Changeset 6747 for trunk/MagicSoft
- Timestamp:
- 03/04/05 14:42:51 (20 years ago)
- Location:
- trunk/MagicSoft/TDAS-Extractor
- Files:
-
- 6 edited
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Algorithms.tex (modified) (5 diffs)
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Calibration.tex (modified) (17 diffs)
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Criteria.tex (modified) (3 diffs)
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Introduction.tex (modified) (2 diffs)
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Pedestal.tex (modified) (4 diffs)
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Reconstruction.tex (modified) (2 diffs)
Legend:
- Unmodified
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trunk/MagicSoft/TDAS-Extractor/Algorithms.tex
r6664 r6747 657 657 658 658 Figure \ref{fig:amp_sliding} shows the result of the applied amplitude and time weights to the recorded FADC time slices of one 659 simulated MC pulse. The left plot display es the result of the applied amplitude weights659 simulated MC pulse. The left plot displays the result of the applied amplitude weights 660 660 $e(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{amp}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ and 661 661 the right plot shows the result of the applied timing weights … … 687 687 one simulated MC pulse. The left plot shows the result of the applied amplitude weights 688 688 $e(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{amp}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ and 689 the right plot display es the result of the applied timing weights689 the right plot displays the result of the applied timing weights 690 690 $e\tau(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{time}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ as a function of the time shift $t_0$.} 691 691 \label{fig:amp_sliding} … … 816 816 {\textit{MExtractor::SetRange(higain first, higain last, logain first, logain last)}} sets the extraction 817 817 range with the high gain start bin {\textit{higain first}} to (including) the last bin {\textit{higain last}}. 818 Analog uefor the low gain extraction range. Note that in MARS, the low-gain FADC samples start with818 Analog for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with 819 819 the index 0 again, thus {\textit{maxbin+0.5}} means in reality {\textit{maxbin+15+0.5}}. } 820 820 : … … 830 830 {\textit{MExtractor::SetRange(higain first, higain last, logain first, logain last)}} sets the extraction 831 831 range with the high gain start bin {\textit{higain first}} to (including) the last bin {\textit{higain last}}. 832 Analog uefor the low gain extraction range. Note that in MARS, the low-gain FADC samples start with832 Analog for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with 833 833 the index 0 again, thus {\textit{maxbin+0.5}} means in reality {\textit{maxbin+15+0.5}}.}: 834 834 \resume{enumerate} … … 889 889 %%% TeX-master: "MAGIC_signal_reco" 890 890 %%% TeX-master: "MAGIC_signal_reco" 891 %%% TeX-master: "Algorithms" 891 892 %%% End: -
trunk/MagicSoft/TDAS-Extractor/Calibration.tex
r6711 r6747 7 7 The LED pulser system is able to provide fast light pulses of 2--4\,ns FWHM 8 8 with intensities ranging from 3--4 to more than 600 photo-electrons in one inner photo-multiplier of the 9 camera. These pulses can be produced in three colo urs {\textit {\bf green, blue}} and9 camera. These pulses can be produced in three colors {\textit {\bf green, blue}} and 10 10 {\textit{\bf UV}}. 11 11 … … 15 15 \hline 16 16 \hline 17 \multicolumn{7}{|c|}{The possible pulsed light colo urs} \\17 \multicolumn{7}{|c|}{The possible pulsed light colors} \\ 18 18 \hline 19 19 \hline … … 29 29 \hline 30 30 \end{tabular} 31 \caption{The pulser colo urs available from the calibration system}31 \caption{The pulser colors available from the calibration system} 32 32 \label{tab:pulsercolours} 33 33 \end{table} 34 34 35 Table~\ref{tab:pulsercolours} lists the available colo urs and intensities and35 Table~\ref{tab:pulsercolours} lists the available colors and intensities and 36 36 figures~\ref{fig:pulseexample1leduv} and~\ref{fig:pulseexample23ledblue} show exemplary pulses 37 37 as registered by the FADCs. … … 53 53 different intensity and colour. 54 54 \item Time resolution: These tests show the time resolution and stability obtained with different 55 intensities and colo urs.55 intensities and colors. 56 56 \end{enumerate} 57 57 … … 161 161 The following figures~\ref{fig:unsuited:5ledsuv},~\ref{fig:unsuited:1leduv},~\ref{fig:unsuited:2ledsgreen} 162 162 and~\ref{fig:unsuited:23ledsblue} show the resulting numbers of un-calibrated pixels and events for 163 different colo urs and intensities. Because there is a strong anti-correlation between the number of163 different colors and intensities. Because there is a strong anti-correlation between the number of 164 164 excluded pixels and the number of outliers per event, we have chosen to show these numbers together. 165 165 … … 254 254 value of about 2.6$\pm$0.1~\cite{michele-diploma}. 255 255 \par 256 In our case, there is an additional complication due to the fact that the green and blue colo ured light pulses256 In our case, there is an additional complication due to the fact that the green and blue colored light pulses 257 257 show secondary pulses which destroy the Poisson behaviour of the number of photo-electrons. We will 258 258 have to split our sample of extractors into those being affected by the secondary pulses and those … … 278 278 Also the sliding windows smaller than 6 FADC slices and the spline smaller than 279 279 2 FADC slices reproduce too small numbers of photo-electrons. Moreover, the digital filter shows a small dependency 280 of the number of photo-electrons w.r.t. the extra tion window.280 of the number of photo-electrons w.r.t. the extraction window. 281 281 \par 282 282 … … 384 384 \par 385 385 Figure~\ref{fig:linear:phevscharge4} shows the conversion factor $c_{phe}$ obtained for different light intensities 386 and colo urs for three exemplary inner and three exemplary outer pixels using a fixed window on386 and colors for three exemplary inner and three exemplary outer pixels using a fixed window on 387 387 8 FADC slices. The conversion factor seems to be linear to a good approximation, with the following restrictions: 388 388 \begin{itemize} … … 441 441 been used in the analysis and to derive a Crab spectrum with the consequence that the spectrum bends down at high energies. We 442 442 suppose that the loss of linearity due to usage of this extractor is responsible for the encountered problems. 443 A simil iar behaviour can be found for all extractors with window sizes smaller than 6 FADC slices, especially in the low-gain region.443 A similar behaviour can be found for all extractors with window sizes smaller than 6 FADC slices, especially in the low-gain region. 444 444 This is understandable since the low-gain pulse covers at least 6 FADC slices. 445 445 (This behaviour … … 622 622 vs. a reference extractor (sliding window over 8 high-gain and 8 low-gain FADC slices, extractor \#21). 623 623 The tested extractors are: top left: integrating spline over 0.5 FADC slices left from maximum and 1.5 624 FADC slice right from maximum (extra tor \#25), top right: integrating spline over 1.5 FADC slices left624 FADC slice right from maximum (extractor \#25), top right: integrating spline over 1.5 FADC slices left 625 625 from maximum and 4.5 FADC slices right from maximum (extractor \#27), bottom left: digital filter fitting 626 626 cosmics pulses over 6 FADC slices, bottom left: digital filter fitting a blue calibration pulse over … … 702 702 to miss the exact arrival time in some events. Only the position of the half-maximum gives the 703 703 expected result of a single Gaussian distribution. 704 A simil iar problem occurs in the case of the digital filter: If one takes the correct weights704 A similar problem occurs in the case of the digital filter: If one takes the correct weights 705 705 (fig.~\ref{fig:reltimesinnerledblue2} bottom), the distribution is perfectly Gaussian and the resolution good, 706 706 however a rather slight change from the blue calibration pulse weights to cosmics pulses weights (top) … … 800 800 \par 801 801 In figure~\ref{fig:timeunsuit:23ledsblue}, one can see the number of outliers from an intense calibration pulse of blue light yielding about 802 600 photo-electrons per inner pixel. All extractors seem to be stable, except for the digital filter with weig ths over 4 FADC slices. This802 600 photo-electrons per inner pixel. All extractors seem to be stable, except for the digital filter with weights over 4 FADC slices. This 803 803 is expected, since the low-gain pulse is wider than 4 FADC slices. 804 804 \par … … 895 895 896 896 Figures~\ref{fig:time:5ledsuv} through~\ref{fig:time:23ledsblue} show the measured time resolutions for very different calibration 897 pulse intensities and colo urs. One can see that the sliding window resolutions are always worse than the spline and digital filter897 pulse intensities and colors. One can see that the sliding window resolutions are always worse than the spline and digital filter 898 898 algorithms. Moreover, the half-maximum position search by the spline is always slightly better than the maximum position search. The 899 899 digital filter does not show notable differences with respect to the pulse form or the extraction window size, except for the low-gain … … 948 948 \clearpage 949 949 950 The following figure~\ref{fig:time:dep} shows the time resolution for various calibration runs taken with different colo urs951 and light intensities as a func ion of the mean number of photo-electrons --950 The following figure~\ref{fig:time:dep} shows the time resolution for various calibration runs taken with different colors 951 and light intensities as a function of the mean number of photo-electrons -- 952 952 reconstructed with the F-Factor method -- for four different time extractors. The dependencies have been fit to the following 953 953 empirical relation: … … 982 982 \end{tabular} 983 983 \caption{The fit results obtained from the fit of equation~\ref{eq:time:fit} to the time resolutions obtained for various 984 intensities and colo urs. The fit probabilities are very small mainly because of the different intrinsic arrival time spreads of985 the photon pulses from different colo urs. }984 intensities and colors. The fit probabilities are very small mainly because of the different intrinsic arrival time spreads of 985 the photon pulses from different colors. } 986 986 \label{tab:time:fitresults}. 987 987 } … … 989 989 990 990 The low fit probabilities are partly due to the systematic differences in the pulse forms in intrinsic arrival time spreads between 991 pulses of different LED colo urs. Nevertheless, we had to include all colours in the fit to cover the full dynamic range. In general,992 one can see that the time resolutions for the UV pulses are systematically better than for the other colo urs which we attribute to the fact991 pulses of different LED colors. Nevertheless, we had to include all colors in the fit to cover the full dynamic range. In general, 992 one can see that the time resolutions for the UV pulses are systematically better than for the other colors which we attribute to the fact 993 993 the these pulses have a smaller intrinsic pulse width -- which is very close to pulses from cosmics. Moreover, there are clear differences 994 994 visible between different time extractors, especially the sliding window extractor yields poor resolutions. The other three extractors are … … 1020 1020 the half-maximum searching spline (extractor~\#25, top right), 1021 1021 the digital filter with correct pulse weights over 6 slices (extractor~\#30 and~\#32, bottom left) 1022 and the digital filter with UV calibration-pulse weights over 4 slices (extractor~\#31 and~\#33, bottom rig th).1022 and the digital filter with UV calibration-pulse weights over 4 slices (extractor~\#31 and~\#33, bottom right). 1023 1023 Error bars denote the spread (RMS) of time resolutions of the investigated channels. 1024 The marker colo urs show the applied1025 pulser colour, except for the last (green) point where all three colo urs were used.}1024 The marker colors show the applied 1025 pulser colour, except for the last (green) point where all three colors were used.} 1026 1026 \label{fig:time:dep} 1027 1027 \end{figure} -
trunk/MagicSoft/TDAS-Extractor/Criteria.tex
r6745 r6747 3 3 The goal for the optimal signal reconstruction algorithm is to compute an unbiased estimate of the strength and arrival time of the 4 4 Cherenkov signal with the highest possible resolution for all signal intensities. The MAGIC telescope has been optimized to 5 lower the energy t reshold of observation in any respect. Particularly the choice for an FADC system has been made with an eye on the5 lower the energy threshold of observation in any respect. Particularly the choice for an FADC system has been made with an eye on the 6 6 possibility to extract the smallest possible signals from air showers. It would be inconsequent not to continue the optimization procedure 7 7 in the signal extraction algorithms and the subsequent image cleaning. … … 82 82 83 83 Because of the peculiarities of the MAGIC data acquisition system, the extraction of the low-gain pulse is somewhat critical: 84 The low-gain pulse shape differs significantly from the high-gain shape. Due to the analog uedelay line, the low-gain pulse is84 The low-gain pulse shape differs significantly from the high-gain shape. Due to the analog delay line, the low-gain pulse is 85 85 wider and the integral charge is distributed over a longer time window. 86 86 … … 121 121 non-trivial for extractors searching the signal in a sliding window. 122 122 \item As the calibration pulses are slightly wider than the cosmics pulses, the obtained conversion factors must not be affected by 123 the difference in pulse shape. This puts severe con traints on all extractors which do not integrate the whole pulse or take the pulse123 the difference in pulse shape. This puts severe constraints on all extractors which do not integrate the whole pulse or take the pulse 124 124 shape into account. 125 125 \end{enumerate} -
trunk/MagicSoft/TDAS-Extractor/Introduction.tex
r6746 r6747 13 13 1.0 - 1.2 ns and rise and fall times of 600 and 700\,ps correspondingly~\cite{Magic-PMT}. By modulating 14 14 vertical-cavity surface-emitting laser (VCSEL) 15 type laser diodes in amplitude, the fast analog uesignals from the PMTs are transferred via 162\,m long,15 type laser diodes in amplitude, the fast analog signals from the PMTs are transferred via 162\,m long, 16 16 50/125\,$\mu$m diameter optical fibers to the counting house \cite{MAGIC-analog-link-2}. After transforming the 17 17 light back to an electrical signal, the original PMT pulse has a FWHM of about 2.2 ns and rise and fall … … 82 82 \item Size: The outer pixels have a factor four bigger area then the inner pixels~\cite{MAGIC-design}. 83 83 Their (quantum-efficiency convoluted) effective area is about a factor 2.6 higher. 84 \item Gain: The camera is flat-fielded in order to yield a simil iar reconstructed charge signal for the same photon illumination intensity.84 \item Gain: The camera is flat-fielded in order to yield a similar reconstructed charge signal for the same photon illumination intensity. 85 85 In order to achieve this, the gain of the inner pixels has been adjusted to about a factor 2.6 higher than the outer 86 86 ones~\cite{tdas-calibration}. This results in lower effective noise charge from the night sky background for the outer pixels. 87 87 \item Delay: The signal of the outer pixels is delayed by about 1.5\,ns with respect to the inner ones. 88 88 \end{enumerate} 89 \item[Clock noise:\xspace] The MAGIC 300\,MHz FADCs have an intrinsic clock noise of a few LSBsoccurring with a frequency of 150\,MHz.89 \item[Clock noise:\xspace] The MAGIC 300\,MHz FADCs have an intrinsic clock noise of a few least significant bits (LSBs) occurring with a frequency of 150\,MHz. 90 90 This clock noise results 91 91 in a superimposed AB-pattern for the read-out pedestals. In the standard analysis, the amplitude of this clock noise gets measured in the 92 92 pedestal extraction algorithms and further corrected for by all signal extractors. 93 93 \item[Trigger Jitter:\xspace] The FADC clock is not synchronized with the trigger. Therefore, the relative position of the recorded 94 signal samples varies uniform ely by one FADC slice with respect to the position of the signal shape by one FADC slice from event to event.94 signal samples varies uniformly by one FADC slice with respect to the position of the signal shape by one FADC slice from event to event. 95 95 \item[DAQ jumps:\xspace] Unfortunately, the position of the signal pulse with respect to the first recorded FADC sample is not constant. 96 96 It varies randomly by an integer number of FADC slices -- typically two -- in about 1\% of the channels per event. -
trunk/MagicSoft/TDAS-Extractor/Pedestal.tex
r6665 r6747 83 83 \item Determine $B$ and $MSE$ from MC events with added noise. 84 84 % Assuming that $MSE$ and $B$ are negligible for the events without noise, one can 85 86 85 With this method, one can get a dependence of both values on the size of the signal, 86 although the MC might contain systematic differences with respect to the real data. 87 87 \item Determine $MSE$ from the error retrieved from the fit results of $\widehat{S}$, which is possible for the 88 88 fit and the digital filter (eq.~\ref{eq:of_noise}). … … 190 190 and for the different levels of (night-sky) background applied to 1000 pedestal events. 191 191 One can see that the bias vanishes to an accuracy of better than 2\% of a photo-electron 192 makefor the extractors which are used in this TDAS.192 for the extractors which are used in this TDAS. 193 193 194 194 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1 … … 564 564 applied on a sliding window of different sizes. 565 565 In the top plot, a pedestal run with extra-galactic star background has been taken and in the bottom, 566 a gala tic star background. An exemplary pixel (Nr. 100) has been used.566 a galactic star background. An exemplary pixel (Nr. 100) has been used. 567 567 Above, a rate of 0.08 phe/ns and below, a rate of 0.1 phe/ns has been obtained.} 568 568 \label{fig:df:ratiofit} … … 613 613 %%% TeX-master: "MAGIC_signal_reco" 614 614 %%% TeX-master: "MAGIC_signal_reco" 615 %%% TeX-master: "MAGIC_signal_reco" 615 616 %%% End: -
trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex
r6745 r6747 25 25 26 26 27 Figure~\ref{fig:raw_shape} shows the raw FADC values as a function of the slice number for 1000 constant pulse generator pulses overlayed. Figure~\ref{fig:reco_time} shows the distribution of the corresponding reconstructed pulse arrival times. The distribution has a width of about 1 FADC period (3.33 27 Figure~\ref{fig:raw_shape} shows the raw FADC values as a function of the slice number for 1000 constant pulse generator pulses overlayed. Figure~\ref{fig:reco_time} shows the distribution of the corresponding reconstructed pulse arrival times. The distribution has a width of about 1 FADC period (3.33\,ns). 28 28 29 29 … … 60 60 % while the FWHM of the average reconstructed low gain pulse shape is 61 61 % Due to the electric delay line for the low gain pules on the receiver board the low gain pulse is widened with respect to the high gain. 62 It has a FWHM of about 10 62 It has a FWHM of about 10\,ns. 63 63 64 64
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