Changeset 6793 for trunk


Ignore:
Timestamp:
03/08/05 17:15:47 (20 years ago)
Author:
gaug
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1 edited

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  • trunk/MagicSoft/TDAS-Extractor/Pedestal.tex

    r6748 r6793  
    9393
    9494
    95 \begin{figure}[htp]
    96 \centering
    97 \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38993_RelMean.eps}
    98 \vspace{\floatsep}
    99 \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38995_RelMean.eps}
    100 \vspace{\floatsep}
    101 \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38996_RelMean.eps}
    102 \caption{MExtractTimeAndChargeSpline with amplitude extraction:
    103 Difference in mean pedestal (per FADC slice) between extraction algorithm
    104 applied on a fixed window of 1 FADC slice (``extractor random'') and a simple addition of
    105 2 fixed FADC slices (``fundamental''). On the left, a run with closed camera has been taken, in the center
    106  an opened camera observing an extra-galactic star field and on the right, an open camera being
    107 illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
    108 pixel.}
    109 \label{fig:amp:relmean}
    110 \end{figure}
    111 
    112 \begin{figure}[htp]
    113 \centering
    114 \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38993_RelMean.eps}
    115 \vspace{\floatsep}
    116 \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38995_RelMean.eps}
    117 \vspace{\floatsep}
    118 \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38996_RelMean.eps}
    119 \caption{MExtractTimeAndChargeSpline with integral over 2 slices:
    120 Difference in mean pedestal (per FADC slice) between extraction algorithm
    121 applied on a fixed window of 2 FADC slices (``extractor random'') and a simple addition of
    122 2 FADC fixed slices (``fundamental''). On the left, a run with closed camera has been taken, in the center
    123  an opened camera observing an extra-galactic star field and on the right, an open camera being
    124 illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
    125 pixel.}
    126 \label{fig:int:relmean}
    127 \end{figure}
    128 
    129 \begin{figure}[htp]
    130 \centering
    131 \vspace{\floatsep}
    132 \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38993_RelMean.eps}
    133 \vspace{\floatsep}
    134 \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38995_RelMean.eps}
    135 \vspace{\floatsep}
    136 \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38996_RelMean.eps}
    137 \caption{MExtractTimeAndChargeDigitalFilter:
    138 Difference in mean pedestal (per FADC slice) between extraction algorithm
    139 applied on a fixed window of 6 FADC slices and time-randomized weights (``extractor random'')
    140 and a simple addition of
    141 6 FADC fixed slices (``fundamental''). On the left, a run with closed camera has been taken, in the center
    142  an opened camera observing an extra-galactic star field and on the right, an open camera being
    143 illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
    144 pixel.}
    145 \label{fig:df:relmean}
    146 \end{figure}
     95%\begin{figure}[htp]
     96%\centering
     97%\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38993_RelMean.eps}
     98%\vspace{\floatsep}
     99%\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38995_RelMean.eps}
     100%\vspace{\floatsep}
     101%\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38996_RelMean.eps}
     102%\caption{MExtractTimeAndChargeSpline with amplitude extraction:
     103%Difference in mean pedestal (per FADC slice) between extraction algorithm
     104%applied on a fixed window of 1 FADC slice (``extractor random'') and a simple addition of
     105%2 fixed FADC slices (``fundamental''). On the left, a run with closed camera has been taken, in the center
     106% an opened camera observing an extra-galactic star field and on the right, an open camera being
     107%illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
     108%pixel.}
     109%\label{fig:amp:relmean}
     110%\end{figure}
     111
     112%\begin{figure}[htp]
     113%\centering
     114%\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38993_RelMean.eps}
     115%\vspace{\floatsep}
     116%\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38995_RelMean.eps}
     117%\vspace{\floatsep}
     118%\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38996_RelMean.eps}
     119%\caption{MExtractTimeAndChargeSpline with integral over 2 slices:
     120%Difference in mean pedestal (per FADC slice) between extraction algorithm
     121%applied on a fixed window of 2 FADC slices (``extractor random'') and a simple addition of
     122%2 FADC fixed slices (``fundamental''). On the left, a run with closed camera has been taken, in the center
     123% an opened camera observing an extra-galactic star field and on the right, an open camera being
     124%illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
     125%pixel.}
     126%\label{fig:int:relmean}
     127%\end{figure}
     128
     129%\begin{figure}[htp]
     130%\centering
     131%\vspace{\floatsep}
     132%\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38993_RelMean.eps}
     133%\vspace{\floatsep}
     134%\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38995_RelMean.eps}
     135%\vspace{\floatsep}
     136%\includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38996_RelMean.eps}
     137%\caption{MExtractTimeAndChargeDigitalFilter:
     138%Difference in mean pedestal (per FADC slice) between extraction algorithm
     139%applied on a fixed window of 6 FADC slices and time-randomized weights (``extractor random'')
     140%and a simple addition of
     141%6 FADC fixed slices (``fundamental''). On the left, a run with closed camera has been taken, in the center
     142% an opened camera observing an extra-galactic star field and on the right, an open camera being
     143%illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one
     144%pixel.}
     145%\label{fig:df:relmean}
     146%\end{figure}
    147147
    148148%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    … …  
    177177\par
    178178
    179 The following figures~\ref{fig:amp:relmean} through~\ref{fig:df:relrms} show results
    180 obtained with the second method for three background intensities:
    181 
    182 \begin{enumerate}
    183 \item Closed camera and no (Poissonian) fluctuation due to photons from the night sky background
    184 \item The camera pointing to an extra-galactic region with stars in the field of view
    185 \item The camera illuminated by a continuous light source of intensity 100.
    186 \end{enumerate}
    187 
    188 Figures~\ref{fig:amp:relmean} through~\ref{fig:df:relmean}
    189 show the calculated biases obtained with this method for all pixels in the camera
    190 and for the different levels of (night-sky) background applied to 1000 pedestal events.
    191 One can see that the bias vanishes to an accuracy of better than 2\% of a photo-electron
     179%The following figures~\ref{fig:amp:relmean} through~\ref{fig:df:relrms} show results
     180%obtained with the second method for three background intensities:
     181
     182%\begin{enumerate}
     183%\item Closed camera and no (Poissonian) fluctuation due to photons from the night sky background
     184%\item The camera pointing to an extra-galactic region with stars in the field of view
     185%\item The camera illuminated by a continuous light source of intensity 100.
     186%\end{enumerate}
     187
     188The calculated biases obtained with this method for all pixels in the camera
     189and for the different levels of (night-sky) background applied vanish
     190to an accuracy of better than 2\% of a photo-electron
    192191for the extractors which are used in this TDAS.
     192\par
     193Table~\ref{tab::ped:fw} shows the resolutions $R$ obtained
     194by applying an extractor to a fixed extraction window,
     195for the inner and outer pixels, respectively, for four different camera illumination conditions:
     196Closed camera (run \#38993), star-field of an extra-galactic source observation (run~\#38995),
     197star-field of the Crab-Nebula observation (run~\#39258) and observation with the almost fully
     198illuminated moon at an angular distance of about~60$^\circ$ from the telescope pointing position
     199(run~\#46471). In the first three cases, the RMS of the values has been calculated while in the
     200fourth case, the high-end side of the signal distributions have been fitted to a Gaussian.
     201\par
     202The entries belonging to the rows denoted as ``Slid. Win.'' are by construction identical to those
     203obtained by simply summing up the FADC slices (the ``fundamental Pedestal RMS'').
     204Note that the digital filter yields much smaller values of $R$ than the ``sliding windows'' of
     205a same window size. This characteristic shows the
     206``filter''--capacity of that algorithm. It ``filters out'' up to 50\% of the night sky
     207background photo-electrons.
     208\par
     209One can see that the ratio between the pedestal RMS of outer and inner pixels is around a factor~3
     210for the closed camera and then 1.6--1.9 for the other conditions.
     211
     212%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     213
    193214
    194215%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1
    195216
    196 \begin{figure}[htp]
    197 \centering
    198 \includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38993_RMSDiff.eps}
    199 \vspace{\floatsep}
    200 \includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38995_RMSDiff.eps}
    201 \vspace{\floatsep}
    202 \includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38996_RMSDiff.eps}
    203 \caption{MExtractTimeAndChargeSpline with amplitude: 
    204 Difference in RMS (per FADC slice) between extraction algorithm
    205 applied on a fixed window and the corresponding pedestal RMS.
    206 Closed camera (left), open camera observing extra-galactic star field (right) and
    207 camera being illuminated by the continuous light (bottom).
    208 Every entry corresponds to one pixel.}
    209 \label{fig:amp:relrms}
    210 \end{figure}
    211 
    212 
    213 \begin{figure}[htp]
    214 \centering
    215 \includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38993_RMSDiff.eps}
    216 \vspace{\floatsep}
    217 \includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38995_RMSDiff.eps}
    218 \vspace{\floatsep}
    219 \includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38996_RMSDiff.eps}
    220 \caption{MExtractTimeAndChargeSpline with integral over 2 slices: 
    221 Difference in RMS (per FADC slice) between extraction algorithm
    222 applied on a fixed window and the corresponding pedestal RMS.
    223 Closed camera (left), open camera observing extra-galactic star field (right) and
    224 camera being illuminated by the continuous light (bottom).
    225 Every entry corresponds to one
    226 pixel.}
    227 \label{fig:int:relrms}
    228 \end{figure}
    229 
    230 
    231 \begin{figure}[htp]
    232 \centering
    233 \includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38993_RMSDiff.eps}
    234 \vspace{\floatsep}
    235 \includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38995_RMSDiff.eps}
    236 \vspace{\floatsep}
    237 \includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38996_RMSDiff.eps}
    238 \caption{MExtractTimeAndChargeDigitalFilter: 
    239 Difference in RMS (per FADC slice) between extraction algorithm
    240 applied on a fixed window and the corresponding pedestal RMS.
    241 Closed camera (left), open camera observing extra-galactic star field (right) and
    242 camera being illuminated by the continuous light (bottom).
    243 Every entry corresponds to one pixel.}
    244 \label{fig:df:relrms}
    245 \end{figure}
    246 
     217%\begin{figure}[htp]
     218%\centering
     219%\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38993_RMSDiff.eps}
     220%\vspace{\floatsep}
     221%\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38995_RMSDiff.eps}
     222%\vspace{\floatsep}
     223%\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38996_RMSDiff.eps}
     224%\caption{MExtractTimeAndChargeSpline with amplitude: 
     225%Difference in RMS (per FADC slice) between extraction algorithm
     226%applied on a fixed window and the corresponding pedestal RMS.
     227%Closed camera (left), open camera observing extra-galactic star field (right) and
     228%camera being illuminated by the continuous light (bottom).
     229%Every entry corresponds to one pixel.}
     230%\label{fig:amp:relrms}
     231%\end{figure}
     232
     233
     234%\begin{figure}[htp]
     235%\centering
     236%\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38993_RMSDiff.eps}
     237%\vspace{\floatsep}
     238%\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38995_RMSDiff.eps}
     239%\vspace{\floatsep}
     240%\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38996_RMSDiff.eps}
     241%\caption{MExtractTimeAndChargeSpline with integral over 2 slices: 
     242%Difference in RMS (per FADC slice) between extraction algorithm
     243%applied on a fixed window and the corresponding pedestal RMS.
     244%Closed camera (left), open camera observing extra-galactic star field (right) and
     245%camera being illuminated by the continuous light (bottom).
     246%Every entry corresponds to one
     247%pixel.}
     248%\label{fig:int:relrms}
     249%\end{figure}
     250
     251
     252%\begin{figure}[htp]
     253%\centering
     254%\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38993_RMSDiff.eps}
     255%\vspace{\floatsep}
     256%\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38995_RMSDiff.eps}
     257%\vspace{\floatsep}
     258%\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38996_RMSDiff.eps}
     259%\caption{MExtractTimeAndChargeDigitalFilter: 
     260%Difference in RMS (per FADC slice) between extraction algorithm
     261%applied on a fixed window and the corresponding pedestal RMS.
     262%Closed camera (left), open camera observing extra-galactic star field (right) and
     263%camera being illuminated by the continuous light (bottom).
     264%Every entry corresponds to one pixel.}
     265%\label{fig:df:relrms}
     266%\end{figure}
     267
     268%\begin{landscape}
     269%\rotatebox{90}{%
     270\begin{table}[htp]
     271\vspace{3cm}
     272\small{%
     273\centering
     274\begin{tabular}{|c|c||c|c||c|c||c|c||c|c|}
     275\hline
     276\hline
     277\multicolumn{10}{|c|}{Resolution for $S=0$ and fixed window (units in $N_{\mathrm{phe}}$)  \rule{0mm}{6mm} \rule[-2mm]{0mm}{6mm} \hspace{-3mm}} \\
     278\hline
     279\hline
     280 & & \multicolumn{2}{|c|}{Closed camera} & \multicolumn{2}{|c|}{Extra-gal. NSB}  & \multicolumn{2}{|c|}{Galactic NSB}  & \multicolumn{2}{|c|}{Moon} \\
     281\hline
     282\hline
     283Nr. & Name         & $R$ & $R$ &  $R$ & $R$ & $R$ & $R$ &  $R$ & $R$ \\
     284    &              & inner & outer & inner & outer & inner & outer & inner & outer \\
     285\hline                                                     
     28617  & Slid. Win. 2  & 0.3 & 0.9 &  1.2 & 2.0 &  1.5 & 2.4 &  3.0 & 5.3   \\
     28718  & Slid. Win. 4  & 0.4 & 1.2 &  1.6 & 2.7 &  2.0 & 3.3 &  3.9 & 7.3   \\
     28820  & Slid. Win. 6  & 0.5 & 1.6 &  2.0 & 3.5 &  2.4 & 4.3 &  4.7 & 9.0   \\
     28921  & Slid. Win. 8  & 0.6 & 2.0 &  2.3 & 4.1 &  2.9 & 5.0 &  5.3 & 10.1  \\
     290\hline                                 
     29123  & Spline Amp.   & 0.3 & 0.8 &  1.0 & 1.8 &  1.2 & 2.2 &  2.5 & 4.9   \\
     29224  & Spline Int. 1 & 0.3 & 0.7 &  0.9 & 1.6 &  1.1 & 1.9 &  2.5 & 4.6   \\
     29325  & Spline Int. 2 & 0.3 & 0.9 &  1.2 & 2.0 &  1.5 & 2.4 &  3.0 & 5.3   \\
     29426  & Spline Int. 4 & 0.4 & 1.2 &  1.6 & 2.8 &  1.9 & 3.4 &  3.6 & 7.1   \\
     29527  & Spline Int. 6 & 0.5 & 1.6 &  1.9 & 3.6 &  2.4 & 4.2 &  4.3 & 8.7   \\
     296\hline                                               
     29728  & Dig. Filt. 6  & 0.3 & 0.8 &  1.0 & 1.6 &  1.2 & 1.9 &  2.8 & 4.3   \\
     29829  & Dig. Filt. 4  & 0.3 & 0.7 &  0.9 & 1.6 &  1.1 & 1.9 &  2.5 & 4.3   \\
     299\hline
     300\hline
     301\end{tabular}
     302\vspace{1cm}
     303\caption{The mean resolution $R$ for different extractors applied to a fixed window of pedestal events.
     304Four different conditions of night sky background are shown:
     305Closed camera, extra-galactic star-field, galactic star-field and almost full moon at 60$^\circ$ angular
     306distance from the pointing position. With the first three conditions, a simple RMS of the extracted
     307signals has been calculated while in the fourth case, a Gauss fit to the high part of the distribution
     308has been made.
     309The obtained values can typically vary by up to 10\% for different channels of the camera readout.}
     310\label{tab:ped:fw}
     311}
     312\end{table}
     313%}
     314%\end{landscape}
    247315
    248316
    249317%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    250318
    251 Figures~\ref{fig:amp:relrms} through~\ref{fig:df:relrms} show the
    252 differences in $R$ between the RMS of simply summing up the FADC slices over the extraction window
    253 (in MARS called: ``Fundamental Pedestal RMS'') and
    254 the one obtained by applying the extractor to the same extraction window
    255 (in MARS called: ``Pedestal RMS with Extractor Rndm''). One entry of each histogram corresponds to one
    256 pixel of the camera.
    257 The distributions have a negative mean in the case of the digital filter showing the
    258 ``filter'' capacity of that algorithm. It ``filters out'' between 0.12 photo-electrons night sky
    259 background for the extra-galactic star-field until 0.2 photo-electrons for the continuous light.
    260 
    261 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    262319
    263320
    … …  
    315372\hline
    316373\hline
    317 \multicolumn{16}{|c|}{Statistical Parameters for $S=0$ units in $N_{\mathrm{phe}}$} \\
     374\multicolumn{16}{|c|}{Statistical Parameters for $S=0$ (units in $N_{\mathrm{phe}}$) \rule{0mm}{6mm} \rule[-2mm]{0mm}{6mm} \hspace{-3mm}} \\
    318375\hline
    319376\hline
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