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02/11/05 17:33:08 (20 years ago)
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gaug
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  • trunk/MagicSoft/TDAS-Extractor/Pedestal.tex

    r6380 r6382  
    100100It can then be obtained from the calculation of the variance $Var[\widehat{Q}]$
    101101by applying the extractor to a fixed window of pure background events (``pedestal events'')
    102 and get rid of the bias in that way. Figures~\ref{fig:amp:relmean} through~\ref{fig:df:relmean}
    103 show that the bias vanishes to an accuracy of better than 1\%
    104 for the extractors which are used in this TDAS.
    105 
    106 \begin{figure}[htp]
    107 \centering
    108 \includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38993_RelMean.eps}
    109 \vspace{\floatsep}
    110 \includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38995_RelMean.eps}
    111 \vspace{\floatsep}
    112 \includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38996_RelMean.eps}
    113 \caption{MExtractTimeAndChargeSpline with amplitude extraction:
    114 Difference in mean pedestal (per FADC slice) between extraction algorithm
    115 applied on a fixed window of 1 FADC slice (``extractor random'') and a simple addition of
    116 2 FADC slices (``fundamental''). On the top, a run with closed camera has been taken, in the center
    117  an opened camera observing an extra-galactic star field and on the bottom, an open camera being
    118 illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
    119 pixel.}
    120 \label{fig:amp:relmean}
    121 \end{figure}
    122 
    123 
    124 \begin{figure}[htp]
    125 \centering
    126 \includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38993_RelMean.eps}
    127 \vspace{\floatsep}
    128 \includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38995_RelMean.eps}
    129 \vspace{\floatsep}
    130 \includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38996_RelMean.eps}
    131 \caption{MExtractTimeAndChargeSpline with integral over 2 slices:
    132 Difference in mean pedestal (per FADC slice) between extraction algorithm
    133 applied on a fixed window of 2 FADC slices (``extractor random'') and a simple addition of
    134 2 FADC slices (``fundamental''). On the top, a run with closed camera has been taken, in the center
    135  an opened camera observing an extra-galactic star field and on the bottom, an open camera being
    136 illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
    137 pixel.}
    138 \label{fig:int:relmean}
    139 \end{figure}
    140 
    141 \begin{figure}[htp]
    142 \centering
    143 \includegraphics[height=0.3\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38993_RelMean.eps}
    144 \vspace{\floatsep}
    145 \includegraphics[height=0.3\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38995_RelMean.eps}
    146 \vspace{\floatsep}
    147 \includegraphics[height=0.3\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38996_RelMean.eps}
    148 \caption{MExtractTimeAndChargeDigitalFilter:
    149 Difference in mean pedestal (per FADC slice) between extraction algorithm
    150 applied on a fixed window of 6 FADC slices and time-randomized weights (``extractor random'')
    151 and a simple addition of
    152 6 FADC slices (``fundamental''). On the top, a run with closed camera has been taken, in the center
    153  an opened camera observing an extra-galactic star field and on the bottom, an open camera being
    154 illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
    155 pixel.}
    156 \label{fig:df:relmean}
    157 \end{figure}
    158 
    159 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     102and get rid of the bias in that way.
     103\par
    160104
    161105In order to calculate bias and Mean-squared error, we proceeded in the following ways:
    … …  
    173117\end{enumerate}
    174118
     119
     120\begin{figure}[htp]
     121\centering
     122\vspace{\floatsep}
     123\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38993_RelMean.eps}
     124\vspace{\floatsep}
     125\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38995_RelMean.eps}
     126\vspace{\floatsep}
     127\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38996_RelMean.eps}
     128\caption{MExtractTimeAndChargeSpline with amplitude extraction:
     129Difference in mean pedestal (per FADC slice) between extraction algorithm
     130applied on a fixed window of 1 FADC slice (``extractor random'') and a simple addition of
     1312 FADC slices (``fundamental''). On the left, a run with closed camera has been taken, in the center
     132 an opened camera observing an extra-galactic star field and on the right, an open camera being
     133illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
     134pixel.}
     135\label{fig:amp:relmean}
     136\end{figure}
     137
     138\begin{figure}[htp]
     139\centering
     140\vspace{-\floatsep}
     141\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38993_RelMean.eps}
     142\vspace{\floatsep}
     143\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38995_RelMean.eps}
     144\vspace{\floatsep}
     145\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38996_RelMean.eps}
     146\caption{MExtractTimeAndChargeSpline with integral over 2 slices:
     147Difference in mean pedestal (per FADC slice) between extraction algorithm
     148applied on a fixed window of 2 FADC slices (``extractor random'') and a simple addition of
     1492 FADC slices (``fundamental''). On the left, a run with closed camera has been taken, in the center
     150 an opened camera observing an extra-galactic star field and on the right, an open camera being
     151illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
     152pixel.}
     153\label{fig:int:relmean}
     154\end{figure}
     155
     156\begin{figure}[htp]
     157\centering
     158\vspace{-\floatsep}
     159\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38993_RelMean.eps}
     160\vspace{\floatsep}
     161\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38995_RelMean.eps}
     162\vspace{\floatsep}
     163\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38996_RelMean.eps}
     164\caption{MExtractTimeAndChargeDigitalFilter:
     165Difference in mean pedestal (per FADC slice) between extraction algorithm
     166applied on a fixed window of 6 FADC slices and time-randomized weights (``extractor random'')
     167and a simple addition of
     1686 FADC slices (``fundamental''). On the left, a run with closed camera has been taken, in the center
     169 an opened camera observing an extra-galactic star field and on the right, an open camera being
     170illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
     171pixel.}
     172\label{fig:df:relmean}
     173\end{figure}
     174
     175%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     176
    175177\subsubsection{ \label{sec:determiner} Application of the Signal Extractor to a Fixed Window
    176178of Pedestal Events}
    … …  
    195197at a random place within the digitizing binning resolution of one central FADC slice.
    196198\item[\textit{MExtractTimeAndChargeDigitalFilter}:\xspace] The second step timing
    197 offset $\tau$ (eq.~\ref{eq:offsettau} gets randomized for each event.
     199offset $\tau$ (eq.~\ref{eq:offsettau}) gets randomized for each event.
    198200\end{description}
     201
     202Figures~\ref{fig:amp:relmean} through~\ref{fig:df:relmean}
     203show the calculated means obtained with this method for all pixels in the camera
     204and for different levels of night-sky background.
     205One can see that the bias vanishes to an accuracy of better than 1\%
     206for the extractors which are used in this TDAS.
     207
     208\par
    199209
    200210The following plots~\ref{fig:sw:distped} through~\ref{fig:amp:relrms} show results
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