[width=0.4\textwidth]{beacon/antenna_setup_two.pdf} + \includegraphics[width=0.6\textwidth]{beacon/antenna_setup_two.pdf} \end{figure} \vskip -2em \begin{equation*} @@ -106,40 +106,65 @@ \includegraphics<-2>[width=1\textwidth]{beacon/08_beacon_sync_coherent_sum.pdf} \end{figure} \only<3>{\begin{equation*}\Delta t'_{ij} = \Delta A_{ij} + \cancel{\Delta t'_\varphi} + \cancel{k_{ij}T} \end{equation*}} + \only<3>\vfill \end{frame} \section{Simulations} -\begin{frame}{Simulation} - \begin{block}{} +\begin{frame}{Simulation: Sine} Apply previous steps to an airshower simulation (which provides the pulse): + \begin{block}{} \begin{itemize} \item Add (sine) beacon to each antenna \item Shift clocks \item Measure phase - \item Repair clocks for small offset $\Delta A_{ij}$ + \item Repair clocks for small offset $\Delta t'_{ij}$ \item Iteratively find best $k_{ij}$ \end{itemize} \end{block} \end{frame} \begin{frame}{Simulation: Antenna Setup} - \begin{figure} - \includegraphics[width=0.5\textwidth]{path_leading_to_array_setup_with_inset_tx_array} - \end{figure} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{figure} + \includegraphics[width=\textwidth]{ZH_simulation/tx_array_geometry.png} + \end{figure} + \end{column} + \hfill + \begin{column}{0.45\textwidth} + \begin{figure} + \includegraphics[width=\textwidth]{ZH_simulation/array_geometry_beacon_amplitude.png} + \end{figure} + \end{column} + \end{columns} \end{frame} -\begin{frame}{Simulation: Local Phase} +\begin{frame}{Simulation: Measure Local Phase} \begin{block}{} @Antenna $i$: measure phase $\varphi_i$ using DTFT, get $\varphi(\sigma_i) = \varphi_i - \varphi(t_0) - \varphi(t_{\mathrm{d}i})$ \end{block} \begin{figure} - \includegraphics<1>[width=1\textwidth]{ba_measure_beacon_phase.py.A63.pdf} - \includegraphics<2>[width=1\textwidth]{ba_measure_beacon_phase.py.A63.zoomed.pdf} - \includegraphics<3>[width=1\textwidth]{bb_measure_true_phase.py.F0.05153.pdf} + \includegraphics<1>[width=0.8\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.pdf} + \includegraphics<2>[width=0.8\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.masked.pdf} \end{figure} \end{frame} -\begin{frame}{Sine: Signal to Noise} +\begin{frame}{Simulation: Phase measurement} + Beacon frequency: $51.53~\mathrm{MHz}$ + \begin{figure} + \includegraphics<1>[width=0.8\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e1.pdf} + \includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e1.pdf} + \hfill + \includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e3.pdf} + \\ + \vspace{0.5cm} + \includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e4.pdf} + \hfill + \includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e5.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Simulation: Signal to Noise} \begin{figure} \includegraphics[width=0.8\textwidth]{beacon/time_res_vs_snr.pdf} \end{figure} @@ -159,49 +184,93 @@ \right)}{2} \cos{\pTrue} \end{equation*} + + \tiny{Random Phasor Sum: ``Statistical Optics'', J. Goodman} \end{column} \end{columns} \end{frame} \begin{frame}{Simulation: Phase: Baseline} - Previously, matrix minimisation - \begin{block}{} + \begin{block}{Correction to previous talk: modifies global phase only} @Baseline $i,j$: $\Delta \varphi_{ij} = \varphi(\sigma_i) - \varphi(\sigma_j)$ \\ Minimise matrix: - $\left(\begin{matrix} + \tiny$\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]{bc_baseline_phase_deltas.py.0ns.1.F0.05153.pdf} - \includegraphics<2>[width=1\textwidth]{bc_baseline_phase_deltas.py.5ns_gauss1.F0.05153.pdf} + \includegraphics<1>[width=0.8\textwidth]{ZH_simulation/bc_baseline_phase_deltas.py.residuals.c5_b_N4096_noise1e3.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{frame}{Simulation: Period $k_i$} + \small{ + Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$ + \\ + Iterative process: \\ + \; Scan positions finding the best $\{k_i\}$ set, then zoom in on strongest. + } + \only<1-4>{\begin{figure} + \includegraphics<1>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i5.loc8.0-2795.4-7816.0.pdf} + \includegraphics<2>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i99.loc8.0-2795.4-7816.0.pdf} + \includegraphics<3>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf} + \includegraphics<4>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf} + \end{figure}} + \only<5>{\begin{figure} + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf} + \vspace{0.5cm} + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run1.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run1.power.pdf} + \end{figure}} +\end{frame} + +\begin{frame}{Simulation: Effects of Corrections} + Found both phase and period differences + \visible<2->{\begin{figure} + \includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_none.scale4d.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf} + \vspace{0.5cm} + \includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.no_offset.scale4d.pdf} + \end{figure}} +\end{frame} + +\begin{frame}{Simulation Conclusions} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item (Single) Sine beacon:\\ + $\sigma < 1\mathrm{ns}$ from $\mathrm{SNR} > 3$. + \vspace{1cm} + \item Pulsed beacon:\\ + (small) ongoing work\\ + while writing thesis. + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \begin{figure} + \includegraphics[width=1.1\textwidth]{beacon/time_res_vs_snr.pdf} + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Simulation: Effects of Corrections (fullsize)} \begin{figure} - \includegraphics<1>[width=0.8\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.pdf} - \includegraphics<2>[width=0.8\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.peak.pdf} - \includegraphics<3>[width=0.8\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.beacon.pdf} - \includegraphics<4>[width=0.8\textwidth]{figs/bc_period_from_shower.py.maxima.run0.0ns.pdf} + \includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_none.scale4d.pdf} + \includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf} + \includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf} + \includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.no_offset.scale4d.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}