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trunk/MagicSoft/TDAS-Extractor/Calibration.tex (modified) (24 diffs)
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trunk/MagicSoft/TDAS-Extractor/Calibration.tex
r6623 r6629 370 370 371 371 As the photo-multiplier and the subsequent 372 optical transmission devices~\cite{david} is a linear device over a372 optical transmission devices~\cite{david} is a relatively linear device over a 373 373 wide dynamic range, the number of photo-electrons per charge has to remain constant over the tested 374 374 linearity region. … … 427 427 \begin{figure}[h!] 428 428 \centering 429 \includegraphics[width=0.99\linewidth]{PheVsCharge-1 1.eps}429 \includegraphics[width=0.99\linewidth]{PheVsCharge-14.eps} 430 430 \caption{Example of a the development of the conversion factor FADC counts to photo-electrons for three 431 431 exemplary inner pixels (upper plots) and three exemplary outer ones (lower plots) obtained with the extractor 432 432 {\textit{MExtractFixedWindowPeakSearch}} 433 on a window size of 2 high-gain and 2low-gain slices (extractor \#11). }433 on a window size of 6 high-gain and 6 low-gain slices (extractor \#11). } 434 434 \label{fig:linear:phevscharge11} 435 435 \end{figure} 436 436 437 437 Figure~\ref{fig:linear:phevscharge11} shows the conversion factors using a fixed window with global peak search 438 integrating a window of 2 FADC slices. One can see that the linearity is completely lost! Especially in the low-gain, 439 the reconstructed number of photo-electrons is much too low and the conversion factors bend down. A similiar behaviour can 440 be found for all extractors with window sizes smaller than 6 FADC slices, especially in the low-gain region. (This behaviour 438 integrating a window of 6 FADC slices. One can see that the linearity is completely lost above 300 photo-electrons in the 439 outer pixels. Especially in the low-gain, 440 the reconstructed mean charge is too low and the conversion factors bend down. We show this extractor especially because it has 441 been used in the analysis and to derive a Crab spectrum with the consequence that the spectrum bends down at high energies. We 442 suppose that the loss of linearity due to usage of this extractor is responsible for the encountered problems. 443 A similiar behaviour can be found for all extractors with window sizes smaller than 6 FADC slices, especially in the low-gain region. 444 This is understandable since the low-gain pulse covers at least 6 FADC slices. 445 (This behaviour 441 446 was already visible in the investigations on the number of photo-electrons in the previous section~\ref{sec:photo-electrons}). 442 447 \par … … 458 463 Figure~\ref{fig:linear:phevscharge23} shows the conversion factors using the amplitude-extracting spline 459 464 (extractor \#23). 460 Here, the linearity worse than in the previous sample. A very clear difference between high-gain and465 Here, the linearity is worse than in the previous sample. A very clear difference between high-gain and 461 466 low-gain regions can be seen as well as a bigger general spread in conversion factors. In order to investigate 462 467 if there is a common, systematic effect of the extractor, we show the averaged conversion factors over all 463 468 inner and outer pixels in figure~\ref{fig:linear:phevschargearea23}. Both characteristics are maintained 464 there. Although the differences between high-gain and low-gain c anbe easily corrected for, we conclude469 there. Although the differences between high-gain and low-gain could be easily corrected for, we conclude 465 470 that extractor \#23 is still unstable against the linearity tests. 466 471 \par … … 482 487 483 488 Figure~\ref{fig:linear:phevscharge24} shows the conversion factors using a spline integrating over 484 one effective FADC slice in the high-gain and 1.5 effective FADC slices in the low-gain (extractor \#24).489 one effective FADC slice in the high-gain and 1.5 effective FADC slices in the low-gain region (extractor \#24). 485 490 The same problems are found as with extractor \#23, however to a much lower extent. 486 491 The difference between high-gain and low-gain regions is less pronounced and the spread … … 488 493 Figure~\ref{fig:linear:phevschargearea24} shows already rather good stability except for the two 489 494 lowest intensity pulses in green and blue. We conclude that extractor \#24 is still un-stable, but 490 preferable to amplitude extractor.495 preferable to the amplitude extractor. 491 496 \par 492 497 … … 511 516 to two effective FADC slices in the high-gain and three effective FADC slices in the low-gain 512 517 (extractor \#25), the stability is completely resumed, except for 513 a small systematic increase of the conversion factor in the low-gain range. This effect 514 is not very significant, however it can be seen in five out of the 515 six tested channels. We conclude that extractor \#25 is almost as stable as the fixed window extractors. 518 a systematic increase of the conversion factor above 200 photo-electrons. 519 We conclude that extractor \#25 is almost as stable as the fixed window extractors. 516 520 \par 517 521 … … 534 538 535 539 Figure~\ref{fig:linear:phevscharge30} and~\ref{fig:linear:phevscharge31} show the conversion factors using a digital filter, 536 applied on 6 FADC slices and respectively 4 FADC slices with weights calculated from the UV-calibration pulse. 540 applied on 6 FADC slices and respectively 4 FADC slices with weights calculated from the UV-calibration pulse in the 541 high-gain region and from the blue calibration pulse in the low-gain region. 537 542 One can see that one or two blue calibration pulses at low and intermediate intensity fall 538 543 out of the linear region, moreover there is a small systematic offset between the high-gain and low-gain region. … … 541 546 will not calculate the number of photo-electrons (with the F-Factor method) for every signal intensity. 542 547 Thus, one possible reason for the instability falls away in the cosmics analysis. However, the limits 543 of this extraction are clearly visible here and have tobe monitored further.548 of this extraction are visible here and should be monitored further. 544 549 545 550 \par … … 584 589 \subsection{Relative Arrival Time Calibration} 585 590 586 The extractors \#17--33 are able to compute the arrival time of each pulse. Thecalibration LEDs591 The calibration LEDs 587 592 deliver a fast-rising pulses, uniform over the camera in signal size and time. 588 593 We estimate the time-uniformity to better 589 594 than 300\,ps, a limit due to the different travel times of the light between inner and outer parts of the 590 camera. Since the calibration does not permit a precise measurement of the absolute arrival time, we measure 591 the relative arrival time for every channel with respect to a reference channel (usually pixel Nr.\,1): 595 camera. 596 597 The extractors \#17--33 are able to compute the arrival time of each pulse. 598 Since the calibration does not permit a precise measurement of the absolute arrival time, we measure 599 the relative arrival time for every channel with respect to a reference channel (usually pixel no.\,1): 592 600 593 601 \begin{equation} … … 596 604 597 605 where $t_i$ denotes the reconstructed arrival time of pixel number $i$ and $t_1$ the reconstructed 598 arrival time of the reference pixel n r. 1 (software numbering). In one calibration run, one can then fill606 arrival time of the reference pixel no. 1 (software numbering). In one calibration run, one can then fill 599 607 histograms of $\delta t_i$ and fit them to the expected Gaussian distribution. The fits 600 608 yield a mean $\mu(\delta t_i)$, comparable to … … 604 612 605 613 \begin{equation} 606 t^{res}_i \approx \sigma(\delta t_i)/\sqrt (2)614 t^{res}_i \approx \sigma(\delta t_i)/\sqrt{2} 607 615 \end{equation} 608 616 … … 622 630 \includegraphics[width=0.45\linewidth]{RelTime_100_Extractor30.eps} 623 631 \includegraphics[width=0.45\linewidth]{RelTime_100_Extractor31.eps} 624 \caption{Examples of a distributions of relative arrival times $\delta t_i$ of an inner pixel ( Nr. 100) \protect\\632 \caption{Examples of a distributions of relative arrival times $\delta t_i$ of an inner pixel (no. 100) \protect\\ 625 633 Top: {\textit{\bf MExtractTimeAndChargeSlidingWindow}} over 2 slices (\#17) and 4 slices (\#18) \protect\\ 626 634 Center: {\textit{\bf MExtractTimeAndChargeSpline}} with maximum (\#23) and half-maximum pos. (\#24) \protect\\ … … 632 640 Figures~\ref{fig:reltimesinnerledblue1} and~\ref{fig:reltimesinnerledblue2} show 633 641 the distributions of $\delta t_i$ for a typical inner pixel and an intense, high-gain-saturating calibration 634 pulse of blue light .642 pulse of blue light, obtained from the low-gain readout channel. 635 643 One can see that the sliding window extractors yield double Gaussian structures, except for the 636 644 largest window sizes of 8 and 10 FADC slices. Even then, the distributions are not exactly Gaussian. … … 651 659 \includegraphics[width=0.45\linewidth]{RelTime_100_Extractor23_logain.eps} 652 660 \includegraphics[width=0.45\linewidth]{RelTime_100_Extractor24_logain.eps} 653 \caption{Examples of a distributions of relative arrival times $\delta t_i$ of an inner pixel ( Nr. 100) \protect\\661 \caption{Examples of a distributions of relative arrival times $\delta t_i$ of an inner pixel (no. 100) \protect\\ 654 662 Top: {\textit{\bf MExtractTimeAndChargeSlidingWindow}} over 4 slices (\#18) and 6 slices (\#19) \protect\\ 655 663 Center: {\textit{\bf MExtractTimeAndChargeSlidingWindow}} over 8 slices (\#20) and 10 slices (\#21)\protect\\ … … 665 673 \includegraphics[width=0.45\linewidth]{RelTime_100_Extractor32_logain.eps} 666 674 \includegraphics[width=0.45\linewidth]{RelTime_100_Extractor33_logain.eps} 667 \caption{Examples of a distributions of relative arrival times $\delta t_i$ of an inner pixel ( Nr. 100) \protect\\675 \caption{Examples of a distributions of relative arrival times $\delta t_i$ of an inner pixel (no. 100) \protect\\ 668 676 Top: {\textit{\bf MExtractTimeAndChargeDigitalFilter}} 669 677 fitted to cosmics pulses over 6 slices (\#30) and 4 slices (\#31) \protect\\ … … 679 687 %\includegraphics[width=0.31\linewidth]{RelArrTime_Pixel400_10LedUV_Extractor17.eps} 680 688 %\caption{Example of a two distributions of relative arrival times of an outer pixel with respect to 681 %the arrival time of the reference pixel Nr. 1. The left plot shows the result using the digital filter689 %the arrival time of the reference pixel no. 1. The left plot shows the result using the digital filter 682 690 % (extractor \#32), the central plot shows the result obtained with the half-maximum of the spline and the 683 691 %right plot the result of the sliding window with a window size of 2 slices (extractor \#17). A … … 691 699 %\includegraphics[width=0.31\linewidth]{RelArrTime_Pixel97_10LedBlue_Extractor32.eps} 692 700 %\caption{Example of a two distributions of relative arrival times of an inner pixel with respect to 693 %the arrival time of the reference pixel Nr. 1. The left plot shows the result using the half-maximum of the spline (extractor \#23), the right plot shows the result obtained with the digital filter701 %the arrival time of the reference pixel no. 1. The left plot shows the result using the half-maximum of the spline (extractor \#23), the right plot shows the result obtained with the digital filter 694 702 %(extractor \#32). A 695 703 %medium sized Blue-pulse (10Leds Blue) has been used which saturates the high-gain readout channel.} … … 704 712 %\includegraphics[width=0.31\linewidth]{RelArrTime_Pixel400_10LedBlue_Extractor32.eps} 705 713 %\caption{Example of a two distributions of relative arrival times of an outer pixel with respect to 706 %the arrival time of the reference pixel Nr. 1. The left plot shows the result using the half-maximum of the spline (extractor \#23), the right plot shows the result obtained with the digital filter714 %the arrival time of the reference pixel no. 1. The left plot shows the result using the half-maximum of the spline (extractor \#23), the right plot shows the result obtained with the digital filter 707 715 %(extractor \#32). A 708 716 %medium sized Blue-pulse (10Leds Blue) has been used which saturates the high-gain readout channel.} … … 710 718 %\end{figure} 711 719 720 \clearpage 721 712 722 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 713 723 … … 716 726 As in section~\ref{sec:uncalibrated}, we tested the number of outliers from the Gaussian distribution 717 727 in order to count how many times the extractor has failed to reconstruct the correct arrival time. 718 719 \begin{figure}[htp] 720 \centering 721 \includegraphics[width=0.95\linewidth]{UnsuitTimeVsExtractor-5LedsUV-Colour-12.eps} 728 \par 729 Figure~\ref{fig:time:5ledsuv} shows the number of outliers for the different time extractors, obtained with 730 a UV pulse of about 20 photo-electrons. One can see that all time extractors yield an acceptable mis-reconstruction 731 rate of about 0.5\%, except for the maximum searching spline yields three times more mis-reconstructions. 732 \par 733 If one goes to very low-intensity pulses, as shown in figure~\ref{fig:time:1leduv}, obtained with on average 4 photo-electrons, 734 the number of mis-reconstructions increases considerably up to 20\% for some extractors. We interpret this high mis-reconstruction 735 rate to the increase possibility to mis-reconstruct a pulse from the night sky background noise instead of the signal pulse from the 736 calibration LEDs. One can see that the digital filter using weights on 4 FADC slices is clear inferior to the one using 6 FADC slices 737 in that respect. 738 \par 739 The same conclusion seems to hold for the green pulse of about 20 photo-electrons (figure~\ref{fig:time:2ledsgreen}) 740 where the digital filter over 6 FADC slices seems to 741 yield more stable results than the one over 4 FADC slices. The half-maximum searching spline seems to be superior to the maximum-searching 742 one. 743 \par 744 In figure~\ref{fig:time:23ledsblue}, one can see the number of outliers from an intense calibration pulse of blue light yielding about 745 600 photo-electrons per inner pixel. All extractors seem to be stable, except for the digital filter with weigths over 4 FADC slices. This 746 is expected, since the low-gain pulse is wider than 4 FADC slices. 747 \par 748 In all previous plots, the sliding window yielded the most stable results, however later we will see that this stability is only due to 749 an increased time spread. 750 751 \begin{figure}[htp] 752 \centering 753 \includegraphics[height=0.35\textheight]{UnsuitTimeVsExtractor-5LedsUV-Colour-12.eps} 722 754 \caption{Reconstructed arrival time resolutions from a typical, not saturating calibration pulse 723 755 of colour UV, reconstructed with each of the tested arrival time extractors. … … 730 762 \begin{figure}[htp] 731 763 \centering 732 \includegraphics[ width=0.95\linewidth]{UnsuitTimeVsExtractor-1LedUV-Colour-04.eps}764 \includegraphics[height=0.35\textheight]{UnsuitTimeVsExtractor-1LedUV-Colour-04.eps} 733 765 \caption{Reconstructed arrival time resolutions from the lowest intensity calibration pulse 734 766 of colour UV (carrying a mean number of 4 photo-electrons), … … 742 774 \begin{figure}[htp] 743 775 \centering 744 \includegraphics[ width=0.95\linewidth]{UnsuitTimeVsExtractor-2LedsGreen-Colour-02.eps}776 \includegraphics[height=0.35\textheight]{UnsuitTimeVsExtractor-2LedsGreen-Colour-02.eps} 745 777 \caption{Reconstructed arrival time resolutions from a typical, not saturating calibration pulse 746 778 of colour Green, reconstructed with each of the tested arrival time extractors. … … 753 785 \begin{figure}[htp] 754 786 \centering 755 \includegraphics[ width=0.95\linewidth]{UnsuitTimeVsExtractor-23LedsBlue-Colour-00.eps}787 \includegraphics[height=0.35\textheight]{UnsuitTimeVsExtractor-23LedsBlue-Colour-00.eps} 756 788 \caption{Reconstructed arrival time resolutions from the highest intensity calibration pulse 757 789 of colour blue, reconstructed with each of the tested arrival time extractors. … … 762 794 \end{figure} 763 795 796 \clearpage 797 764 798 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 765 799 766 800 \subsection{Time Resolution} 801 802 There are three intrinsic contributions to the timing accuracy of the signal: 803 804 \begin{enumerate} 805 \item Intrinsic transit time spread TTS of the PMT. It can be in the order 806 of a few hundreds of ps per single photo electron. When we reconstruct 807 the mean pulse arrival time the error of the mean is given by the time 808 spread per single photo electron dividid by the square root of number of 809 photo electrons. 810 \item Intrinsic arrival time spread of the photons on the PMT. For our 811 calibration LEDs this can be up to about 2 ns, for muons it is about a 812 few hundreds of ps and for hadrons a few ns. The error of the mean 813 arrival time of the total pulse is again the arrival time spread of the 814 photons divided by the number of photo electrons. 815 \item reconstruction error due to noise and error of the numeric fit in 816 case of the digital filter. In case of the digital filter the error for 817 the standard noise level in the MC is about 2.7 ns divided by the signal 818 in photo electrons. 819 \end{enumerate} 820 821 All this seems to quite agree with the results obtained with the MC 822 TestPulses. As 1) and 2) are proportional to one over the square root of 823 the signal and 3 is proportional to one over the signal, for small 824 pulses the noise determins the resolution, but for larger pulses the 825 intrinsic fluctuations limit the timing resolution. 826 827 When we get a time resolution of about 300 ps for calibration LED pulses 828 we can not distinquish 1) and 2). Thus we have to wait for the exact 829 measurement. 830 767 831 768 832 \begin{figure}[htp]
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