Index: /trunk/MagicSoft/TDAS-Extractor/Pedestal.tex =================================================================== --- /trunk/MagicSoft/TDAS-Extractor/Pedestal.tex (revision 6382) +++ /trunk/MagicSoft/TDAS-Extractor/Pedestal.tex (revision 6383) @@ -120,5 +120,4 @@ \begin{figure}[htp] \centering -\vspace{\floatsep} \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38993_RelMean.eps} \vspace{\floatsep} @@ -138,5 +137,4 @@ \begin{figure}[htp] \centering -\vspace{-\floatsep} \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38993_RelMean.eps} \vspace{\floatsep} @@ -156,5 +154,5 @@ \begin{figure}[htp] \centering -\vspace{-\floatsep} +\vspace{\floatsep} \includegraphics[width=0.3\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38993_RelMean.eps} \vspace{\floatsep} @@ -200,13 +198,7 @@ \end{description} -Figures~\ref{fig:amp:relmean} through~\ref{fig:df:relmean} -show the calculated means obtained with this method for all pixels in the camera -and for different levels of night-sky background. -One can see that the bias vanishes to an accuracy of better than 1\% -for the extractors which are used in this TDAS. - -\par - -The following plots~\ref{fig:sw:distped} through~\ref{fig:amp:relrms} show results +\par + +The following figures~\ref{fig:amp:relmean} through~\ref{fig:df:relrms} show results obtained with the second method for three background intensities: @@ -214,9 +206,102 @@ \item Closed camera and no (Poissonian) fluctuation due to photons from the night sky background \item The camera pointing to an extra-galactic region with stars in the field of view -\item The camera illuminated by a continuous light source of high intensity causing much higher pedestal -fluctuations than in usual observation conditions. +\item The camera illuminated by a continuous light source of intensity 100. \end{enumerate} +Figures~\ref{fig:amp:relmean} through~\ref{fig:df:relmean} +show the calculated biases obtained with this method for all pixels in the camera +and for the different levels of (night-sky) background. +One can see that the bias vanishes to an accuracy of better than 1\% +for the extractors which are used in this TDAS. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1 + +\begin{figure}[htp] +\centering +\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38993_RMSDiff.eps} +\vspace{\floatsep} +\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38995_RMSDiff.eps} +\vspace{\floatsep} +\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38996_RMSDiff.eps} +\caption{MExtractTimeAndChargeSpline with amplitude: +Difference in RMS (per FADC slice) between extraction algorithm +applied on a fixed window and the corresponding pedestal RMS. +Closed camera (left), open camera observing extra-galactic star field (right) and +camera being illuminated by the continuous light (bottom). +Every entry corresponds to one pixel.} +\label{fig:amp:relrms} +\end{figure} + + +\begin{figure}[htp] +\centering +\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38993_RMSDiff.eps} +\vspace{\floatsep} +\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38995_RMSDiff.eps} +\vspace{\floatsep} +\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38996_RMSDiff.eps} +\caption{MExtractTimeAndChargeSpline with integral over 2 slices: +Difference in RMS (per FADC slice) between extraction algorithm +applied on a fixed window and the corresponding pedestal RMS. +Closed camera (left), open camera observing extra-galactic star field (right) and +camera being illuminated by the continuous light (bottom). +Every entry corresponds to one +pixel.} +\label{fig:amp:relrms} +\end{figure} + + +\begin{figure}[htp] +\centering +\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38993_RMSDiff.eps} +\vspace{\floatsep} +\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38995_RMSDiff.eps} +\vspace{\floatsep} +\includegraphics[width=0.47\linewidth]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38996_RMSDiff.eps} +\caption{MExtractTimeAndChargeDigitalFilter: +Difference in RMS (per FADC slice) between extraction algorithm +applied on a fixed window and the corresponding pedestal RMS. +Closed camera (left), open camera observing extra-galactic star field (right) and +camera being illuminated by the continuous light (bottom). +Every entry corresponds to one pixel.} +\label{fig:df:relrms} +\end{figure} + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Figures~\ref{fig:amp:relrms} through~\ref{fig:amp:relrms} show the +differences in $R$ between the calculated pedestal RMS and +the one obtained by applying the extractor, converted to equivalent photo-electrons. One entry +corresponds to one pixel of the camera. +The distributions have a negative mean in the case of the digital filter showing the +``filter'' capacity of that algorithm. It ``filters out'' between 0.12 photo-electrons night sky +background for the extra-galactic star-field until 0.2 photo-electrons for the continuous light. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\subsubsection{ \label{sec:determiner} Application of the Signal Extractor to a Sliding Window +of Pedestal Events} + +By applying the signal extractor to a global extraction window of pedestal events, allowing +it to ``slide'' and maximize the encountered signal, we +determine the bias $B$ and the mean-squared error $MSE$ for the case of no signal ($S=0$). +\par +In MARS, this functionality is implemented with a function-call to: \\ + +{\textit{\bf MJPedestal::SetExtractionWithExtractor()}} \\ + +\par + +Figures~\ref{fig:amp:distped} through~\ref{fig:df:distped} show the +extracted pedestal distributions for the digital filter with cosmics weights (extractor~\#28) and the +spline amplitude (extractor~\#27), respectively for one examplary channel (corresponding to pixel 200). +One can see the (asymmetric) Poisson behaviour of the +night sky background photons for the distributions with open camera and the cutoff at the lower egde +for the distribution with high-intensity continuous light due to a limited pedestal offset and the cutoff +to negative fluctuations. +\par \begin{figure}[htp] @@ -286,107 +371,6 @@ \end{figure} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1 - -\begin{figure}[htp] -\centering -\includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38993_RMSDiff.eps} -\vspace{\floatsep} -\includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38995_RMSDiff.eps} -\vspace{\floatsep} -\includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Amplitude_Amplitude_Range_01_09_01_10_Run_38996_RMSDiff.eps} -\caption{MExtractTimeAndChargeSpline with amplitude: -Difference in pedestal RMS (per FADC slice) between extraction algorithm -applied on a fixed window of 1 FADC slice (``extractor random'') and a simple addition of -2 FADC slices (``fundamental''). On the top, a run with closed camera has been taken, in the center - an opened camera observing an extra-galactic star field and on the bottom, an open camera being -illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one -pixel.} -\label{fig:amp:relrms} -\end{figure} - - -\begin{figure}[htp] -\centering -\includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38993_RMSDiff.eps} -\vspace{\floatsep} -\includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38995_RMSDiff.eps} -\vspace{\floatsep} -\includegraphics[height=0.3\textheight]{MExtractTimeAndChargeSpline_Rise-and-Fall-Time_0.5_1.5_Range_01_10_02_12_Run_38996_RMSDiff.eps} -\caption{MExtractTimeAndChargeSpline with integral over 2 slices: -Difference in pedestal RMS (per FADC slice) between extraction algorithm -applied on a fixed window of 2 FADC slices (``extractor random'') and a simple addition of -2 FADC slices (``fundamental''). On the top, a run with closed camera has been taken, in the center - an opened camera observing an extra-galactic star field and on the bottom, an open camera being -illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one -pixel.} -\label{fig:amp:relrms} -\end{figure} - - -\begin{figure}[htp] -\centering -\includegraphics[height=0.3\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38993_RMSDiff.eps} -\vspace{\floatsep} -\includegraphics[height=0.3\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38995_RMSDiff.eps} -\vspace{\floatsep} -\includegraphics[height=0.3\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_01_14_02_14_Run_38996_RMSDiff.eps} -\caption{MExtractTimeAndChargeDigitalFilter: -Difference in pedestal RMS (per FADC slice) between extraction algorithm -applied on a fixed window of 6 FADC slices and time-randomized weights (``extractor random'') -and a simple addition of 6 FADC slices (``fundamental''). On the top, a run with closed camera -has been taken, in the center - an opened camera observing an extra-galactic star field and on the bottom, an open camera being -illuminated by the continuous light of the calibration (level: 100). Every entry corresponds to one -pixel.} -\label{fig:df:relrms} -\end{figure} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -Figures~\ref{fig:df:distped},~\ref{fig:amp:distped} -and~\ref{fig:amp:distped} show the -extracted pedestal distributions for the digital filter with cosmics weights (extractor~\#28) and the -spline amplitude (extractor~\#27), respectively for one examplary channel (corresponding to pixel 200). -One can see the (asymmetric) Poisson behaviour of the -night sky background photons for the distributions with open camera and the cutoff at the lower egde -for the distribution with high-intensity continuous light due to a limited pedestal offset and the cutoff -to negative fluctuations. -\par -Figures~\ref{fig:df:relmean} -and~\ref{fig:amp:relmean} show the -relative difference between the calculated pedestal mean and -the one obtained by applying the extractor for -all channels of the MAGIC camera. One can see that in all cases, the distribution is centered around zero, -while its width is never larger than 0.01 which corresponds about to the precision of the extracted mean for -the number of used events. (A very similar distribution is obtained by comparing the results -of the same pedestal calculator applied to different ranges of FADC slices.) -\par -Figures~\ref{fig:df:relrms} -and~\ref{fig:amp:relrms} show the -relative difference between the calculated pedestal RMS, normalized to an equivalent number of slices -(2.5 for the digital filter and 1. for the amplitude of the spline) and -the one obtained by applying the extractor for all channels of the MAGIC camera. -One can see that in all cases, the distribution is not centered around zero, but shows an offset depending -on the light intensity. The difference can be 10\% in the case of the digital filter and even 25\% for the -spline. This big difference for the spline is partly explained by the fact that the pedestals have to be -calculated from an even number of slices to account for the clock-noise. However, the (normalized) pedestal -RMS depends critically on the number of summed FADC slices, especially at very low numbers. In general, -the higher the number of summed FADC slices, the higher the (to the square root of the number of slices) -normalized pedestal RMS. - - -\subsubsection{ \label{sec:determiner} Application of the Signal Extractor to a Sliding Window -of Pedestal Events} - -In this section, we apply the signal extractor to a sliding window of pedestal events. -\par -In MARS, this possibility can be used with a call to -{\textit{\bf MJPedestal::SetExtractionWithExtractor()}}. -\par +\par + Because the background is determined by the single photo-electrons from the night-sky background, the following possibilities can occur: