Waiting for reruns of vary-fixes script

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{columns}
+		\begin{column}{0.5\textwidth}
 			\begin{figure}
-		\includegraphics[width=0.5\textwidth]{path_leading_to_array_setup_with_inset_tx_array}
+				\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}{}
+\begin{frame}{Simulation: Period $k_i$}
+	\small{
 	Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$
-	\end{block}
+	\\
+	Iterative process: \\
+	\; Scan positions finding the best $\{k_i\}$ set, then zoom in on strongest.
+	}
 
-	\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}
-	\end{figure}
+	\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}{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}
+\begin{frame}{Simulation: Effects of Corrections (fullsize)}
+	\begin{figure}
+		\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}
 \end{document}