- Timestamp:
- 02/23/05 16:33:26 (20 years ago)
- Location:
- trunk/MagicSoft/TDAS-Extractor
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- 2 edited
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Calibration.tex (modified) (18 diffs)
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Criteria.tex (modified) (1 diff)
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trunk/MagicSoft/TDAS-Extractor/Calibration.tex
r6650 r6666 90 90 \par 91 91 Although we had looked at and tested all colour and extractor combinations resulting from these data, 92 we re frainourselves to show here only exemplary behaviour and results of extractors.92 we restrict ourselves to show here only exemplary behaviour and results of extractors. 93 93 All plots, including those which are not displayed in this TDAS, can be retrieved from the following 94 94 locations: … … 107 107 108 108 \begin{enumerate} 109 \item The reconstructed mean signal is less than 2.5 times the extractor resolution $R$ from zero.109 \item The reconstructed mean signal $\widehat{Q}$ is less than 2.5 times the extractor resolution $R$: $\widehat{Q}<2.5\cdot R$. 110 110 (2.5 Pedestal RMS in the case of the simple fixed window extractors, see section~\ref{sec:pedestals}). 111 111 This criterium essentially cuts out 112 112 dead pixels. 113 \item The reconstructed mean signal error is smaller than its value. This criterium cuts out 113 \item The error of the mean reconstructed signal $\delta \widehat{Q}$ is larger than the mean reconstructed signal $\widehat{Q}$: 114 $\delta \widehat{Q} > \widehat{Q}$. This criterion cuts out 114 115 signal distributions which fluctuate so much that their RMS is bigger than its mean value. This 115 116 criterium cuts out ``ringing'' pixels or mal-functioning extractors. … … 121 122 \item All pixels with reconstructed negative mean signal or with a 122 123 mean numbers of photo-electrons smaller than one. Pixels with a negative pedestal RMS subtracted 123 sigma occur, especially when stars are focused onto that pixel during the pedestal taking(resulting124 sigma occur, especially when stars are focused onto that pixel during the pedestal run (resulting 124 125 in a large pedestal RMS), but have moved to another pixel during the calibration run. In this case, the 125 126 number of photo-electrons would result artificially negative. If these … … 129 130 130 131 Moreover, the number of events are counted which have been reconstructed outside a 5$\sigma$ region 131 from the mean signal . These events are called ``outliers''. Figure~\ref{fig:outlier} shows a typical132 from the mean signal $<\widehat{Q}>$. These events are called ``outliers''. Figure~\ref{fig:outlier} shows a typical 132 133 outlier obtained with the digital filter applied on a low-gain signal, and figure~\ref{fig:unsuited:all} 133 134 shows the average number of all excluded pixels and outliers obtained from all 19 calibration configurations. … … 229 230 230 231 \begin{equation} 231 Var (S) = F^2 \cdot Var(N_{phe})\cdot \frac{<S>^2}{<N_{phe}>^2}232 Var[S] = F^2 \cdot Var[N_{phe}] \cdot \frac{<S>^2}{<N_{phe}>^2} 232 233 \label{eq:excessnoise} 233 234 \end{equation} … … 236 237 and assuming that the variance of the number of photo-electrons is equal 237 238 to the mean number of photo-electrons (because of the Poisson distribution), 238 one obtains an expression to retrieve the mean number of photo-electrons impinging on the photo-multiplierfrom the239 one obtains an expression to retrieve the mean number of photo-electrons released at the photo-multiplier cathode from the 239 240 mean extracted signal, $\widehat{S}$, and the RMS of the extracted signal obtained from 240 241 pure pedestal runs $R$ (see section~\ref{sec:ffactor}): 241 242 242 243 \begin{equation} 243 <N_{phe}> \approx F^2 \cdot \frac{<\widehat{S}>^2}{Var (\widehat{S})- R^2}244 <N_{phe}> \approx F^2 \cdot \frac{<\widehat{S}>^2}{Var[\widehat{S}] - R^2} 244 245 \label{eq:pheffactor} 245 246 \end{equation} … … 247 248 In theory, eq.~\ref{eq:pheffactor} must not depend on the extractor! Effectively, we will use it to test the 248 249 quality of our extractors by requiring that a valid extractor yields the same number of photo-electrons 249 for all pixels of a same typeand does not deviate from the number obtained with other extractors.250 for all pixels individually and does not deviate from the number obtained with other extractors. 250 251 As the camera is flat-fielded, but the number of photo-electrons impinging on an inner and an outer pixel is 251 252 different, we also use the ratio of the mean numbers of photo-electrons from the outer pixels to the one … … 265 266 There is a considerable difference for all shown non-standard pulses. Especially the pulses from green 266 267 and blue LEDs 267 show a clear dependenc yof the number of photo-electrons on the extraction window. Only the largest268 show a clear dependence of the number of photo-electrons on the extraction window. Only the largest 268 269 extraction windows seem to catch the entire range of (jittering) secondary pulses and get the ratio 269 270 of outer vs. inner pixels right. However, they (obviously) over-estimate the number of photo-electrons … … 384 385 Figure~\ref{fig:linear:phevscharge4} shows the conversion factor $c_{phe}$ obtained for different light intensities 385 386 and colours for three exemplary inner and three exemplary outer pixels using a fixed window on 386 8 FADC slices. The conversion factor seems to be linear to a good approximation, 387 except for two cases: 387 8 FADC slices. The conversion factor seems to be linear to a good approximation, with the following restrictions: 388 388 \begin{itemize} 389 389 \item The green pulses yield systematically low conversion factors … … 394 394 \end{itemize} 395 395 396 We conclude that, apart from the two reasons above,396 We conclude that, with the above restrictions, 397 397 the fixed window extractor \#4 is a linear extractor for both high-gain 398 398 and low-gain regions, separately. … … 402 402 using an integrated spline and a fixed window with global peak search, respectively, over 403 403 an extraction window of 8 FADC slices. The same behaviour is obtained as before. These extractors are 404 linear to a good approximation, except for the two cases mention ned above.404 linear to a good approximation, except for the two cases mentioned above. 405 405 \par 406 406 … … 447 447 \par 448 448 Figure~\ref{fig:linear:phevscharge20} shows the conversion factors using a sliding window of 6 FADC slices. 449 The linearity is maintained like in the previous examples, except for the smallest signals the effect449 The linearity is maintained like in the previous examples, except that for the smallest signals the effect 450 450 of the bias is already visible. 451 451 \par … … 463 463 Figure~\ref{fig:linear:phevscharge23} shows the conversion factors using the amplitude-extracting spline 464 464 (extractor \#23). 465 Here, the linearity is worse than in the previous sample. A very clear difference between high-gain and465 Here, the linearity is worse than in the previous examples. A very clear difference between high-gain and 466 466 low-gain regions can be seen as well as a bigger general spread in conversion factors. In order to investigate 467 467 if there is a common, systematic effect of the extractor, we show the averaged conversion factors over all … … 514 514 515 515 Looking at figure~\ref{fig:linear:phevscharge25}, one can see that raising the integration window 516 totwo effective FADC slices in the high-gain and three effective FADC slices in the low-gain516 by two effective FADC slices in the high-gain and three effective FADC slices in the low-gain 517 517 (extractor \#25), the stability is completely resumed, except for 518 518 a systematic increase of the conversion factor above 200 photo-electrons. … … 545 545 expected one. The effect is not as problematic as it may appear here, because the actual calibration 546 546 will not calculate the number of photo-electrons (with the F-Factor method) for every signal intensity. 547 Thus, one possible reason for the instability falls awayin the cosmics analysis. However, the limits547 Thus, one possible reason for the instability is not relevant in the cosmics analysis. However, the limits 548 548 of this extraction are visible here and should be monitored further. 549 549 … … 590 590 591 591 The calibration LEDs 592 deliver afast-rising pulses, uniform over the camera in signal size and time.593 We estimate the time-uniformity to better594 than 300\,ps, a limit due to the different travel times of the light between inner and outer parts of the 595 camera. 596 592 deliver fast-rising pulses, uniform over the camera in signal size and time. 593 We estimate the time-uniformity to as good as about~30\,ps, a limit due to the different travel times of the light 594 from the light source to the inner and outer parts of the camera. For cosmics data, however, the staggering of the 595 mirrors limits the time uniformity to about 600\,ps. 596 \par 597 597 The extractors \#17--33 are able to compute the arrival time of each pulse. 598 598 Since the calibration does not permit a precise measurement of the absolute arrival time, we measure … … 609 609 systematic delays in the signal travel time, and a sigma $\sigma(\delta t_i)$, a measure of the 610 610 combined time resolutions of pixel $i$ and pixel 1. Assuming that the PMTs and readout channels are 611 of asame kind, we obtain an approximate time resolution of pixel $i$:611 of the same kind, we obtain an approximate time resolution of pixel $i$: 612 612 613 613 \begin{equation} … … 649 649 (fig.~\ref{fig:reltimesinnerledblue2} bottom), the distribution is perfectly Gaussian and the resolution good, 650 650 however a rather slight change from the blue calibration pulse weights to cosmics pulses weights (top) 651 adds a secondary peak of events with mis-reconstructed arrival times. 651 adds a secondary peak of events with mis-reconstructed arrival times. In principle, the $\chi^2$ of the digital filter 652 fit gives an information about whether the correct shape has been used. 652 653 653 654 \begin{figure}[htp] -
trunk/MagicSoft/TDAS-Extractor/Criteria.tex
r6640 r6666 30 30 \subsection{Bias and Mean-squared Error} 31 31 32 Consider a large number of same signals $S$. By applying a signal extractor32 Consider a large number of identical signals $S$, corresponding to a fixed number of photo-electrons. By applying a signal extractor 33 33 we obtain a distribution of estimated signals $\widehat{S}$ (for fixed $S$ and 34 34 fixed background fluctuations $BG$). The distribution of the quantity
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