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Thesis: change sectioning Single Sine

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Eric Teunis de Boone 2023-11-06 13:55:29 +01:00
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documents/thesis/chapters/single_sine_interferometry.tex
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@ -116,9 +116,10 @@ Of course, a limit on the number of periods is required to prevent over-optimisa
In general, they can be constrained using estimates of the accuracy of other timing mechanisms (see below). In general, they can be constrained using estimates of the accuracy of other timing mechanisms (see below).
\\ \\
With a restricted set of allowed period shifts, we can alternate optimising the calibration signal's origin and optimising the set of period time delays of the array. With a restricted set of allowed period shifts, we can alternate optimising the calibration signal's origin and optimising the set of period time delays of the array.
\\
% >>> % >>>
\section{Lifting the Period Degeneracy with an Air Shower}% <<< %\section{Lifting the Period Degeneracy with an Air Shower}% <<<
% <<<< % <<<<
% Airshower gives t0 % Airshower gives t0
In the case of radio detection of air showers, the very signal of the air shower itself can be used as the calibration signal. In the case of radio detection of air showers, the very signal of the air shower itself can be used as the calibration signal.
@ -128,7 +129,7 @@ The best period defects must thus be recovered from a single event.
When doing the interferometric analysis for a sine beacon synchronised array, waveforms can only be delayed by an integer amount of periods, thereby giving discrete solutions to maximising the interferometric signal. When doing the interferometric analysis for a sine beacon synchronised array, waveforms can only be delayed by an integer amount of periods, thereby giving discrete solutions to maximising the interferometric signal.
\Todo{add size of shower at plane vs period defects in meters} \Todo{add size of shower at plane vs period defects in meters}
\subsection{Air Shower simulation} \section{Air Shower simulation}
% simulation of proton E15 on 10x10 antenna % simulation of proton E15 on 10x10 antenna
To test the idea of combining a single sine beacon with an air shower, we simulated a set of recordings of a single air shower that also contains a beacon signal. To test the idea of combining a single sine beacon with an air shower, we simulated a set of recordings of a single air shower that also contains a beacon signal.
\footnote{\url{https://gitlab.science.ru.nl/mthesis-edeboone/m-thesis-introduction/-/tree/main/airshower_beacon_simulation}} \footnote{\url{https://gitlab.science.ru.nl/mthesis-edeboone/m-thesis-introduction/-/tree/main/airshower_beacon_simulation}}
@ -230,7 +231,7 @@ Shifting the waveforms to remove these small clocks defects, we are left with re
\end{figure}%>>> \end{figure}%>>>
% >>>> % >>>>
\subsection{\textit{k}-finding} % <<< \section{\textit{k}-finding} % <<<
% unknown origin of air shower signal % unknown origin of air shower signal
Up until now, the shower axis and thus the origin of the air shower signal have not been resolved. Up until now, the shower axis and thus the origin of the air shower signal have not been resolved.
@ -331,7 +332,7 @@ Afterwards, a new grid zooms in on the power maximum and the process is repeated
\clearpage \clearpage
%\phantomsection %\phantomsection
\subsection{Strategy / Result} %<<< \section{Strategy / Result} %<<<
Figure~\ref{fig:grid_power_time_fixes} shows the effect of the various synchronisation stages on both the alignment of the air shower waveforms, and the interferometric power measurement near the true shower axis. Figure~\ref{fig:grid_power_time_fixes} shows the effect of the various synchronisation stages on both the alignment of the air shower waveforms, and the interferometric power measurement near the true shower axis.
Phase synchronising the antennas gives a small increase in observed power, while further aligning the periods after the optimisation process significantly enhances this power. Phase synchronising the antennas gives a small increase in observed power, while further aligning the periods after the optimisation process significantly enhances this power.