Changeset 6437


Ignore:
Timestamp:
02/13/05 21:07:35 (20 years ago)
Author:
gaug
Message:
*** empty log message ***
Location:
trunk/MagicSoft/TDAS-Extractor
Files:
5 edited

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  • trunk/MagicSoft/TDAS-Extractor/Algorithms.tex

    r6435 r6437  
    1616\begin{figure}[htp]
    1717\includegraphics[width=0.99\linewidth]{ExtractorClasses.eps}
    18 \caption{Sketch of the inheritances of three examplary MARS signal extractor classes:
     18\caption{Sketch of the inheritances of three exemplary MARS signal extractor classes:
    1919MExtractFixedWindow, MExtractTimeFastSpline and MExtractTimeAndChargeDigitalFilter}
    2020\label{fig:extractorclasses}
    … …  
    302302\begin{description}
    303303\item[Extraction Type Amplitude:\xspace] The amplitude of the spline maximum is taken as charge signal
    304 and the (precisee) position of the maximum is returned as arrival time. This type is faster, since it
    305 performs not spline intergraion.
     304and the (precise) position of the maximum is returned as arrival time. This type is faster, since it
     305performs not spline integration.
    306306\item[Extraction Type Integral:\xspace] The integrated spline between maximum position minus
    307307rise time (default: 1.5 slices) and maximum position plus fall time (default: 4.5 slices)
    … …  
    359359
    360360
    361 The pulse shape is mainly determined by the artificial pulse stretching by about 6 ns on the receiver board. Thus the first assumption is hold. Also the second assumption is fullfilled: Signal and noise are independent and the measured pulse is the linear superposition of the signal and noise. The validity of the third assumption is discussed below, especially for diffent night sky background conditions.
     361The pulse shape is mainly determined by the artificial pulse stretching by about 6 ns on the receiver board.
     362Thus the first assumption holds. Also the second assumption is fulfilled: Signal and noise are independent
     363and the measured pulse is the linear superposition of the signal and noise. The validity of the third
     364assumption is discussed below, especially for different night sky background conditions.
    362365
    363366Let $g(t)$ be the normalized signal shape, $E$ the signal amplitude and $\tau$ the time shift
    … …  
    452455\par
    453456Because of the truncation of the Taylor series in equation (\ref{shape_taylor_approx}) the above results are
    454 only valid for vanishing time offsets $\tau$. For non-zero time offsets one has to iterate the problem using
     457only valid for vanishing time offsets $\tau$. For non-zero time offsets, one has to iterate the problem using
    455458the time shifted signal shape $g(t-\tau)$.
    456459
    … …  
    458461
    459462\begin{equation}
    460 \left(\boldsymbol{V}^{-1}\right)_{i,j}
     463\left(\boldsymbol{V}^{-1}\right)_{ij}
    461464        =\frac{1}{2}\left(\frac{\partial^2 \chi^2(E, E\tau)}{\partial \alpha_i \partial \alpha_j} \right) \quad
    462465        \text{with} \quad \alpha_i,\alpha_j \in \{E, E\tau\} \ .
    … …  
    482485
    483486
    484 In the MAGIC MC simulations \cite{MC-Camera} a LONS rate of 0.13 photoelectrons per ns, an FADC gain of 7.8 FADC counts per photoelectron and an intrinsic FADC noise of 1.3 FADC counts per FADC slice is implemented. This simulates the night sky background conditions for an extragalactic source. This results in a noise of about 4 FADC counts per single FADC slice: $<b_i^2> \approx 4$~FADC counts. Using the digital filter with weights parameterized over 6 FADC slices ($i=1...5$) the error of the reconstructed signal and time is give by:
    485 
    486 \begin{equation}
    487 \sigma_E \approx 8.3 \ \mathrm{FADC\ counts} \qquad \sigma_{\tau}  \approx  \frac{6.5\ \Delta T_{\mathrm{FADC}}}{(E\ /\ \mathrm{FADC\ counts})} \ ,
     487In the MAGIC MC simulations~\cite{MC-Camera}, an night-sky background rate of 0.13 photoelectrons per ns,
     488an FADC gain of 7.8 FADC counts per photo-electron and an intrinsic FADC noise of 1.3 FADC counts
     489per FADC slice is implemented.
     490These numbers simulate the night sky background conditions for an extragalactic source and result
     491in a noise contribution of about 4 FADC counts per single FADC slice:
     492$\sqrt{B_{ii}} \approx 4$~FADC counts.
     493Using the digital filter with weights parameterized over 6 FADC slices ($i=0...5$) the errors of the
     494reconstructed signal and time amount to:
     495
     496\begin{equation}
     497\sigma_E \approx 8.3 \ \mathrm{FADC\ counts} \ (\approx 1.1\,\mathrm{phe}) \qquad
     498\sigma_{\tau}  \approx  \frac{6.5\ \Delta T_{\mathrm{FADC}}}{(E\ /\ \mathrm{FADC\ counts})} \ (\approx \frac{2.8\,\mathrm{ns}}{E\,/\ \mathrm{N_{phe}}})\ ,
    488499\label{eq:of_noise_calc}
    489500\end{equation}
    490501
    491 where $\Delta T_{\mathrm{FADC}} = 3.33$ ns is the sampling interval of the MAGIC FADCs. The error in the reconstructed signal correspons to about one photo electron. For signals of two photo electrons size the timing error is about 1 ns.
    492 
    493 %For the MAGIC signals, as implemented in the MC simulations \cite{MC-Camera}, a pedestal RMS of a single FADC slice of 6 FADC counts introduces an error in the reconstructed signal and time of:
    494 
    495 For an IACT there are two types of background noise. On the one hand, there is the constantly present
    496 electronics noise,
    497 on the other hand, the light of the night sky introduces a sizeable background noise to the measurement of
    498 Cherenkov photons from air showers.
    499 
    500 The electronics noise is largely white, uncorrelated in time. The noise from the night sky background photons
    501 is the superposition of the
     502where $\Delta T_{\mathrm{FADC}} = 3.33$ ns is the sampling interval of the MAGIC FADCs.
     503The error in the reconstructed signal corresponds to about one photo electron.
     504For signals of the size of two photo electrons, the timing error is a bit higher than 1\,ns.
     505\par
     506
     507An IACT has typically two types of background noise:
     508On the one hand, there is the constantly present electronics noise,
     509while on the other hand, the light of the night sky introduces a sizeable background
     510to the measurement of the Cherenkov photons from air showers.
     511
     512The electronics noise is largely white, i.e. uncorrelated in time.
     513The noise from the night sky background photons is the superposition of the
    502514detector response to single photo electrons following a Poisson distribution in time.
    503515Figure \ref{fig:noise_autocorr_allpixels} shows the noise
    504 autocorrelation matrix for an open camera. The large noise autocorrelation in time of the current FADC
    505 system is due to the pulse shaping with a shaping constant of 6 ns.
    506 
    507 In general, the amplitude and time weights, $\boldsymbol{w}_{\text{amp}}$ and $\boldsymbol{w}_{\text{time}}$, depend on the pulse shape, the
    508 derivative of the pulse shape and the noise autocorrelation. In the high gain samples the correlated night sky background noise dominates over
    509 the white electronics noise. Thus different noise levels just cause the noise autocorrelation matrix $\boldsymbol{B}$ to change by a same factor,
    510 which cancels out in the weights calculation. Thus in the high gain the weights are to a very good approximation independent of the night
    511 sky background noise level.
     516autocorrelation matrix for an open camera. The large noise autocorrelation of the current FADC
     517system is due to the pulse shaping (with the shaping constant equivalent to about two FADC slices).
     518
     519In general, the amplitude and time weights, $\boldsymbol{w}_{\text{amp}}$ and $\boldsymbol{w}_{\text{time}}$,
     520depend on the pulse shape, the derivative of the pulse shape and the noise autocorrelation.
     521In the high gain samples, the correlated night sky background noise dominates over
     522the white electronics noise. Thus, different noise levels just cause the members of the noise autocorrelation
     523matrix to change by a same factor,
     524which cancels out in the weights calculation.
     525Thus, the weights are to a very good approximation independent from the night
     526sky background noise level in the high gain.
    512527
    513528Contrary to that in the low gain samples ... .
    … …  
    518533
    519534
    520 \begin{figure}[h!]
    521 \begin{center}
    522 \includegraphics[totalheight=7cm]{noise_autocorr_AB_36038_TDAS.eps}
    523 \end{center}
    524 \caption[Noise autocorrelation one pixel.]{Noise autocorrelation
    525 matrix $\boldsymbol{B}$ for open camera including the noise due to night sky background fluctuations
    526 for one single pixel (obtained from 1000 events).}
    527 \label{fig:noise_autocorr_1pix}
    528 \end{figure}
     535%\begin{figure}[h!]
     536%\begin{center}
     537%\includegraphics[totalheight=7cm]{noise_autocorr_AB_36038_TDAS.eps}
     538%\end{center}
     539%\caption[Noise autocorrelation one pixel.]{Noise autocorrelation
     540%matrix $\boldsymbol{B}$ for open camera including the noise due to night sky background fluctuations
     541%for one single pixel (obtained from 1000 events).}
     542%\label{fig:noise_autocorr_1pix}
     543%\end{figure}
    529544
    530545\begin{figure}[htp]
    … …  
    641656$e\tau(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{time}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ as a function of the time shift $t_0$.}
    642657\label{fig:amp_sliding}
    643 \end{figure}
     658\end{figure}in the high gain
    644659
    645660
    … …  
    679694\item "calibration\_weights4\_blue.dat'' with a window size of 4 FADC slices
    680695\item "calibration\_weights\_UV.dat'' with a window size of 6 FADC slices and in the low-gain the
    681 calibration weigths obtained from blue pulses\footnote{UV-pulses saturating the high-gain are not yet
     696calibration weights obtained from blue pulses\footnote{UV-pulses saturating the high-gain are not yet
    682697available.}.
    683698\item "calibration\_weights4\_UV.dat'' with a window size of 4 FADC slices and in the low-gain the
    684 calibration weigths obtained from blue pulses\footnote{UV-pulses saturating the high-gain are not yet
     699calibration weights obtained from blue pulses\footnote{UV-pulses saturating the high-gain are not yet
    685700available.}.
    686701\item "cosmics\_weights\_logaintest.dat'' with a window size of 6 FADC slices and swapped high-gain and low-gain
    … …  
    779794
    780795\begin{description}
    781 \item[MExtractFixedWindow]: with the following intialization, if {\textit{maxbin}} defines the
     796\item[MExtractFixedWindow]: with the following initialization, if {\textit{maxbin}} defines the
    782797   mean position of the high-gain FADC slice which carries the pulse maximum \footnote{The function
    783798{\textit{MExtractor::SetRange(higain first, higain last, logain first, logain last)}} sets the extraction
    784799range with the high gain start bin {\textit{higain first}} to (including) the last bin {\textit{higain last}}.
    785 Analoguously for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with
     800Analogue for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with
    786801the index 0 again, thus {\textit{maxbin+0.5}} means in reality {\textit{maxbin+15+0.5}}. }
    787802:
    … …  
    797812{\textit{MExtractor::SetRange(higain first, higain last, logain first, logain last)}} sets the extraction
    798813range with the high gain start bin {\textit{higain first}} to (including) the last bin {\textit{higain last}}.
    799 Analoguously for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with
     814Analogue for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with
    800815the index 0 again, thus {\textit{maxbin+0.5}} means in reality {\textit{maxbin+15+0.5}}.}:
    801816\resume{enumerate}
    … …  
    874889%%% mode: latex
    875890%%% TeX-master: "MAGIC_signal_reco"
     891%%% TeX-master: "MAGIC_signal_reco"
    876892%%% End:

  • trunk/MagicSoft/TDAS-Extractor/Calibration.tex

    r6429 r6437  
     1\section{Calibration \label{sec:calibration}}
    12
    23
    … …  
    4546\begin{enumerate}
    4647\item Un-calibrated pixels and events: These tests measure the percentage of failures of the extractor
    47 resulting either in a pixel declared as un-calibrated or in an event which produces a signal ouside
     48resulting either in a pixel declared as un-calibrated or in an event which produces a signal outside
    4849of the expected Gaussian distribution.
    4950\item Number of photo-electrons: These tests measure the reconstructed numbers of photo-electrons, their
    … …  
    8485The corresponding MAGIC data run numbers range from nr. 31741 to 31772. These data was taken
    8586before the latest camera repair access which resulted in a replacement of about 2\% of the pixels known to be
    86 mal-functionning at that time.
     87mal-functioning at that time.
    8788There is thus a lower limit to the number of un-calibrated pixels of about 1.5--2\% of known
    88 mal-functionning photo-multipliers.
     89mal-functioning photo-multipliers.
    8990\par
    9091Although we had looked at and tested all colour and extractor combinations resulting from these data,
    … …  
    102103\subsection{Un-Calibrated Pixels and Events}
    103104
    104 The MAGIC calibration software incorporates a series of checks to sort out mal-functionning pixels.
     105The MAGIC calibration software incorporates a series of checks to sort out mal-functioning pixels.
    105106Except for the software bug searching criteria, the following exclusion criteria can apply:
    106107
    … …  
    112113\item The reconstructed mean signal error is smaller than its value. This criterium cuts out
    113114signal distributions which fluctuate so much that their RMS is bigger than its mean value. This
    114 criterium cuts out ``ringing'' pixels or mal-functionning extractors.
     115criterium cuts out ``ringing'' pixels or mal-functioning extractors.
    115116\item The reconstructed mean number of photo-electrons lies 4.5 sigma outside
    116117the distribution of photo-electrons obtained with the inner or outer pixels in the camera, respectively.
    … …  
    120121\item All pixels with reconstructed negative mean signal or with a
    121122mean numbers of photo-electrons smaller than one. Pixels with a negative pedestal RMS subtracted
    122 sigma occur, especially when stars are focussed onto that pixel during the pedestal taking (resulting
     123sigma occur, especially when stars are focused onto that pixel during the pedestal taking (resulting
    123124in a large pedestal RMS), but have moved to another pixel during the calibration run. In this case, the
    124125number of photo-electrons would result artificially negative. If these
    … …  
    152153\centering
    153154\includegraphics[height=0.75\textheight]{UnsuitVsExtractor-all.eps}
    154 \caption{Uncalibrated pixels and outlier events averaged over all available
     155\caption{Un-calibrated pixels and outlier events averaged over all available
    155156calibration runs.}
    156157\label{fig:unsuited:all}
    … …  
    167168\centering
    168169\includegraphics[height=0.95\textheight]{UnsuitVsExtractor-5LedsUV-Colour-13.eps}
    169 \caption{Uncalibrated pixels and outlier events for a typical calibration 
     170\caption{Un-calibrated pixels and outlier events for a typical calibration 
    170171pulse of UV-light which does not saturate the high-gain readout.}
    171172\label{fig:unsuited:5ledsuv}
    … …  
    175176\centering
    176177\includegraphics[height=0.95\textheight]{UnsuitVsExtractor-1LedUV-Colour-04.eps}
    177 \caption{Uncalibrated pixels and outlier events for a very low
     178\caption{Un-calibrated pixels and outlier events for a very low
    178179intensity pulse.}
    179180\label{fig:unsuited:1leduv}
    … …  
    183184\centering
    184185\includegraphics[height=0.95\textheight]{UnsuitVsExtractor-2LedsGreen-Colour-02.eps}
    185 \caption{Uncalibrated pixels and outlier events for a typical green pulse.}
     186\caption{Un-calibrated pixels and outlier events for a typical green pulse.}
    186187\label{fig:unsuited:2ledsgreen}
    187188\end{figure}
    … …  
    190191\centering
    191192\includegraphics[height=0.95\textheight]{UnsuitVsExtractor-23LedsBlue-Colour-00.eps}
    192 \caption{Uncalibrated pixels and outlier events for a high-intensity blue pulse.}
     193\caption{Un-calibrated pixels and outlier events for a high-intensity blue pulse.}
    193194\label{fig:unsuited:23ledsblue}
    194195\end{figure}
    … …  
    216217\par
    217218Concerning the numbers of outliers, one can conclude that in general, the numbers are very low never exceeding
    218 0.1\% except for the ampltiude-extracting spline which seems to mis-reconstruct a certain type of events.
     2190.1\% except for the amplitude-extracting spline which seems to mis-reconstruct a certain type of events.
    219220\par
    220221In conclusion, already this first test excludes all extractors with too large window sizes because
    … …  
    396397\end{figure}
    397398
    398 In this section, we test the lineary of the conversion factors FADC counts to photo-electrons:
     399In this section, we test the linearity of the conversion factors FADC counts to photo-electrons:
    399400
    400401\begin{equation}
    … …  
    410411A first test concerns the stability of the conversion factor: mean number of averaged photo-electrons
    411412per FADC counts over the
    412 tested intensity region. A much more detailed investigation on the linearity will be shwon in a
     413tested intensity region. A much more detailed investigation on the linearity will be shown in a
    413414separate TDAS~\cite{tdas-calibration}.
    414415
    … …  
    437438Figures~\ref{fig:linear:phevscharge9} and~\ref{fig:linear:phevscharge15} shows the conversion factors
    438439using an integrated spline and a fixed window with global peak search, respectively, over
    439 an extration window of 8 FADC slices. The same behaviour as before is obtained. These extractors are
     440an extraction window of 8 FADC slices. The same behaviour as before is obtained. These extractors are
    440441thus linear to good approximation, for the two amplification regions, separately.
    441442\par
    … …  
    568569{\textit{MExtractTimeAndChargeDigitalFilter}} with window size of 6 high-gain and 6 low-gain slices and blue weights
    569570(extractor \#31). }
    570 \label{fig:linear:phevschargearea31}
     571\label{fig:linear:phevschargearea3}
    571572\end{figure}
    572573
    … …  
    579580We estimate the time-uniformity to better
    580581than 300\,ps, a limit due to the different travel times of the light between inner and outer parts of the
    581 camera. Since the calibraion does not permit a precise measurement of the absolute arrival time, we measure
     582camera. Since the calibration does not permit a precise measurement of the absolute arrival time, we measure
    582583the relative arrival time for every channel with respect to a reference channel (usually pixel Nr.\,1):
    583584

  • trunk/MagicSoft/TDAS-Extractor/Changelog

    r6431 r6437  
    1919
    2020                                                 -*-*- END OF LINE -*-*-
     212004/02/13: Markus Gaug
     22  * Algorithms.tex: updated spelling and grammar
     23
    21242004/02/13: Hendrik Bartko
    2225  * Reconstruction.tex: updated+new figures

  • trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex

    r6435 r6437  
    4040\includegraphics[totalheight=7cm]{pulpo_shape_high_low_TDAS.eps}%{pulpo_shape_high.eps}
    4141\end{center}
    42 \caption[Reconstructed high gain shape.]{Average reconstructed pulse shape from a pulpo run showing the highgain and the low gain pulse. The FWHM of the high gain pulse is about 6.2 ns while the FWHM of the low gain pulse is about 10ns.}
     42\caption[Reconstructed high gain shape.]{Average reconstructed pulse shape from a pulpo run showing the high-gain and the low gain pulse. The FWHM of the high gain pulse is about 6.3\,ns while the FWHM of the low gain
     43pulse is about 10\,ns.}
    4344\label{fig:pulpo_shape_high}
    4445\end{figure}
    … …  
    4647
    4748Figure~\ref{fig:pulpo_shape_high} shows the averaged and shifted reconstructed signal of a fast pulser in the so called pulse generator (``pulpo'') setup. Thereby
    48 the response of the photomultipliers to Cherenkov light is simulated by a fast electrical pulse generator which generates unipolar pulses of about 2.5 ns FWHM and preset amplitude. These electrical pulses are transmitted using the same analog-optical link as the PMT pulses and are fed to the MAGIC receiver board. The pulse generator setup is mainly used for test purposes of the receiver board, trigger logic and FADCs.
     49the response of the photo-multipliers to Cherenkov light is simulated by a fast electrical pulse generator which generates unipolar pulses of about 2.5 ns FWHM and preset amplitude. These electrical pulses are transmitted using the same analog-optical link as the PMT pulses and are fed to the MAGIC receiver board. The pulse generator setup is mainly used for test purposes of the receiver board, trigger logic and FADCs.
    4950
    5051
    … …  
    6667\includegraphics[totalheight=7cm]{pulpo_shape_high_low_MC_TDAS.eps}%{pulpo_shape_low.eps}
    6768\end{center}
    68 \caption[Reconstructed pulpo low gain shape.]{Average normalized reconstructed high gain and low gain pulse shapes from a pulpo run.
     69\caption[Reconstructed pulpo low gain shape.]{Average normalized reconstructed high gain and low gain pulse
     70shapes from a pulpo run.
    6971The FWHM of the low gain pulse is about 10 ns. The black line corresponds to the pulse shape implemented into the MC simulations \cite{MC-Camera}.}
    7072\label{fig:pulpo_shape_low}
    … …  
    107109%%% mode: latex
    108110%%% TeX-master: "MAGIC_signal_reco"
     111%%% TeX-master: "MAGIC_signal_reco"
    109112%%% End:

  • trunk/MagicSoft/TDAS-Extractor/pulpo_shape_high_low_TDAS.eps

    r6434 r6437  
    154154 t 0 r 0 0 m /Helvetica-Bold findfont 137.437 sf 0 0 m (high gain pulse) show  gr
    155155 gsave  1231 613
    156  t 0 r 0 0 m /Helvetica-Bold findfont 137.437 sf 0 0 m (log gain pulse) show  gr  1 1 0 c
     156 t 0 r 0 0 m /Helvetica-Bold findfont 137.437 sf 0 0 m (low gain pulse) show  gr  1 1 0 c
    157157 gr  gr
    158158showpage
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