Changeset 6416 for trunk/MagicSoft/TDAS-Extractor

Timestamp:

02/12/05 19:03:47 (20 years ago)

Author:

gaug

Message:

*** empty log message ***

File:

• trunk/MagicSoft/TDAS-Extractor/Calibration.tex (modified) (5 diffs)

trunk/MagicSoft/TDAS-Extractor/Calibration.tex

@@ -202 +202 @@
 \par
 In general, one can also find that all ``sliding window''-algorithms (extractors \#17-32) discard 
-less pixels than the ``fixed window''-ones (extractors \#1--16). The digital filter with 
+less pixels than the corresponding ``fixed window''-ones (extractors \#1--16). The digital filter with 
 the correct weights (extractors \#30-33) discards the least number of pixels and is also robust against 
 slight modifications of its weights (extractors \#28--30). The robustness gets lost when the high-gain and 
@@ -218 +218 @@
 0.1\% except for the ampltiude-extracting spline which seems to mis-reconstruct a certain type of events.
 \par
-In conclusion, already this first test excludes all extractors with too big window sizes because 
+In conclusion, already this first test excludes all extractors with too large window sizes because 
 they are not able to extract cleanly small signals produced by about 4 photo-electrons. Moreover, 
 some extractors do not reproduce the signals as expected in the low-gain. 
-The excluded extractors are:
-\begin{itemize}
-\item: MExtractFixedWindow Nr. 3--5
-\item: MExtractFixedWindowSpline Nr. 6--11 (all)
-\item: MExtractFixedWindowPeakSearch Nr. 14--16
-\item: MExtractTimeAndChargeSlidingWindow Nr. 21--22
-\item: MExtractTimeAndChargeSpline Nr. 23 and 27
-\end{itemize}
+
+%The excluded extractors are:
+%\begin{itemize}
+%\item: MExtractFixedWindow Nr. 3--5
+%\item: MExtractFixedWindowSpline Nr. 6--11 (all)
+%\item: MExtractFixedWindowPeakSearch Nr. 14--16
+%\item: MExtractTimeAndChargeSlidingWindow Nr. 21--22
+%\item: MExtractTimeAndChargeSpline Nr. 23 and 27
+%\end{itemize}
+
+\clearpage
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -236 +239 @@
 Assuming that the readout chain adds only negligible noise to the one 
 introduced by the photo-multiplier itself, one can make the assumption that the variance of the 
-true (non-extracted) signal $ST$ is the amplified Poisson variance of the number of photo-electrons, 
+true signal $S$ is the amplified Poisson variance of the number of photo-electrons, 
 multiplied with the excess noise of the photo-multiplier which itself is 
 characterized by the excess-noise factor $F$.
 
 \begin{equation}
-Var(ST) = F^2 \cdot Var(N_{phe}) \cdot \frac{<ST>^2}{<N_{phe}>^2}
+Var(S) = F^2 \cdot Var(N_{phe}) \cdot \frac{<S>^2}{<N_{phe}>^2}
 \label{eq:excessnoise}
 \end{equation}
@@ -249 +252 @@
 to the mean number of photo-electrons (because of the Poisson distribution), 
 one obtains an expression to retrieve the mean number of photo-electrons  impinging on the pixel from the 
-mean extracted signal $<SE>$, its variance $Var(SE)$ and the RMS of the extracted signal obtained from 
+mean extracted signal $<\widehat{S}>$, 
+its variance $Var(\widehat{S})$ and the RMS of the extracted signal obtained from 
 pure pedestal runs $R$ (see section~\ref{sec:determiner}):
 
 \begin{equation}
-<N_{phe}> \approx F^2 \cdot \frac{<SE>^2}{Var(SE) - R^2}
+<N_{phe}> \approx F^2 \cdot \frac{<\widehat{S}>^2}{Var(\widehat{S}) - R^2}
 \label{eq:pheffactor}
 \end{equation}
@@ -471 +475 @@
 \end{figure}
 
-
+\clearpage
 
 \subsection{Time Resolution}