Index: trunk/MagicSoft/TDAS-Extractor/Algorithms.tex =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Algorithms.tex (revision 6436) +++ trunk/MagicSoft/TDAS-Extractor/Algorithms.tex (revision 6437) @@ -16,5 +16,5 @@ \begin{figure}[htp] \includegraphics[width=0.99\linewidth]{ExtractorClasses.eps} -\caption{Sketch of the inheritances of three examplary MARS signal extractor classes: +\caption{Sketch of the inheritances of three exemplary MARS signal extractor classes: MExtractFixedWindow, MExtractTimeFastSpline and MExtractTimeAndChargeDigitalFilter} \label{fig:extractorclasses} @@ -302,6 +302,6 @@ \begin{description} \item[Extraction Type Amplitude:\xspace] The amplitude of the spline maximum is taken as charge signal -and the (precisee) position of the maximum is returned as arrival time. This type is faster, since it -performs not spline intergraion. +and the (precise) position of the maximum is returned as arrival time. This type is faster, since it +performs not spline integration. \item[Extraction Type Integral:\xspace] The integrated spline between maximum position minus rise time (default: 1.5 slices) and maximum position plus fall time (default: 4.5 slices) @@ -359,5 +359,8 @@ -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. +The pulse shape is mainly determined by the artificial pulse stretching by about 6 ns on the receiver board. +Thus the first assumption holds. Also the second assumption is fulfilled: 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 different night sky background conditions. Let $g(t)$ be the normalized signal shape, $E$ the signal amplitude and $\tau$ the time shift @@ -452,5 +455,5 @@ \par Because of the truncation of the Taylor series in equation (\ref{shape_taylor_approx}) the above results are -only valid for vanishing time offsets $\tau$. For non-zero time offsets one has to iterate the problem using +only valid for vanishing time offsets $\tau$. For non-zero time offsets, one has to iterate the problem using the time shifted signal shape $g(t-\tau)$. @@ -458,5 +461,5 @@ \begin{equation} -\left(\boldsymbol{V}^{-1}\right)_{i,j} +\left(\boldsymbol{V}^{-1}\right)_{ij} =\frac{1}{2}\left(\frac{\partial^2 \chi^2(E, E\tau)}{\partial \alpha_i \partial \alpha_j} \right) \quad \text{with} \quad \alpha_i,\alpha_j \in \{E, E\tau\} \ . @@ -482,32 +485,44 @@ -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: $ \approx 4$~FADC counts. Using the digital filter with weights parameterized over 6 FADC slices ($i=1...5$) the error of the reconstructed signal and time is give by: - -\begin{equation} -\sigma_E \approx 8.3 \ \mathrm{FADC\ counts} \qquad \sigma_{\tau} \approx \frac{6.5\ \Delta T_{\mathrm{FADC}}}{(E\ /\ \mathrm{FADC\ counts})} \ , +In the MAGIC MC simulations~\cite{MC-Camera}, an night-sky background rate of 0.13 photoelectrons per ns, +an FADC gain of 7.8 FADC counts per photo-electron and an intrinsic FADC noise of 1.3 FADC counts +per FADC slice is implemented. +These numbers simulate the night sky background conditions for an extragalactic source and result +in a noise contribution of about 4 FADC counts per single FADC slice: +$\sqrt{B_{ii}} \approx 4$~FADC counts. +Using the digital filter with weights parameterized over 6 FADC slices ($i=0...5$) the errors of the +reconstructed signal and time amount to: + +\begin{equation} +\sigma_E \approx 8.3 \ \mathrm{FADC\ counts} \ (\approx 1.1\,\mathrm{phe}) \qquad +\sigma_{\tau} \approx \frac{6.5\ \Delta T_{\mathrm{FADC}}}{(E\ /\ \mathrm{FADC\ counts})} \ (\approx \frac{2.8\,\mathrm{ns}}{E\,/\ \mathrm{N_{phe}}})\ , \label{eq:of_noise_calc} \end{equation} -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. - -%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: - -For an IACT there are two types of background noise. On the one hand, there is the constantly present -electronics noise, -on the other hand, the light of the night sky introduces a sizeable background noise to the measurement of -Cherenkov photons from air showers. - -The electronics noise is largely white, uncorrelated in time. The noise from the night sky background photons -is the superposition of the +where $\Delta T_{\mathrm{FADC}} = 3.33$ ns is the sampling interval of the MAGIC FADCs. +The error in the reconstructed signal corresponds to about one photo electron. +For signals of the size of two photo electrons, the timing error is a bit higher than 1\,ns. +\par + +An IACT has typically two types of background noise: +On the one hand, there is the constantly present electronics noise, +while on the other hand, the light of the night sky introduces a sizeable background +to the measurement of the Cherenkov photons from air showers. + +The electronics noise is largely white, i.e. uncorrelated in time. +The noise from the night sky background photons is the superposition of the detector response to single photo electrons following a Poisson distribution in time. Figure \ref{fig:noise_autocorr_allpixels} shows the noise -autocorrelation matrix for an open camera. The large noise autocorrelation in time of the current FADC -system is due to the pulse shaping with a shaping constant of 6 ns. - -In general, the amplitude and time weights, $\boldsymbol{w}_{\text{amp}}$ and $\boldsymbol{w}_{\text{time}}$, depend on the pulse shape, the -derivative of the pulse shape and the noise autocorrelation. In the high gain samples the correlated night sky background noise dominates over -the white electronics noise. Thus different noise levels just cause the noise autocorrelation matrix $\boldsymbol{B}$ to change by a same factor, -which cancels out in the weights calculation. Thus in the high gain the weights are to a very good approximation independent of the night -sky background noise level. +autocorrelation matrix for an open camera. The large noise autocorrelation of the current FADC +system is due to the pulse shaping (with the shaping constant equivalent to about two FADC slices). + +In general, the amplitude and time weights, $\boldsymbol{w}_{\text{amp}}$ and $\boldsymbol{w}_{\text{time}}$, +depend on the pulse shape, the derivative of the pulse shape and the noise autocorrelation. +In the high gain samples, the correlated night sky background noise dominates over +the white electronics noise. Thus, different noise levels just cause the members of the noise autocorrelation +matrix to change by a same factor, +which cancels out in the weights calculation. +Thus, the weights are to a very good approximation independent from the night +sky background noise level in the high gain. Contrary to that in the low gain samples ... . @@ -518,13 +533,13 @@ -\begin{figure}[h!] -\begin{center} -\includegraphics[totalheight=7cm]{noise_autocorr_AB_36038_TDAS.eps} -\end{center} -\caption[Noise autocorrelation one pixel.]{Noise autocorrelation -matrix $\boldsymbol{B}$ for open camera including the noise due to night sky background fluctuations -for one single pixel (obtained from 1000 events).} -\label{fig:noise_autocorr_1pix} -\end{figure} +%\begin{figure}[h!] +%\begin{center} +%\includegraphics[totalheight=7cm]{noise_autocorr_AB_36038_TDAS.eps} +%\end{center} +%\caption[Noise autocorrelation one pixel.]{Noise autocorrelation +%matrix $\boldsymbol{B}$ for open camera including the noise due to night sky background fluctuations +%for one single pixel (obtained from 1000 events).} +%\label{fig:noise_autocorr_1pix} +%\end{figure} \begin{figure}[htp] @@ -641,5 +656,5 @@ $e\tau(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{time}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ as a function of the time shift $t_0$.} \label{fig:amp_sliding} -\end{figure} +\end{figure}in the high gain @@ -679,8 +694,8 @@ \item "calibration\_weights4\_blue.dat'' with a window size of 4 FADC slices \item "calibration\_weights\_UV.dat'' with a window size of 6 FADC slices and in the low-gain the -calibration weigths obtained from blue pulses\footnote{UV-pulses saturating the high-gain are not yet +calibration weights obtained from blue pulses\footnote{UV-pulses saturating the high-gain are not yet available.}. \item "calibration\_weights4\_UV.dat'' with a window size of 4 FADC slices and in the low-gain the -calibration weigths obtained from blue pulses\footnote{UV-pulses saturating the high-gain are not yet +calibration weights obtained from blue pulses\footnote{UV-pulses saturating the high-gain are not yet available.}. \item "cosmics\_weights\_logaintest.dat'' with a window size of 6 FADC slices and swapped high-gain and low-gain @@ -779,9 +794,9 @@ \begin{description} -\item[MExtractFixedWindow]: with the following intialization, if {\textit{maxbin}} defines the +\item[MExtractFixedWindow]: with the following initialization, if {\textit{maxbin}} defines the mean position of the high-gain FADC slice which carries the pulse maximum \footnote{The function {\textit{MExtractor::SetRange(higain first, higain last, logain first, logain last)}} sets the extraction range with the high gain start bin {\textit{higain first}} to (including) the last bin {\textit{higain last}}. -Analoguously for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with +Analogue for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with the index 0 again, thus {\textit{maxbin+0.5}} means in reality {\textit{maxbin+15+0.5}}. } : @@ -797,5 +812,5 @@ {\textit{MExtractor::SetRange(higain first, higain last, logain first, logain last)}} sets the extraction range with the high gain start bin {\textit{higain first}} to (including) the last bin {\textit{higain last}}. -Analoguously for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with +Analogue for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with the index 0 again, thus {\textit{maxbin+0.5}} means in reality {\textit{maxbin+15+0.5}}.}: \resume{enumerate} @@ -874,3 +889,4 @@ %%% mode: latex %%% TeX-master: "MAGIC_signal_reco" +%%% TeX-master: "MAGIC_signal_reco" %%% End: Index: trunk/MagicSoft/TDAS-Extractor/Calibration.tex =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Calibration.tex (revision 6436) +++ trunk/MagicSoft/TDAS-Extractor/Calibration.tex (revision 6437) @@ -1,2 +1,3 @@ +\section{Calibration \label{sec:calibration}} @@ -45,5 +46,5 @@ \begin{enumerate} \item Un-calibrated pixels and events: These tests measure the percentage of failures of the extractor -resulting either in a pixel declared as un-calibrated or in an event which produces a signal ouside +resulting either in a pixel declared as un-calibrated or in an event which produces a signal outside of the expected Gaussian distribution. \item Number of photo-electrons: These tests measure the reconstructed numbers of photo-electrons, their @@ -84,7 +85,7 @@ The corresponding MAGIC data run numbers range from nr. 31741 to 31772. These data was taken before the latest camera repair access which resulted in a replacement of about 2\% of the pixels known to be -mal-functionning at that time. +mal-functioning at that time. There is thus a lower limit to the number of un-calibrated pixels of about 1.5--2\% of known -mal-functionning photo-multipliers. +mal-functioning photo-multipliers. \par Although we had looked at and tested all colour and extractor combinations resulting from these data, @@ -102,5 +103,5 @@ \subsection{Un-Calibrated Pixels and Events} -The MAGIC calibration software incorporates a series of checks to sort out mal-functionning pixels. +The MAGIC calibration software incorporates a series of checks to sort out mal-functioning pixels. Except for the software bug searching criteria, the following exclusion criteria can apply: @@ -112,5 +113,5 @@ \item The reconstructed mean signal error is smaller than its value. This criterium cuts out signal distributions which fluctuate so much that their RMS is bigger than its mean value. This -criterium cuts out ``ringing'' pixels or mal-functionning extractors. +criterium cuts out ``ringing'' pixels or mal-functioning extractors. \item The reconstructed mean number of photo-electrons lies 4.5 sigma outside the distribution of photo-electrons obtained with the inner or outer pixels in the camera, respectively. @@ -120,5 +121,5 @@ \item All pixels with reconstructed negative mean signal or with a mean numbers of photo-electrons smaller than one. Pixels with a negative pedestal RMS subtracted -sigma occur, especially when stars are focussed onto that pixel during the pedestal taking (resulting +sigma occur, especially when stars are focused onto that pixel during the pedestal taking (resulting in a large pedestal RMS), but have moved to another pixel during the calibration run. In this case, the number of photo-electrons would result artificially negative. If these @@ -152,5 +153,5 @@ \centering \includegraphics[height=0.75\textheight]{UnsuitVsExtractor-all.eps} -\caption{Uncalibrated pixels and outlier events averaged over all available +\caption{Un-calibrated pixels and outlier events averaged over all available calibration runs.} \label{fig:unsuited:all} @@ -167,5 +168,5 @@ \centering \includegraphics[height=0.95\textheight]{UnsuitVsExtractor-5LedsUV-Colour-13.eps} -\caption{Uncalibrated pixels and outlier events for a typical calibration +\caption{Un-calibrated pixels and outlier events for a typical calibration pulse of UV-light which does not saturate the high-gain readout.} \label{fig:unsuited:5ledsuv} @@ -175,5 +176,5 @@ \centering \includegraphics[height=0.95\textheight]{UnsuitVsExtractor-1LedUV-Colour-04.eps} -\caption{Uncalibrated pixels and outlier events for a very low +\caption{Un-calibrated pixels and outlier events for a very low intensity pulse.} \label{fig:unsuited:1leduv} @@ -183,5 +184,5 @@ \centering \includegraphics[height=0.95\textheight]{UnsuitVsExtractor-2LedsGreen-Colour-02.eps} -\caption{Uncalibrated pixels and outlier events for a typical green pulse.} +\caption{Un-calibrated pixels and outlier events for a typical green pulse.} \label{fig:unsuited:2ledsgreen} \end{figure} @@ -190,5 +191,5 @@ \centering \includegraphics[height=0.95\textheight]{UnsuitVsExtractor-23LedsBlue-Colour-00.eps} -\caption{Uncalibrated pixels and outlier events for a high-intensity blue pulse.} +\caption{Un-calibrated pixels and outlier events for a high-intensity blue pulse.} \label{fig:unsuited:23ledsblue} \end{figure} @@ -216,5 +217,5 @@ \par Concerning the numbers of outliers, one can conclude that in general, the numbers are very low never exceeding -0.1\% except for the ampltiude-extracting spline which seems to mis-reconstruct a certain type of events. +0.1\% except for the amplitude-extracting spline which seems to mis-reconstruct a certain type of events. \par In conclusion, already this first test excludes all extractors with too large window sizes because @@ -396,5 +397,5 @@ \end{figure} -In this section, we test the lineary of the conversion factors FADC counts to photo-electrons: +In this section, we test the linearity of the conversion factors FADC counts to photo-electrons: \begin{equation} @@ -410,5 +411,5 @@ A first test concerns the stability of the conversion factor: mean number of averaged photo-electrons per FADC counts over the -tested intensity region. A much more detailed investigation on the linearity will be shwon in a +tested intensity region. A much more detailed investigation on the linearity will be shown in a separate TDAS~\cite{tdas-calibration}. @@ -437,5 +438,5 @@ Figures~\ref{fig:linear:phevscharge9} and~\ref{fig:linear:phevscharge15} shows the conversion factors using an integrated spline and a fixed window with global peak search, respectively, over -an extration window of 8 FADC slices. The same behaviour as before is obtained. These extractors are +an extraction window of 8 FADC slices. The same behaviour as before is obtained. These extractors are thus linear to good approximation, for the two amplification regions, separately. \par @@ -568,5 +569,5 @@ {\textit{MExtractTimeAndChargeDigitalFilter}} with window size of 6 high-gain and 6 low-gain slices and blue weights (extractor \#31). } -\label{fig:linear:phevschargearea31} +\label{fig:linear:phevschargearea3} \end{figure} @@ -579,5 +580,5 @@ We estimate the time-uniformity to better than 300\,ps, a limit due to the different travel times of the light between inner and outer parts of the -camera. Since the calibraion does not permit a precise measurement of the absolute arrival time, we measure +camera. Since the calibration does not permit a precise measurement of the absolute arrival time, we measure the relative arrival time for every channel with respect to a reference channel (usually pixel Nr.\,1): Index: trunk/MagicSoft/TDAS-Extractor/Changelog =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Changelog (revision 6436) +++ trunk/MagicSoft/TDAS-Extractor/Changelog (revision 6437) @@ -19,4 +19,7 @@ -*-*- END OF LINE -*-*- +2004/02/13: Markus Gaug + * Algorithms.tex: updated spelling and grammar + 2004/02/13: Hendrik Bartko * Reconstruction.tex: updated+new figures Index: trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex (revision 6436) +++ trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex (revision 6437) @@ -40,5 +40,6 @@ \includegraphics[totalheight=7cm]{pulpo_shape_high_low_TDAS.eps}%{pulpo_shape_high.eps} \end{center} -\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.} +\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 +pulse is about 10\,ns.} \label{fig:pulpo_shape_high} \end{figure} @@ -46,5 +47,5 @@ Figure~\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 -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. +the 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. @@ -66,5 +67,6 @@ \includegraphics[totalheight=7cm]{pulpo_shape_high_low_MC_TDAS.eps}%{pulpo_shape_low.eps} \end{center} -\caption[Reconstructed pulpo low gain shape.]{Average normalized reconstructed high gain and low gain pulse shapes from a pulpo run. +\caption[Reconstructed pulpo low gain shape.]{Average normalized reconstructed high gain and low gain pulse +shapes from a pulpo run. The 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}.} \label{fig:pulpo_shape_low} @@ -107,3 +109,4 @@ %%% mode: latex %%% TeX-master: "MAGIC_signal_reco" +%%% TeX-master: "MAGIC_signal_reco" %%% End: Index: trunk/MagicSoft/TDAS-Extractor/pulpo_shape_high_low_TDAS.eps =================================================================== --- trunk/MagicSoft/TDAS-Extractor/pulpo_shape_high_low_TDAS.eps (revision 6436) +++ trunk/MagicSoft/TDAS-Extractor/pulpo_shape_high_low_TDAS.eps (revision 6437) @@ -154,5 +154,5 @@ t 0 r 0 0 m /Helvetica-Bold findfont 137.437 sf 0 0 m (high gain pulse) show gr gsave 1231 613 - t 0 r 0 0 m /Helvetica-Bold findfont 137.437 sf 0 0 m (log gain pulse) show gr 1 1 0 c + t 0 r 0 0 m /Helvetica-Bold findfont 137.437 sf 0 0 m (low gain pulse) show gr 1 1 0 c gr gr showpage