Index: trunk/MagicSoft/TDAS-Extractor/Introduction.tex =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Introduction.tex (revision 6647) +++ trunk/MagicSoft/TDAS-Extractor/Introduction.tex (revision 6648) @@ -24,6 +24,6 @@ \end{center} \caption[Current MAGIC read-out scheme.]{Current MAGIC read-out scheme: the analog PMT signals are -transferred via an analog optical link to the counting house where after the trigger decision the signals -are digitized by using a 300 MHz FADCs system and written to the hard disk of a DAQ PC.} +transferred via an analog optical link to the counting house -- where after the trigger decision -- the signals +are digitized by a 300 MHz FADCs system and written to the hard disk of a DAQ PC.} \label{fig:MAGIC_read-out_scheme} \end{figure} @@ -34,10 +34,8 @@ -In order to sample this pulse shape with the used 300 MSamples/s FADC system, the pulse is shaped to a -FWHM greater than 6\,ns -(the original pulse is folded with a stretching function of 6ns). Because the MAGIC FADCs have a +In order to sample this pulse shape with the 300 MSamples/s FADC system, the original pulse is folded with a stretching function of 6ns leading to a FWHM greater than 6\,ns. Because the MAGIC FADCs have a resolution of 8 bit only, the signals are split into two branches with gains differing by a factor 10. One branch is delayed by 55\,ns and then both branches are multiplexed and consecutively read-out by one FADC. -Figure~\ref{fig:pulpo_shape_high} shows a typical average of identical input signals. A more detailed overview about the MAGIC read-out and DAQ system is given in \cite{Magic-DAQ}. +Figure~\ref{fig:pulpo_shape_high} shows a typical average of identical signals. A more detailed overview about the MAGIC read-out and DAQ system is given in \cite{Magic-DAQ}. % The maximum sustained trigger rate could be 1 kHz. The FADCs feature a FIFO memory which allows a significantly higher short-time rate. % Obviously by doing this, more LONS is integrated and thus the performance of the telescope on the analysis level is degraded. Index: trunk/MagicSoft/TDAS-Extractor/MonteCarlo.tex =================================================================== --- trunk/MagicSoft/TDAS-Extractor/MonteCarlo.tex (revision 6647) +++ trunk/MagicSoft/TDAS-Extractor/MonteCarlo.tex (revision 6648) @@ -255,7 +255,71 @@ \clearpage -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\subsection{Arrival Times \label{sec:mc:times}} + +Like in the case of the charge resolution, we calculated the RMS of the distribution of the deviation of the +reconstructed arrival time with respect to the simulated time: + +\begin{equation} +\Delta T_{\mathrm{MC}} \approx RMS(\widehat{T}_{rec} - T_{sim}) +\end{equation} + +where $\widehat{T}_{rec}$ is the reconstructed arrival time and $T_{sim}$ the simulated one. +\par + + + +\begin{figure}[htp]%%[t!] +\centering + \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_NoNoise_HiGain.eps} +\vspace{\floatsep} + \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_WithNoise_HiGain.eps} +\vspace{\floatsep} + \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_NoNoise_LoGain.eps} +\vspace{\floatsep} + \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_WithNoise_LoGain.eps} +\caption[Time Resolution Sliding Windows]{The measured time resolution (RMS of extracted time minus simulated time) +versus number of photoelectrons, +for sliding window extractors in different window sizes. The top plots show the high-gain and the bottom ones +low-gain regions. Left: without noise, right: with simulated noise.} +\label{fig:mc:TimeRes_SlidW} +\end{figure} + +\begin{figure}[htp] +\centering + \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_NoNoise_HiGain.eps} +\vspace{\floatsep} + \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_WithNoise_HiGain.eps} +\vspace{\floatsep} + \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_NoNoise_LoGain.eps} +\vspace{\floatsep} + \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_WithNoise_LoGain.eps} +\caption[Time Resolution Spline and Digital Filter]{The measured time resolution (RMS of extracted time minus simulated time) +versus number of photoelectrons, +for spline and digital filter window extractors in different window sizes. The top plots show the high-gain and the bottom ones +low-gain regions. Left: without noise, right: with simulated noise.} +\label{fig:mc:TimeRes_DFSpline} +\end{figure} + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "MAGIC_signal_reco" +%%% End: + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\clearpage \subsection{Charge Signals with and without Simulated Noise \label{fig:mc:sec:mc:chargenoise}} + \begin{figure}[htp] @@ -282,44 +346,2 @@ \label{fig:mc:Bias_LoGain} \end{figure} - -\clearpage - -\subsection{Arrival Times \label{sec:mc:times}} - -\begin{figure}[htp]%%[t!] -\centering - \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_NoNoise_HiGain.eps} -\vspace{\floatsep} - \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_WithNoise_HiGain.eps} -\vspace{\floatsep} - \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_NoNoise_LoGain.eps} -\vspace{\floatsep} - \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_SlidW_WithNoise_LoGain.eps} -\caption[Time Resolution Sliding Windows]{The measured time resolution (RMS of extracted time minus simulated time) -versus number of photoelectrons, -for sliding window extractors in different window sizes. The top plots show the high-gain and the bottom ones -low-gain regions. Left: without noise, right: with simulated noise.} -\label{fig:mc:TimeRes_SlidW} -\end{figure} - -\begin{figure}[htp] -\centering - \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_NoNoise_HiGain.eps} -\vspace{\floatsep} - \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_WithNoise_HiGain.eps} -\vspace{\floatsep} - \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_NoNoise_LoGain.eps} -\vspace{\floatsep} - \includegraphics[width=0.49\linewidth]{TimeAndChargePlots/TDAS_TimeRes_DFSpline_WithNoise_LoGain.eps} -\caption[Time Resolution Spline and Digital Filter]{The measured time resolution (RMS of extracted time minus simulated time) -versus number of photoelectrons, -for spline and digital filter window extractors in different window sizes. The top plots show the high-gain and the bottom ones -low-gain regions. Left: without noise, right: with simulated noise.} -\label{fig:mc:TimeRes_DFSpline} -\end{figure} - - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "MAGIC_signal_reco" -%%% End: Index: trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex (revision 6647) +++ trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex (revision 6648) @@ -3,7 +3,7 @@ The FADC clock is not synchronized with the trigger. Therefore, the relative position of the recorded signal samples varies from event to event with respect to the position of the signal shape. -The time between the trigger decision and the first read-out sample is uniformly distributed in the range +The time $\Delta t$ between the trigger decision and the first read-out sample is uniformly distributed in the range $t_{\text{rel}} \in [0,T_{\mathrm{FADC}}[$, where $T_{\mathrm{FADC}}=3.33$\,ns is the digitization period of the MAGIC 300\,MHz FADCs. -It can be determined using the reconstructed arrival time +$\Delta t$ can be determined using the reconstructed arrival time $t_{\mathrm{arrival}}$.%directly by a time to digital converter (TDC) or @@ -30,8 +30,8 @@ The asynchronous sampling of the pulse shape allows to determine an average pulse shape from the recorded -signal samples: The recorded signal samples can be shifted in time such that the shifted arrival times +signal samples: The recorded signal samples are shifted in time such that the shifted arrival times of all events are equal. In addition, the signal samples are normalized event by event using the reconstructed charge of the pulse. The accuracy of the signal shape reconstruction depends on the accuracy -of the arrival time and charge reconstruction. The statistical error of the reconstructed pulse shape is well below $10^{-2}$ while the systematical error is by definition unknown at first hand. +of the arrival time and charge reconstruction. The relative statistical error of the reconstructed pulse shape is well below $10^{-2}$ while the systematical error is by definition unknown at first hand. @@ -81,5 +81,5 @@ reconstructed pulse shape for cosmics events, both have a FWHM of about 6.3 ns. As air showers due to hadronic cosmic rays trigger the telescope much more frequently than gamma showers the reconstructed pulse shape of the cosmics events corresponds mainly to hadron induced showers. -The pulse shape due to electromagnetic air showers might be slightly different. The pulse shape for green calibration LED pulses is wider +The pulse shape due to electromagnetic air showers might be slightly different as indicated by MC simulations \cite{MC_timing_Indians}. The pulse shape for green calibration LED pulses is wider and has a pronounced tail. Index: trunk/MagicSoft/TDAS-Extractor/bibfile.bib =================================================================== --- trunk/MagicSoft/TDAS-Extractor/bibfile.bib (revision 6647) +++ trunk/MagicSoft/TDAS-Extractor/bibfile.bib (revision 6648) @@ -1,2 +1,15 @@ +@ARTICLE{MC_timing_Indians, + author = {{Chitnis}, V.~R. and {Bhat}, P.~N.}, + title = "{Possible discrimination between gamma rays and hadrons using {\v C}erenkov photon timing measurements}", + journal = {Astroparticle Physics}, + year = 2001, + month = mar, + volume = 15, + pages = {29-47}, + adsurl = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2001APh....15...29C&db_key=AST}, + adsnote = {Provided by the NASA Astrophysics Data System} +} + + @Article{low_energy, author = "Baixeras, C. and others",