Changeset 6527 for trunk/MagicSoft/TDAS-Extractor

Timestamp:

02/16/05 15:45:18 (20 years ago)

Author:

gaug

Message:

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File:

• trunk/MagicSoft/TDAS-Extractor/Calibration.tex (modified) (7 diffs)

trunk/MagicSoft/TDAS-Extractor/Calibration.tex

@@ -168 +168 @@
 \begin{figure}[htp]
 \centering
-\includegraphics[height=0.95\textheight]{UnsuitVsExtractor-5LedsUV-Colour-13.eps}
+\includegraphics[height=0.95\textheight]{UnsuitVsExtractor-5LedsUV-Colour-12.eps}
 \caption{Un-calibrated pixels and outlier events for a typical calibration  
 pulse of UV-light which does not saturate the high-gain readout.}
@@ -204 +204 @@
 \par
 In general, one can also find that all ``sliding window''-algorithms (extractors \#17-32) discard 
-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). 
-\par
-Also the ``spline'' algorithms on small  
-windows (extractors \#23--25) discard less pixels than the previous extractors.
-\par
-It seems also that the spline algorithm extracting the amplitude of the signal produces an over-proportional
-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.
+less pixels than the corresponding ``fixed window''-ones (extractors \#1--16). 
+
+The spline (extractors \#23--27) and the digital filter with the correct weights (extractors \#30-33) discard 
+the least number of pixels and are also robust against slight modifications of the pulse form 
+(of the weights for the digital filter). 
 \par
 Concerning the numbers of outliers, one can conclude that in general, the numbers are very low never exceeding
 0.1\% except for the amplitude-extracting spline which seems to mis-reconstruct a certain type of events.
+It seems however that the spline algorithm extracting the amplitude of the signal produces an over-proportional
 \par
 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 amplitude extracting spline produces a significantly higher number of outlier events.
 
 \clearpage
@@ -240 +226 @@
 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 signal $S$ 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 $F$.
+characterized by the excess-noise factor $F$:
 
 \begin{equation}
@@ -250 +236 @@
 
 After introducing the effect of the night-sky background (eq.~\ref{eq:rmssubtraction}) 
-in formula~\ref{eq:excessnoise} and assuming that the variance of the number of photo-electrons is equal 
+and assuming that the variance of the number of photo-electrons is equal 
 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 $<\widehat{S}>$, 
-its variance $Var(\widehat{S})$ and the RMS of the extracted signal obtained from 
+one obtains an expression to retrieve the mean number of photo-electrons  impinging on the photo-multiplier from the 
+mean extracted signal, $\widehat{S}$, and the RMS of the extracted signal obtained from 
 pure pedestal runs $R$ (see section~\ref{sec:ffactor}):
 
@@ -276 +261 @@
 \par
 Figures~\ref{fig:phe:5ledsuv},~\ref{fig:phe:1leduv},~\ref{fig:phe:2ledsgreen}~and~\ref{fig:phe:23ledsblue} show 
-some of the obtained results. Although one can see a rather good stability for the standard 
+some of the obtained results. One can see a rather good stability for the standard 
 {\textit{\bf 5\,Leds\,UV}}\ pulse, except for the extractors {\textit{\bf MExtractFixedWindowPeakSearch}}, initialized 
-with an extraction window of 2 slices and  {\textit{\bf MExtractTimeAndChargeDigitalFilter}}, initialized with 
-an extraction window of 4 slices (extractor \#29).
+with an extraction window of 2 slices.
 \par
 There is a considerable difference for all shown non-standard pulses. Especially the pulses from green 
@@ -289 +273 @@
 \par
 The strongest discrepancy is observed in the low-gain extraction (fig.~\ref{fig:phe:23ledsblue}) where all 
-fixed window extractors with too small extraction windows fail to reconstruct the correct numbers. 
+fixed window extractors with extraction windows smaller than 8 FADC slices fail to reconstruct the correct numbers. 
 This has to do with the fact that 
-the fixed window extractors fail to do catch a significant part of the (larger) pulse because of the 
-1~FADC slice event-to-event jitter.
+the fixed window extractors fail to catch a significant part of the (larger) pulse because of the 
+1~FADC slice event-to-event jitter. Also the sliding windows smaller than 6 FADC slices and the spline smaller than 
+2 FADC slices reproduce too small numbers of photo-electrons. Moreover, the digital filter shows a small dependency 
+of the number of photo-electrons w.r.t. the extration window.
+\par
 
 
@@ -345 +332 @@
 
 One can see that all extractors using a large window belong to the class of extractors being affected 
-by the secondary pulses, except for the digital filter. The only exception to this rule is the digital filter 
-which - despite of its 6 slices extraction window - seems to filter out all the secondary pulses. 
-\par
-The extractor {\textit{\bf MExtractFixedWindowPeakSearch}} at low extraction windows apparently yields chronically low 
-numbers of photo-electrons. This is due to the fact that the decision to fix the extraction window is 
-made sometimes by an inner pixel and sometimes by an outer one since the camera is flat-fielded and the 
-pixel carrying the largest non-saturated peak-search window is more or less found by a random signal 
-fluctuation. However, inner and outer pixels have a systematic offset of about 0.5 to 1 FADC slices. 
-Thus, the extraction fluctuates artificially for one given channel which results in a systematically 
-large variance and thus in a systematically low reconstructed number of photo-electrons. This test thus 
-excludes the extractors \#11--13.
-\par
-Moreover, one can see that the extractors applying a small fixed window do not get the ratio of 
-photo-electrons correctly between outer to inner pixels for the green and blue pulses. 
+by the secondary pulses, except for the digital filter. 
 \par
 The extractor {\textit{\bf MExtractTimeAndChargeDigitalFilter}} seems to be stable against modifications in the 
 exact form of the weights in the high-gain readout channel since all applied weights yield about 
-the same number of photo-electrons and the same ratio of outer vs. inner pixels. This statement does not 
-hold any more for the low-gain, as can be seen in figure~\ref{fig:phe:23ledsblue}. There, the application 
-of high-gain weights to the low-gain signal (extractors \#34--39) produces a too low number of photo-electrons
-and also a too low ratio of outer vs. inner pixels.
-\par
-All sliding window and spline algorithms yield a stable ratio of outer vs. inner pixels in the low-gain, 
-however the effect of raising the number of photo-electrons with the extraction window is very pronounced. 
-Note that in figure~\ref{fig:phe:23ledsblue}, the number of photo-electrons rises by about a factor 1.4, 
-which is slightly higher than in the case of the high-gain channel (figure~\ref{fig:phe:2ledsgreen}). 
-\par
-Concluding, there is no fixed window extractor yielding the correct number of photo-electrons 
-for the low-gain, except for the largest extraction window of 8 and 10 low-gain slices. 
+the same number of photo-electrons and the same ratio of outer vs. inner pixels, except if one applies the cosmics 
+weights to the very low-intensity pulse $1\,LED\,UV$ where a slight increase in photo-electrons is observed.
+\par
+All sliding window and spline algorithms yield a stable ratio of outer vs. inner pixels in the high and the low-gain. 
+\par
+Concluding, there is no fixed window extractor yielding always the correct number of photo-electrons, 
+except for the extraction window of 8 FADC slices. 
 Either the number of photo-electrons itself is wrong or the ratio of outer vs. inner pixels is 
 not correct. All sliding window algorithms seem to reproduce the correct numbers if one takes into 
 account the after-pulse behaviour of the light pulser itself. The digital filter seems to be 
-unstable against exchanging the pulse form to match the slimmer high-gain pulses, though.
-
-\par
-\ldots {\textit{\bf EXCLUDED : CW4, UV4 No stability High-gain vs. LoGain}}
-\par
+stable against exchanging the pulse width from 1~to~4\,ns.
 
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