Changeset 5995 for trunk/MagicSoft/TDAS-Extractor/Performance.tex
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trunk/MagicSoft/TDAS-Extractor/Performance.tex
r5919 r5995 7 7 \par 8 8 The LED pulser system is able to provide fast light pulses of 3--4\,ns FWHM 9 with intensities ranging from 3--4 photo-electrons to more than 500 in one inner pixel of the 10 camera. These pulses can be produced in three colours $green$, $blue$ and $UV$. 9 with intensities ranging from 3--4 to more than 500 photo-electrons in one inner photo-multiplier of the 10 camera. These pulses can be produced in three colours {\textit {\bf green, blue}} and 11 {\textit{\bf UV}}. 11 12 12 13 \begin{table}[htp] … … 82 83 83 84 We used data taken on the 7$^{th}$ of June, 2004 with different pulser LED combinations, each taken with 84 16384 events. The corresponding run numbers range from nr. 31741 to 31772. This data was taken before the85 latest camera repair access which resulted in a replacement of about 2\% of the pixels known to be85 16384 events. The corresponding MAGIC data run numbers range from nr. 31741 to 31772. These data was taken 86 before the latest camera repair access which resulted in a replacement of about 2\% of the pixels known to be 86 87 mal-functionning at that time. 87 Th us, there is a lower limit to the number of un-calibrated pixels of about 1.5--2\%known88 mal-functionning p ixels.88 There is thus a lower limit to the number of un-calibrated pixels of about 1.5--2\% of known 89 mal-functionning photo-multipliers. 89 90 \par 90 91 Although we had looked at and tested all colour and extractor combinations resulting from these data, … … 103 104 104 105 The MAGIC calibration software incorporates a series of checks to sort out mal-functionning pixels. 105 Except for the software bug searching criteria, the following exclusion reasonscan apply:106 Except for the software bug searching criteria, the following exclusion criteria can apply: 106 107 107 108 \begin{enumerate} … … 116 117 the distribution of photo-electrons obtained with the inner or outer pixels in the camera, respectively. 117 118 This criterium cuts out pixels channels with apparently deviating (hardware) behaviour compared to 118 the rest of the camera readout. 119 the rest of the camera readout\footnote{This criteria is not applied any more in the standard analysis, 120 although here, we kept using it}. 119 121 \item All pixels with reconstructed negative mean signal or with a 120 122 mean numbers of photo-electrons smaller than one. Pixels with a negative pedestal RMS subtracted … … 142 144 The following figures~\ref{fig:unsuited:5ledsuv},~\ref{fig:unsuited:1leduv},~\ref{fig:unsuited:2ledsgreen} 143 145 and~\ref{fig:unsuited:23ledsblue} show the resulting numbers of un-calibrated pixels and events for 144 different colours and intensities. 146 different colours and intensities. Because there is a strong anti-correlation between the number of 147 excluded channels and the number of outliers per event, we have chosen to show these numbers together. 145 148 146 149 \par … … 178 181 One can see that in general, big extraction windows raise the 179 182 number of un-calibrated pixels and are thus less stable. Especially for the very low-intensity 180 $1Led\,UV$-pulse, the big extraction windows summing 8 or more slices, cannot calibrate more than 50\% 183 \textit{\bf 1Led\,UV}-pulse, the big extraction windows summing 8 or more slices, cannot calibrate more 184 than 50\% 181 185 of the inner pixels (fig.~\ref{fig:unsuited:1leduv}). This is an expected behavior since big windows 182 add up more noise which in turn makes the for the small signal more difficult. 186 add up more noise which in turn makes the search for the small signal more difficult. 187 \par 188 \ldots {\bf WHICH EXTRACTOR HAS THE LEAST NUMBER OF EXCLUDED PIXELS ???} 183 189 \par 184 190 In general, one can also find that all ``sliding window''-algorithms (extractors \#17-32) discard 185 191 less pixels than the ``fixed window''-ones (extractors \#1--16). The digital filter with 186 the correct weights (extractor \#32) discards the least number of pixels and is also robust against 187 slight modifications of its weights (extractors \#28--31). Also the ``spline'' algorithms on small 188 windows (extractors \#23--25) discard less pixels than the previous extractors, although slightly more 189 than the digital filter. 190 \par 191 Particularly in the low-gain channel, 192 there is one extractor discarding a too high amount of events which is the 193 MExtractFixedWindowPeakSearch. The reason becomes clear when one keeps in mind that this extractor 194 defines its extraction window by searching for the highest signal found in a sliding peak search window 195 looping only over {\textit{non-saturating pixels}}. In the case of an intense calibration pulse, only 196 the dead pixels match this requirement and define thus an alleatory window fluctuating like the noise 197 does in these channels. It is clear that one cannot use this extractor for the intense calibration pulses. 192 the correct weights (extractors \#30-33) discards the least number of pixels and is also robust against 193 slight modifications of its weights (extractors \#28--30). The robustness gets lost when the high-gain and 194 low-gain weights are inverted (extractors \#31--39, see fig.~\ref{fig:unsuited:23ledsblue}). 195 \par 196 Also the ``spline'' algorithms on small 197 windows (extractors \#23--25) discard less pixels than the previous extractors. 198 198 \par 199 199 It seems also that the spline algorithm extracting the amplitude of the signal produces an over-proportional … … 203 203 \par 204 204 Concerning the numbers of outliers, one can conclude that in general, the numbers are very low never exceeding 205 0.25\%. There seems to be the opposite trend of larger windows producing less 206 outliers. However, one has to take into account that already more ``unsuited'' pixels have 207 been excluded thus cleaning up the sample of pixels somewhat. It seems that the ``digital filter'' and a 208 medium-sized ``spline'' (extractors \#25--26) yield the best result except for the outer pixels 209 in fig~\ref{fig:unsuited:5ledsuv} where the digital filter produces a worse result than the rest 210 of the extractors. 205 0.1\% except for the ampltiude-extracting spline which seems to mis-reconstruct a certain type of events. 211 206 \par 212 207 In conclusion, already this first test excludes all extractors with too big window sizes because … … 216 211 \begin{itemize} 217 212 \item: MExtractFixedWindow Nr. 3--5 218 \item: MExtractFixedWindowSpline Nr. 6--11 213 \item: MExtractFixedWindowSpline Nr. 6--11 (all) 219 214 \item: MExtractFixedWindowPeakSearch Nr. 14--16 220 215 \item: MExtractTimeAndChargeSlidingWindow Nr. 21--22 221 \item: MExtractTimeAndChargeSpline Nr. 2 7216 \item: MExtractTimeAndChargeSpline Nr. 23 and 27 222 217 \end{itemize} 223 218 224 The best extractors after this test are:225 \begin{itemize}226 \item: MExtractFixedWindow Nr. 1--2227 \item: MExtractFixedWindowPeakSearch Nr. 13228 \item: MExtractTimeAndChargeSlidingWindow Nr. 17--19229 \item: MExtractTimeAndChargeSpline Nr. 24--25230 \item: MExtractTimeAndChargeDigitalFilter Nr. 28--32231 \end{itemize}232 233 219 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 234 220 235 221 \subsubsection{Number of Photo-Electrons \label{sec:photo-electrons}} 236 222 237 Assuming that the readout chain is clean andadds only negligible noise to the one223 Assuming that the readout chain adds only negligible noise to the one 238 224 introduced by the photo-multiplier itself, one can make the assumption that the variance of the 239 225 true (non-extracted) signal $ST$ is the amplified Poisson variance of the number of photo-electrons, … … 247 233 248 234 After introducing the effect of the night-sky background (eq.~\ref{eq:rmssubtraction}) 249 in formula~\ref{eq:excessnoise} and assuming that the number of photo-electrons per event follows a250 Poisson distribution, one obtains an expression to retrieve the mean number of photo-electrons251 impinging on the pixel from the235 in formula~\ref{eq:excessnoise} and assuming that the variance of the number of photo-electrons is equal 236 to the mean number of photo-electrons (because of the Poisson distribution), 237 one obtains an expression to retrieve the mean number of photo-electrons impinging on the pixel from the 252 238 mean extracted signal $<SE>$, its variance $Var(SE)$ and the RMS of the extracted signal obtained from 253 239 pure pedestal runs $R$ (see section~\ref{sec:determiner}): … … 267 253 \par 268 254 In our case, there is an additional complication due to the fact that the green and blue coloured light pulses 269 show secondary pulses which destroy the Poisson behaviour of the number of photo-electrons. We will thus255 show secondary pulses which destroy the Poisson behaviour of the number of photo-electrons. We will 270 256 have to split our sample of extractors into those being affected by the secondary pulses and those 271 257 being immune to this effect. 272 258 \par 273 259 Figures~\ref{fig:phe:5ledsuv},~\ref{fig:phe:1leduv},~\ref{fig:phe:2ledsgreen}~and~\ref{fig:phe:23ledsblue} show 274 some of the obtained results. Although one can see an amazing stability for the standard 5\,Leds\,UV pulse, 275 there is a considerable difference for all shown non-standard pulses. Especially the pulses from green 260 some of the obtained results. Although one can see a rather good stability for the standard 261 {\textit{\bf 5\,Leds\,UV}}\ pulse, except for the extractors {\textit{\bf MExtractFixedWindowPeakSearch}}, initialized 262 with an extraction window of 2 slices and {\textit{\bf MExtractTimeAndChargeDigitalFilter}}, initialized with 263 an extraction window of 4 slices (extractor \#29). 264 \par 265 There is a considerable difference for all shown non-standard pulses. Especially the pulses from green 276 266 and blue LEDs 277 267 show a clear dependency of the number of photo-electrons on the extraction window. Only the largest … … 281 271 \par 282 272 The strongest discrepancy is observed in the low-gain extraction (fig.~\ref{fig:phe:23ledsblue}) where all 283 fixed window extractors essentially fail to reconstruct the correct numbers. This has to do with the fact284 that the tail of the high-gain pulse is usually very close to the low-gain one and thus, the extraction range 285 has to be determined with great precision, what the fixed window extractors fail to do due because of the273 fixed window extractors with too small extraction windows fail to reconstruct the correct numbers. 274 This has to do with the fact that 275 the fixed window extractors fail to do catch a significant part of the (larger) pulse because of the 286 276 1~FADC slice event-to-event jitter. 287 277 … … 337 327 338 328 One can see that all extractors using a large window belong to the class of extractors being affected 339 by the secondary pulses. The only exception to this rule is the digital filter which - despite of its 340 6 slices extraction window - seems to filter out all the secondary pulses. 341 \par 342 Moreover, one can see in fig.~\ref{fig:phe:1leduv} that all peak searching extractors show the influence of 343 the bias at low numbers of photo-electrons. 344 \par 345 The extractor MExtractFixedWindowPeakSearch at low extraction windows apparently yields chronically low 329 by the secondary pulses, except for the digital filter. The only exception to this rule is the digital filter 330 which - despite of its 6 slices extraction window - seems to filter out all the secondary pulses. 331 \par 332 The extractor \textit{\bf MExtractFixedWindowPeakSearch}} at low extraction windows apparently yields chronically low 346 333 numbers of photo-electrons. This is due to the fact that the decision to fix the extraction window is 347 334 made sometimes by an inner pixel and sometimes by an outer one since the camera is flat-fielded and the … … 355 342 photo-electrons correctly between outer to inner pixels for the green and blue pulses. 356 343 \par 357 The extractor MExtractTimeAndChargeDigitalFilterseems to be stable against modifications in the344 The extractor \textit{\bf MExtractTimeAndChargeDigitalFilter}} seems to be stable against modifications in the 358 345 exact form of the weights in the high-gain readout channel since all applied weights yield about 359 346 the same number of photo-electrons and the same ratio of outer vs. inner pixels. This statement does not 360 347 hold any more for the low-gain, as can be seen in figure~\ref{fig:phe:23ledsblue}. There, the application 361 of high-gain weights to the low-gain signal (extractors \#3 0--31) produces a too low number of photo-electrons348 of high-gain weights to the low-gain signal (extractors \#34--39) produces a too low number of photo-electrons 362 349 and also a too low ratio of outer vs. inner pixels. 363 350 \par … … 368 355 \par 369 356 Concluding, there is no fixed window extractor yielding the correct number of photo-electrons 370 for the low-gain, except for the largest extraction window of 10 low-gain slices.357 for the low-gain, except for the largest extraction window of 8 and 10 low-gain slices. 371 358 Either the number of photo-electrons itself is wrong or the ratio of outer vs. inner pixels is 372 359 not correct. All sliding window algorithms seem to reproduce the correct numbers if one takes into … … 374 361 unstable against exchanging the pulse form to match the slimmer high-gain pulses, though. 375 362 363 \par 364 \ldots {\textit{\bf EXCLUDED : CW4, UV4 No stability High-gain vs. LoGain}} 365 \par 376 366 377 367 \subsubsection{Linearity Tests} … … 454 444 exemplary inner pixels (upper plots) and two exemplary outer ones (lower plots). 455 445 A digital filter extractor on a window size of 6 high-gain and 6 low-gain slices has been used 456 (extractor \#32). }446 with UV-weights (extractor \#30). } 457 447 \label{fig:linear:phevscharge30} 458 448 \end{figure} … … 464 454 exemplary inner pixels (upper plots) and two exemplary outer ones (lower plots). 465 455 A digital filter extractor on a window size of 4 high-gain and 4 low-gain slices has been used 466 (extractor \#3 2). }456 (extractor \#31). } 467 457 \label{fig:linear:phevscharge31} 468 458 \end{figure} … … 532 522 one typical inner and one typical outer pixel and a high-gain-saturating calibration pulse of blue-light, 533 523 obtained with two different extractors. One can see that the first (extractor \#23) yields a Gaussian 534 distribution to a good approximation, whereas the second (extractor \#32) shows a two-peak structure 535 and cannot be fitted. 536 \par 537 \ldots {\it Unfortunately, this happens for all digital filter extractors in the low-gain. 538 The reason is not yet understood, and has to be found by Hendrik... } \ldots 539 \par 524 distribution to a good approximation. 540 525 541 526 \begin{figure}[htp]
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