Changeset 6407 for trunk/MagicSoft

Timestamp:

02/12/05 16:55:47 (20 years ago)

Author:

gaug

Message:

*** empty log message ***

File:

• trunk/MagicSoft/TDAS-Extractor/Pedestal.tex (modified) (14 diffs)

trunk/MagicSoft/TDAS-Extractor/Pedestal.tex

@@ -173 +173 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\subsubsection{ \label{sec:determiner} Application of the Signal Extractor to a Fixed Window
+\subsubsection{ \label{sec:ped:fixedwindow} Application of the Signal Extractor to a Fixed Window
 of Pedestal Events}
 
@@ -283 +283 @@
 
 
-\subsubsection{ \label{sec:determiner} Application of the Signal Extractor to a Sliding Window
+\subsubsection{ \label{sec:ped:slidingwindow} Application of the Signal Extractor to a Sliding Window
 of Pedestal Events}
 
@@ -298 +298 @@
 a sliding window. In this sample, every extractor had the freedom to move 5 slices, 
 i.e. the global window size was fixed to five plus the extractor window size. This first line 
-shows the resolution of the smallest, robust fixed window algorithm in order to give a reference.
+shows the resolution of the smallest existing robust fixed window algorithm in order to give the reference 
+value of 2.5 and 3 photo-electrons RMS.
+\par
 One can see that the bias $B$ typically decreases 
 with increasing window size (except for the digital filter), while the error $R$ increases with 
@@ -308 +310 @@
 at 4 slices. The global winners are extractors \#25 (spline with integration of 1 slice) and \#29 
 (digital filter with integration of 4 slices). All sliding window extractors -- except \#21 -- 
-have a smaller mean-square error than the resolution of the fixed window reference extractor.
+have a smaller mean-square error than the resolution of the fixed window reference extractor. This means 
+that the global error of the sliding window extractors is smaller than the one of the fixed window extractors
+even if the first have a bias.
 
 \begin{table}[htp]
@@ -328 +332 @@
 4   & Fixed Win. 8  & 1.2  & --  & 0.0 & 1.2  & 2.5  & --  & 0.0 &  2.5 & 3.0 &  -- & 0.0 & 3.0 \\   
 \hline                                                     
+--  & Slid. Win. 1  & 0.4  & 0.4 & 0.4 & 0.6  & 1.2  & 1.2 & 1.3 &  1.8 & 1.4 & 1.4 & 1.5 & 2.0 \\
 17  & Slid. Win. 2  & 0.5  & 0.5 & 0.4 & 0.6  & 1.4  & 1.4 & 1.2 &  1.8 & 1.6 & 1.6 & 1.5 & 2.2 \\
 18  & Slid. Win. 4  & 0.8  & 0.8 & 0.5 & 0.9  & 1.9  & 1.9 & 1.2 &  2.2 & 2.2 & 2.3 & 1.6 & 2.8 \\
@@ -346 +351 @@
 }
 \caption{The statistical parameters bias, resolution and mean error for the sliding window 
-algorithm. The first line displays the resolution of the smallest, robust fixed window extractor 
+algorithm. The first line displays the resolution of the smallest existing robust fixed--window extractor 
 for reference. All units in equiv. 
 photo-electrons, uncertainty: 0.1 phes. All extractors were allowed to move 5 FADC slices plus 
@@ -356 +361 @@
 \end{table}
 
-
-
-
-\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). 
+Figures~\ref{fig:sw:distped} through~\ref{fig:df:distped} show the 
+extracted pedestal distributions for some selected extractors (\#18, \#23, \#25 and \#28)
+ for one examplary channel (pixel 100) and two background situations: Closed camera with only electronic
+noise and open camera pointing to an extra-galactic source.
 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
+night sky background photons for the distributions with open camera.
 
 \begin{figure}[htp]
@@ -435 +434 @@
 \end{figure}
 
-\par
-
+\subsection{ \label{sec:ped:singlephe} Single Photo-Electron Extraction with the Digital Filter}
+
+Figures~\ref{fig:df:sphespectrum} show spectra 
+obtained with the digital filter applied on two different global search windows.
+One can clearly distinguish a pedestal peak (fitted to Gaussian with index 0)
+and further, positive contributions.
+\par
 Because the background is determined by the single photo-electrons from the night-sky background,
 the following possibilities can occur:
@@ -444 +448 @@
 finds only electronic noise. 
 Usually, the returned signal charge is then negative.
-\item The extractor finds the signal from one photo-electron
+\item There is one photo-electron in the extraction window and the extractor finds it.
+\item There are more than on photo-electrons in the extraction window, but separated by more than 
+two FADC slices whereupon the extractor finds the one with the highest charge (upward fluctuation).
 \item The extractor finds an overlap of two or more photo-electrons.
 \end{enumerate}
@@ -460 +466 @@
 Given a global extraction window of size $WS$ and an average rate of photo-electrons from the night-sky 
 background $R$, we will now calculate the probability for the extractor to find zero photo-electrons in the 
-$WS$. The probability to find $k$ photo-electrons can be written as:
+$WS$. The probability to find any number of $k$ photo-electrons can be written as:
 
 \begin{equation}
@@ -472 +478 @@
 \end{equation}
 
-The probability to find more than one photo-electron is then:
+The probability to find one or more photo-electrons is then:
 
 \begin{equation}
@@ -478 +484 @@
 \end{equation}
 
-Figures~\ref{fig:sphe:sphespectrum} show spectra 
-obtained with the digital filter applied on two different global search windows.
-One can clearly distinguish a pedestal peak (fitted to Gaussian with index 0), 
+In figures~\ref{fig:df:sphespectrum},
+one can clearly distinguish the pedestal peak (fitted to Gaussian with index 0), 
 corresponding to the case of  $P(0)$ and further 
 contributions of $P(1)$ and $P(2)$ (fitted to Gaussians with index 1 and 2). 
@@ -518 +523 @@
 
 We estimated the effective window size $WS$ as the sum of the range in which the digital filter 
-amplitude weights are greater than 0.5 (1.6 FADC slices) and the global search window minus the 
-size of the window size of the weights (which is 6 FADC slices). Figures~\ref{fig::df:ratiofit}
-show the result for two different levels of night-sky background.
-
+amplitude weights are greater than 0.5 (1.5 FADC slices) and the global search window minus the 
+size of the window size of the weights (which is 6 FADC slices). Figures~\ref{fig:df:ratiofit}
+show the result for two different levels of night-sky background. The fitted rates deliver 
+0.08 and 0.1 phes/ns, respectively. These rates are about 50\% too low compared to the results obtained 
+in the November 2004 test campaign. However, we should take into account that the method is at 
+the limit of distinguishing single photo-electrons. It may occur often that a single photo-electron 
+signal is too low in order to get recognized as such. We tried various pixels and found that 
+some of them do not permit to apply this method at all. The ones which succeed, however, yield about 
+the same fitted rates. To conclude, one may say that there is consistency within the double-peak 
+structure of the pedestal spectrum found by the digital filter which can be explained by the fact that 
+single photo-electrons are found. 
 \par
 
@@ -534 +546 @@
 In the top plot, a pedestal run with extra-galactic star background has been taken and in the bottom, 
 a galatic star background. An exemplary pixel (Nr. 100) has been used.
-Above, a rate of 0.8 phe/ns and below, a rate of 1.0 phe/ns has been obtained.}
+Above, a rate of 0.08 phe/ns and below, a rate of 0.1 phe/ns has been obtained.}
 \label{fig:df:ratiofit}
+\end{figure}
+
+Figure~\ref{fig:df:convfit} shows the obtained ``conversion factors'' and ``F-Factor'' computed as: 
+
+\begin{eqnarray}
+c_{phe} &=& \frac{1}{\mu_1 - \mu_0} \\
+F_{phe} &=& \sqrt{1 + \frac{\sigma_1^2 - \sigma_0^2}{(\mu_1 - \mu_0)^2} }
+\end{eqnarray}
+
+where $\mu_0$ is the mean position of the pedestal peak and $\mu_1$ the mean position of the (assumed) 
+single photo-electron peak. The obtained conversion factors are systematically lower than the ones 
+obtained from the standard calibration and decrease with increasing window size. This is consistent 
+with the assumption that the digital filter finds the upward fluctuating pulse out of several. Therefore,
+$\mu_1$ is biased against higher values. The F-Factor is also systematically low, which is also consistent 
+with the assumption that the spacing between $\mu_1$ and $\mu_0$ is artificially high. One can also see 
+that the error bars are too high for a ``calibration'' of the F-Factor. 
+\par
+In conclusion, one can say that the digital filter is at the edge of being able to see single photo-electrons, 
+however a single photo-electron calibration cannot yet be done with the current FADC system because the 
+resolution is too poor.
+
+\begin{figure}[htp]
+\centering
+\includegraphics[height=0.4\textheight]{ConvFactor-28-Run38995.eps}
+\vspace{\floatsep}
+\includegraphics[height=0.4\textheight]{FFactor-28-Run38995.eps}
+\caption{MExtractTimeAndChargeDigitalFilter: Obtained conversion factors (top) and F-Factors (bottom)
+from the position and width of 
+the fitted Gaussian mean of the single photo-electron peak and the pedestal peak depending on 
+the applied global extraction window sizes.
+A pedestal run with extra-galactic star background has been taken and 
+an exemplary pixel (Nr. 100) used. The conversion factor obtained from the 
+standard calibration is shown as a reference line. The obtained conversion factors are systematically
+lower than the reference one.}
+\label{fig:df:convfit}
 \end{figure}