Changeset 5787

Timestamp:

01/10/05 19:12:33 (20 years ago)

Author:

gaug

Message:

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File:

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

trunk/MagicSoft/TDAS-Extractor/Performance.tex

@@ -182 +182 @@
 add up more noise which in turn makes the for the small signal more difficult.
 \par
-In general, one can also say that all ``sliding window''-algorithms (extractors \#17-32) discard 
+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 
-the correct weights (extractor \#32) discards the least number of pixels, but is also robust against 
+the correct weights (extractor \#32) discards the least number of pixels and is also robust against 
 slight modifications of its weights (extractors \#28--31). Also the ``spline'' algorithms on small  
 windows (extractors \#23--25) discard less pixels than the previous extractors, although slightly more 
-then the digital filter.
-\par
-In the low-gain, there is one extractor discarding a too high amount of events which is the 
+than the digital filter.
+\par
+Particularly in the low-gain channel, 
+there is one extractor discarding a too high amount of events which is the 
 MExtractFixedWindowPeakSearch. The reason becomes clear when one keeps in mind that this extractor 
 defines its extraction window by searching for the highest signal found in a sliding peak search window
- looping only over {\textit non-saturating pixels}. In the case of an intense calibration pulse, only 
+ looping only over {\textit{non-saturating pixels}}. In the case of an intense calibration pulse, only 
 the dead pixels match this requirement and define thus an alleatory window fluctuating like the noise 
 does in these channels. It is clear that one cannot use this extractor for the intense calibration pulses. 
 \par
 It seems also that the spline algorithm extracting the amplitude of the signal produces an over-proportional
-number of excluded pixels in the low-gain. The same, however in a less significant manner, holds for 
+number of excluded events in the low-gain. The same, however in a less significant manner, holds for 
 the digital filter with high-low-gain inverted weights. The limit of stability with respect to 
 changes  in the pulse form seems to be reached, there.
@@ -204 +205 @@
 0.25\%. There seems to be the opposite trend of larger windows producing less 
 outliers. However, one has to take into account that already more ``unsuited'' pixels have 
-been excluded thus cleaning up the sample somewhat. It seems that the ``digital filter'' and a 
+been excluded thus cleaning up the sample of pixels somewhat. It seems that the ``digital filter'' and a 
 medium-sized ``spline'' (extractors \#25--26) yield the best result except for the outer pixels 
 in fig~\ref{fig:unsuited:5ledsuv} where the digital filter produces a worse result than the rest 
 of the extractors.
 \par
-In conclusion, one can say that this test excludes all extractors with too big window sizes because 
-they are not able to extract small signals produced by about 4 photo-electrons. The excluded extractors 
-are:
+In conclusion, already this first test excludes all extractors with too big 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
@@ -233 +235 @@
 \subsubsection{Number of Photo-Electrons \label{sec:photo-electrons}}
 
-Assuming that the readout chain is clean and adds only negligible noise with respect to the one 
-introduced by the photo-multiplier itself, one can make the assumption that variance of the 
-true (non-extracted) signal $ST$ is the amplified Poisson variance on the number of photo-electrons, 
-multiplied with the excess noise of the photo-multiplier, characterized by the excess-noise factor $F$.
+Assuming that the readout chain is clean and 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, 
+multiplied with the excess noise of the photo-multiplier which itself is 
+characterized by the excess-noise factor $F$.
 
 \begin{equation}
@@ -245 +248 @@
 After introducing the effect of the night-sky background (eq.~\ref{eq:rmssubtraction}) 
 in formula~\ref{eq:excessnoise} and assuming that the number of photo-electrons per event follows a 
-Poisson distribution, one can 
-get an expression to retrieve the mean number of photo-electrons impinging on the pixel from 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 
 pure pedestal runs $R$ (see section~\ref{sec:determiner}):
 
 \begin{equation}
-<N_{phe}> \approx F^2 \cdot \frac{Var(SE) - R^2}{<SE>^2}
+<N_{phe}> \approx F^2 \cdot \frac{<SE>^2}{Var(SE) - R^2}
 \label{eq:pheffactor}
 \end{equation}
 
-Equation~\ref{eq:pheffactor} must not depend on the extractor! Effectively, we will use it to test the 
+In theory, eq.~\ref{eq:pheffactor} must not depend on the extractor! Effectively, we will use it to test the 
 quality of our extractors by requiring that a valid extractor yields the same number of photo-electrons 
 for all pixels of a same type and does not deviate from the number obtained with other extractors. 
@@ -261 +264 @@
 different, we also use the ratio of the mean numbers of photo-electrons from the outer pixels to the one 
 obtained from the inner pixels as a test variable. In the ideal case, it should always yield its central 
-value of about 2.4--2.8.
+value of about 2.6$\pm$0.1~\cite{michele-diploma}.
 \par
 In our case, there is an additional complication due to the fact that the green and blue coloured pulses