Index: /trunk/MagicSoft/TDAS-Extractor/Pedestal.tex
===================================================================
--- /trunk/MagicSoft/TDAS-Extractor/Pedestal.tex	(revision 5555)
+++ /trunk/MagicSoft/TDAS-Extractor/Pedestal.tex	(revision 5556)
@@ -147,6 +147,6 @@
     to get information about the bias $B$ (valid for low signals). 
 \item Applying the signal extractor to a fixed window, to get something like 
-    $R$. In the case of the digital filter, this has to be done by randomizing 
-    the time slice indices.
+    $R$. In the case of the digital filter and the spline, this has to be done 
+    by randomizing the time slice indices.
 \end{enumerate}
 
@@ -155,4 +155,44 @@
 \vspace{1cm}
 \par
+
+The following plots~\ref{fig:df:distped:run38993} through~\ref{fig:amp:relrms:run38996} show results 
+obtained with the second method for three background intensities: 
+\begin{enumerate}
+\item Closed camera and no (Poissonian) fluctuation due to photons from the night sky background
+\item The camera pointing to a 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.
+\end{enumerate}
+
+Figures~\ref{fig:df:distped:run38993},~\ref{fig:df:distped:run38995},~\ref{fig:df:distped:run38996},
+and~\ref{fig:amp:distped:run38993},~\ref{fig:amp:distped:run38995},~\ref{fig:amp:distped:run38996} 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:run38993},~\ref{fig:df:relmean:run38995},~\ref{fig:df:relmean:run38996},
+and~\ref{fig:amp:relmean:run38993},~\ref{fig:amp:relmean:run38995},~\ref{fig:amp:relmean:run38996} 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:run38993},~\ref{fig:df:relrms:run38995},~\ref{fig:df:relrms:run38996},
+and~\ref{fig:amp:relrms:run38993},~\ref{fig:amp:relrms:run38995},~\ref{fig:amp:relrms:run38996} 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.
 
 \begin{figure}[htp]
@@ -161,11 +201,14 @@
 \caption{MExtractTimeAndChargeDigitalFilter: Distribution of extracted "pedestals"  from pedestal run with 
 closed camera lids for one channel.}
+\label{fig:df:distped:run38993}
 \vspace{\floatsep}
 \includegraphics[height=0.29\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_00_18_02_14_Run_38995_Signal_Pixel200.eps}
 \caption{MExtractTimeAndChargeDigitalFilter: Distribution of extracted "pedestals"  from pedestal run with galactic star background for one channel.}
+\label{fig:df:distped:run38995}
 \vspace{\floatsep}
 \includegraphics[height=0.29\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_00_18_02_14_Run_38996_Signal_Pixel200.eps}
 \caption{MExtractTimeAndChargeDigitalFilter: Distribution of extracted "pedestals"  from run with 
 continuous light level 100 for one channel.}
+\label{fig:df:distped:run38996}
 \end{figure}
 
@@ -173,11 +216,17 @@
 \centering
 \includegraphics[height=0.27\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_00_18_02_14_Run_38993_RelMean.eps}
-\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Mean Pedestal per FADC slice from pedestal run with closed camera lids}
+\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Mean Pedestal per FADC slice from pedestal 
+run with closed camera lids}
+\label{fig:df:relmean:run38993}
 \vspace{\floatsep}
 \includegraphics[height=0.27\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_00_18_02_14_Run_38995_RelMean.eps}
-\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Mean Pedestal per FADC slice from pedestal run with galactic star background}
+\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Mean Pedestal per FADC slice from pedestal 
+run with galactic star background}
+\label{fig:df:relmean:run38995}
 \vspace{\floatsep}
 \includegraphics[height=0.27\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_00_18_02_14_Run_38996_RelMean.eps}
-\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Mean Pedestal per FADC slice from run with continuous light level: 100}
+\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Mean Pedestal per FADC slice from run 
+with continuous light level: 100}
+\label{fig:df:relmean:run38996}
 \end{figure}
 
@@ -186,17 +235,23 @@
 \centering
 \includegraphics[height=0.23\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_00_18_02_14_Run_38993_RMSRelDiff.eps}
-\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Pedestal RMS per FADC slice (calculated out of 2 FADC slices each) from pedestal run 
-with closed camera lids for inner (left) and outer (right) pixels. An equivalent number of 2.5 FADC slices has been 
-used for the normalization of the pedestal RMS. The difference amounts to about 10\%.}
+\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Pedestal RMS per FADC slice 
+(calculated out of 2 FADC slices each) from pedestal run 
+with closed camera lids for inner (left) and outer (right) pixels. An equivalent number of 2.5 FADC slices 
+has been used for the normalization of the pedestal RMS. The difference amounts to about 10\%.}
+\label{fig:df:relrms:run38993}
 \vspace{\floatsep}
 \includegraphics[height=0.23\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_00_18_02_14_Run_38995_RMSRelDiff.eps}
-\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Pedestal RMS per FADC slice (calculated out of 2 FADC slices each) from pedestal run 
- with galactic star background for inner (left) and outer (right) pixels. An equivalent number of 2.5 FADC slices 
+\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Pedestal RMS per FADC slice 
+(calculated out of 2 FADC slices each) from pedestal run with galactic star background for inner (left) 
+and outer (right) pixels. An equivalent number of 2.5 FADC slices 
 has been used for the normalization of the pedestal RMS. The difference amounts to about 4\%.}
+\label{fig:df:relrms:run38995}
 \vspace{\floatsep}
 \includegraphics[height=0.23\textheight]{MExtractTimeAndChargeDigitalFilter_Weights_cosmics_weights.dat_Range_00_18_02_14_Run_38996_RMSRelDiff.eps}
-\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Pedestal RMS per FADC slice (calculated out of 2 FADC slices each) from run 
- with continuous light level: 100 for inner (left) and outer (right) pixels. An equivalent number of 2.5 FADC slices 
+\caption{MExtractTimeAndChargeDigitalFilter: Relative Difference Pedestal RMS per FADC slice 
+(calculated out of 2 FADC slices each) from run with continuous light level: 100 for inner (left) 
+and outer (right) pixels. An equivalent number of 2.5 FADC slices 
 has been used for the normalization of the pedestal RMS. The difference amounts to about 3--5\%.} 
+\label{fig:df:relrms:run38996}
 \end{figure}
 
@@ -207,12 +262,15 @@
 \caption{MExtractTimeAndChargeSpline with amplitude: Distribution of extracted "pedestals"  from pedestal run 
 with closed camera lids for one channel.}
+\label{fig:amp:distped:run38993}
 \vspace{\floatsep}
 \includegraphics[height=0.29\textheight]{MExtractTimeAndChargeSpline_Amplitude_Range_00_10_04_11_Run_38995_Signal_Pixel200.eps}
 \caption{MExtractTimeAndChargeSpline with amplitude: Distribution of extracted "pedestals"  from pedestal run 
 with galactic star background for one channel.}
+\label{fig:amp:distped:run38995}
 \vspace{\floatsep}
 \includegraphics[height=0.29\textheight]{MExtractTimeAndChargeSpline_Amplitude_Range_00_10_04_11_Run_38996_Signal_Pixel200.eps}
 \caption{MExtractTimeAndChargeSpline with amplitude: Distribution of extracted "pedestals"  from run with 
 continuous light level: 100 for one channel.}
+\label{fig:amp:distped:run38996}
 \end{figure}
 
@@ -220,11 +278,17 @@
 \centering
 \includegraphics[height=0.27\textheight]{MExtractTimeAndChargeSpline_Amplitude_Range_00_10_04_11_Run_38993_RelMean.eps}
-\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Mean Pedestal per FADC slice from pedestal run with closed camera lids}
+\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Mean Pedestal per FADC slice 
+from pedestal run with closed camera lids}
+\label{fig:amp:relmean:run38993}
 \vspace{\floatsep}
 \includegraphics[height=0.27\textheight]{MExtractTimeAndChargeSpline_Amplitude_Range_00_10_04_11_Run_38995_RelMean.eps}
-\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Mean Pedestal per FADC slice from pedestal run with galactic star background}
+\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Mean Pedestal per FADC slice 
+from pedestal run with galactic star background}
+\label{fig:amp:relmean:run38995}
 \vspace{\floatsep}
 \includegraphics[height=0.27\textheight]{MExtractTimeAndChargeSpline_Amplitude_Range_00_10_04_11_Run_38996_RelMean.eps}
-\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Mean Pedestal per FADC slice from run with continuous light level: 100}
+\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Mean Pedestal per FADC slice 
+from run with continuous light level: 100}
+\label{fig:amp:relmean:run38996}
 \end{figure}
 
@@ -233,17 +297,23 @@
 \centering
 \includegraphics[height=0.23\textheight]{MExtractTimeAndChargeSpline_Amplitude_Range_00_10_04_11_Run_38993_RMSRelDiff.eps}
-\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Pedestal RMS per FADC slice (calculated out of 2 FADC slices each)  from pedestal run 
-with closed camera lids for inner (left) and outer (right) pixels. An equivalent number of 1 FADC slice has been 
-used for the normalization of the pedestal RMS. The difference amounts to about 20\%.}
+\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Pedestal RMS per FADC slice 
+(calculated out of 2 FADC slices each)  from pedestal run 
+with closed camera lids for inner (left) and outer (right) pixels. An equivalent number of 1 FADC slice 
+has been used for the normalization of the pedestal RMS. The difference amounts to about 20\%.}
+\label{fig:amp:relrms:run38993}
 \vspace{\floatsep}
 \includegraphics[height=0.23\textheight]{MExtractTimeAndChargeSpline_Amplitude_Range_00_10_04_11_Run_38995_RMSRelDiff.eps}
-\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Pedestal RMS per FADC slice (calculated out of 2 FADC slices each)  from pedestal run 
- with galactic star background for inner (left) and outer (right) pixels. An equivalent number of 1 FADC slice 
+\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Pedestal RMS per FADC slice 
+(calculated out of 2 FADC slices each)  from pedestal run with galactic star background for inner (left) 
+and outer (right) pixels. An equivalent number of 1 FADC slice 
 has been used for the normalization of the pedestal RMS. The difference amounts to about 25\%.}
+\label{fig:amp:relrms:run38995}
 \vspace{\floatsep}
 \includegraphics[height=0.23\textheight]{MExtractTimeAndChargeSpline_Amplitude_Range_00_10_04_11_Run_38996_RMSRelDiff.eps}
-\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Pedestal RMS per FADC slice (calculated out of 2 FADC slices each)  from run 
- with continuous light level: 100 for inner (left) and outer (right) pixels. An equivalent number of 1 FADC slice 
+\caption{MExtractTimeAndChargeSpline with amplitude: Relative Difference Pedestal RMS per FADC slice 
+(calculated out of 2 FADC slices each)  from run with continuous light level: 100 for inner (left) 
+and outer (right) pixels. An equivalent number of 1 FADC slice 
 has been used for the normalization of the pedestal RMS. The difference amounts to about 25\%.} 
+\label{fig:amp:relrms:run38996}
 \end{figure}