Index: trunk/MagicSoft/TDAS-Extractor/Changelog =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Changelog (revision 5994) +++ trunk/MagicSoft/TDAS-Extractor/Changelog (revision 5995) @@ -22,5 +22,5 @@ 2004/01/26: Markus Gaug * Algorithms.tex: text updated and new figures - + * Performance.tex: text updated and new figures 2004/01/18: Markus Gaug Index: trunk/MagicSoft/TDAS-Extractor/Performance.tex =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Performance.tex (revision 5994) +++ trunk/MagicSoft/TDAS-Extractor/Performance.tex (revision 5995) @@ -7,6 +7,7 @@ \par The LED pulser system is able to provide fast light pulses of 3--4\,ns FWHM -with intensities ranging from 3--4 photo-electrons to more than 500 in one inner pixel of the -camera. These pulses can be produced in three colours $green$, $blue$ and $UV$. +with intensities ranging from 3--4 to more than 500 photo-electrons in one inner photo-multiplier of the +camera. These pulses can be produced in three colours {\textit {\bf green, blue}} and +{\textit{\bf UV}}. \begin{table}[htp] @@ -82,9 +83,9 @@ We used data taken on the 7$^{th}$ of June, 2004 with different pulser LED combinations, each taken with -16384 events. The corresponding run numbers range from nr. 31741 to 31772. This data was taken before the -latest camera repair access which resulted in a replacement of about 2\% of the pixels known to be +16384 events. The corresponding MAGIC data run numbers range from nr. 31741 to 31772. These data was taken +before the latest camera repair access which resulted in a replacement of about 2\% of the pixels known to be mal-functionning at that time. -Thus, there is a lower limit to the number of un-calibrated pixels of about 1.5--2\% known -mal-functionning pixels. +There is thus a lower limit to the number of un-calibrated pixels of about 1.5--2\% of known +mal-functionning photo-multipliers. \par Although we had looked at and tested all colour and extractor combinations resulting from these data, @@ -103,5 +104,5 @@ The MAGIC calibration software incorporates a series of checks to sort out mal-functionning pixels. -Except for the software bug searching criteria, the following exclusion reasons can apply: +Except for the software bug searching criteria, the following exclusion criteria can apply: \begin{enumerate} @@ -116,5 +117,6 @@ the distribution of photo-electrons obtained with the inner or outer pixels in the camera, respectively. This criterium cuts out pixels channels with apparently deviating (hardware) behaviour compared to -the rest of the camera readout. +the rest of the camera readout\footnote{This criteria is not applied any more in the standard analysis, +although here, we kept using it}. \item All pixels with reconstructed negative mean signal or with a mean numbers of photo-electrons smaller than one. Pixels with a negative pedestal RMS subtracted @@ -142,5 +144,6 @@ The following figures~\ref{fig:unsuited:5ledsuv},~\ref{fig:unsuited:1leduv},~\ref{fig:unsuited:2ledsgreen} and~\ref{fig:unsuited:23ledsblue} show the resulting numbers of un-calibrated pixels and events for -different colours and intensities. +different colours and intensities. Because there is a strong anti-correlation between the number of +excluded channels and the number of outliers per event, we have chosen to show these numbers together. \par @@ -178,22 +181,19 @@ One can see that in general, big extraction windows raise the number of un-calibrated pixels and are thus less stable. Especially for the very low-intensity -$1Led\,UV$-pulse, the big extraction windows summing 8 or more slices, cannot calibrate more than 50\% +\textit{\bf 1Led\,UV}-pulse, the big extraction windows summing 8 or more slices, cannot calibrate more +than 50\% of the inner pixels (fig.~\ref{fig:unsuited:1leduv}). This is an expected behavior since big windows -add up more noise which in turn makes the for the small signal more difficult. +add up more noise which in turn makes the search for the small signal more difficult. +\par +\ldots {\bf WHICH EXTRACTOR HAS THE LEAST NUMBER OF EXCLUDED PIXELS ???} \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 -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 -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 -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. +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 +low-gain weights are inverted (extractors \#31--39, see fig.~\ref{fig:unsuited:23ledsblue}). +\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 @@ -203,10 +203,5 @@ \par Concerning the numbers of outliers, one can conclude that in general, the numbers are very low never exceeding -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 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. +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 @@ -216,24 +211,15 @@ \begin{itemize} \item: MExtractFixedWindow Nr. 3--5 -\item: MExtractFixedWindowSpline Nr. 6--11 +\item: MExtractFixedWindowSpline Nr. 6--11 (all) \item: MExtractFixedWindowPeakSearch Nr. 14--16 \item: MExtractTimeAndChargeSlidingWindow Nr. 21--22 -\item: MExtractTimeAndChargeSpline Nr. 27 +\item: MExtractTimeAndChargeSpline Nr. 23 and 27 \end{itemize} -The best extractors after this test are: -\begin{itemize} -\item: MExtractFixedWindow Nr. 1--2 -\item: MExtractFixedWindowPeakSearch Nr. 13 -\item: MExtractTimeAndChargeSlidingWindow Nr. 17--19 -\item: MExtractTimeAndChargeSpline Nr. 24--25 -\item: MExtractTimeAndChargeDigitalFilter Nr. 28--32 -\end{itemize} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsubsection{Number of Photo-Electrons \label{sec:photo-electrons}} -Assuming that the readout chain is clean and adds only negligible noise to the one +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, @@ -247,7 +233,7 @@ 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 obtains an expression to retrieve the mean number of photo-electrons -impinging on the pixel from the +in formula~\ref{eq:excessnoise} 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 $$, its variance $Var(SE)$ and the RMS of the extracted signal obtained from pure pedestal runs $R$ (see section~\ref{sec:determiner}): @@ -267,11 +253,15 @@ \par In our case, there is an additional complication due to the fact that the green and blue coloured light pulses -show secondary pulses which destroy the Poisson behaviour of the number of photo-electrons. We will thus +show secondary pulses which destroy the Poisson behaviour of the number of photo-electrons. We will have to split our sample of extractors into those being affected by the secondary pulses and those being immune to this effect. \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 an amazing stability for the standard 5\,Leds\,UV pulse, -there is a considerable difference for all shown non-standard pulses. Especially the pulses from green +some of the obtained results. Although 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). +\par +There is a considerable difference for all shown non-standard pulses. Especially the pulses from green and blue LEDs show a clear dependency of the number of photo-electrons on the extraction window. Only the largest @@ -281,7 +271,7 @@ \par The strongest discrepancy is observed in the low-gain extraction (fig.~\ref{fig:phe:23ledsblue}) where all -fixed window extractors essentially fail to reconstruct the correct numbers. This has to do with the fact -that the tail of the high-gain pulse is usually very close to the low-gain one and thus, the extraction range -has to be determined with great precision, what the fixed window extractors fail to do due because of the +fixed window extractors with too small extraction windows 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. @@ -337,11 +327,8 @@ One can see that all extractors using a large window belong to the class of extractors being affected -by the secondary pulses. 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 -Moreover, one can see in fig.~\ref{fig:phe:1leduv} that all peak searching extractors show the influence of -the bias at low numbers of photo-electrons. -\par -The extractor MExtractFixedWindowPeakSearch at low extraction windows apparently yields chronically low +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 @@ -355,9 +342,9 @@ photo-electrons correctly between outer to inner pixels for the green and blue pulses. \par -The extractor MExtractTimeAndChargeDigitalFilter seems to be stable against modifications in the +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 \#30--31) produces a too low number of photo-electrons +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 @@ -368,5 +355,5 @@ \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 10 low-gain slices. +for the low-gain, except for the largest extraction window of 8 and 10 low-gain 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 @@ -374,4 +361,7 @@ 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 \subsubsection{Linearity Tests} @@ -454,5 +444,5 @@ exemplary inner pixels (upper plots) and two exemplary outer ones (lower plots). A digital filter extractor on a window size of 6 high-gain and 6 low-gain slices has been used - (extractor \#32). } +with UV-weights (extractor \#30). } \label{fig:linear:phevscharge30} \end{figure} @@ -464,5 +454,5 @@ exemplary inner pixels (upper plots) and two exemplary outer ones (lower plots). A digital filter extractor on a window size of 4 high-gain and 4 low-gain slices has been used - (extractor \#32). } + (extractor \#31). } \label{fig:linear:phevscharge31} \end{figure} @@ -532,10 +522,5 @@ one typical inner and one typical outer pixel and a high-gain-saturating calibration pulse of blue-light, obtained with two different extractors. One can see that the first (extractor \#23) yields a Gaussian -distribution to a good approximation, whereas the second (extractor \#32) shows a two-peak structure -and cannot be fitted. -\par -\ldots {\it Unfortunately, this happens for all digital filter extractors in the low-gain. -The reason is not yet understood, and has to be found by Hendrik... } \ldots -\par +distribution to a good approximation. \begin{figure}[htp]