Index: /trunk/MagicSoft/TDAS-Extractor/Algorithms.tex =================================================================== --- /trunk/MagicSoft/TDAS-Extractor/Algorithms.tex (revision 6746) +++ /trunk/MagicSoft/TDAS-Extractor/Algorithms.tex (revision 6747) @@ -657,5 +657,5 @@ Figure \ref{fig:amp_sliding} shows the result of the applied amplitude and time weights to the recorded FADC time slices of one -simulated MC pulse. The left plot displayes the result of the applied amplitude weights +simulated MC pulse. The left plot displays the result of the applied amplitude weights $e(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{amp}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ and the right plot shows the result of the applied timing weights @@ -687,5 +687,5 @@ one simulated MC pulse. The left plot shows the result of the applied amplitude weights $e(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{amp}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ and -the right plot displayes the result of the applied timing weights +the right plot displays the result of the applied timing weights $e\tau(t_0)=\sum_{i=0}^{i=n-1} w_{\mathrm{time}}(t_0+i \cdot T_{\text{ADC}})y(t_0+i \cdot T_{\text{ADC}})$ as a function of the time shift $t_0$.} \label{fig:amp_sliding} @@ -816,5 +816,5 @@ {\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}}. -Analogue for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with +Analog 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}}. } : @@ -830,5 +830,5 @@ {\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}}. -Analogue for the low gain extraction range. Note that in MARS, the low-gain FADC samples start with +Analog 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} @@ -889,3 +889,4 @@ %%% TeX-master: "MAGIC_signal_reco" %%% TeX-master: "MAGIC_signal_reco" +%%% TeX-master: "Algorithms" %%% End: Index: /trunk/MagicSoft/TDAS-Extractor/Calibration.tex =================================================================== --- /trunk/MagicSoft/TDAS-Extractor/Calibration.tex (revision 6746) +++ /trunk/MagicSoft/TDAS-Extractor/Calibration.tex (revision 6747) @@ -7,5 +7,5 @@ The LED pulser system is able to provide fast light pulses of 2--4\,ns FWHM with intensities ranging from 3--4 to more than 600 photo-electrons in one inner photo-multiplier of the -camera. These pulses can be produced in three colours {\textit {\bf green, blue}} and +camera. These pulses can be produced in three colors {\textit {\bf green, blue}} and {\textit{\bf UV}}. @@ -15,5 +15,5 @@ \hline \hline -\multicolumn{7}{|c|}{The possible pulsed light colours} \\ +\multicolumn{7}{|c|}{The possible pulsed light colors} \\ \hline \hline @@ -29,9 +29,9 @@ \hline \end{tabular} -\caption{The pulser colours available from the calibration system} +\caption{The pulser colors available from the calibration system} \label{tab:pulsercolours} \end{table} -Table~\ref{tab:pulsercolours} lists the available colours and intensities and +Table~\ref{tab:pulsercolours} lists the available colors and intensities and figures~\ref{fig:pulseexample1leduv} and~\ref{fig:pulseexample23ledblue} show exemplary pulses as registered by the FADCs. @@ -53,5 +53,5 @@ different intensity and colour. \item Time resolution: These tests show the time resolution and stability obtained with different -intensities and colours. +intensities and colors. \end{enumerate} @@ -161,5 +161,5 @@ The following figures~\ref{fig:unsuited:5ledsuv},~\ref{fig:unsuited:1leduv},~\ref{fig:unsuited:2ledsgreen} and~\ref{fig:unsuited:23ledsblue} show the resulting numbers of un-calibrated pixels and events for -different colours and intensities. Because there is a strong anti-correlation between the number of +different colors and intensities. Because there is a strong anti-correlation between the number of excluded pixels and the number of outliers per event, we have chosen to show these numbers together. @@ -254,5 +254,5 @@ value of about 2.6$\pm$0.1~\cite{michele-diploma}. \par -In our case, there is an additional complication due to the fact that the green and blue coloured light pulses +In our case, there is an additional complication due to the fact that the green and blue colored light pulses show secondary pulses which destroy the Poisson behaviour of the number of photo-electrons. We will have to split our sample of extractors into those being affected by the secondary pulses and those @@ -278,5 +278,5 @@ Also the sliding windows smaller than 6 FADC slices and the spline smaller than 2 FADC slices reproduce too small numbers of photo-electrons. Moreover, the digital filter shows a small dependency -of the number of photo-electrons w.r.t. the extration window. +of the number of photo-electrons w.r.t. the extraction window. \par @@ -384,5 +384,5 @@ \par Figure~\ref{fig:linear:phevscharge4} shows the conversion factor $c_{phe}$ obtained for different light intensities -and colours for three exemplary inner and three exemplary outer pixels using a fixed window on +and colors for three exemplary inner and three exemplary outer pixels using a fixed window on 8 FADC slices. The conversion factor seems to be linear to a good approximation, with the following restrictions: \begin{itemize} @@ -441,5 +441,5 @@ been used in the analysis and to derive a Crab spectrum with the consequence that the spectrum bends down at high energies. We suppose that the loss of linearity due to usage of this extractor is responsible for the encountered problems. -A similiar behaviour can be found for all extractors with window sizes smaller than 6 FADC slices, especially in the low-gain region. +A similar behaviour can be found for all extractors with window sizes smaller than 6 FADC slices, especially in the low-gain region. This is understandable since the low-gain pulse covers at least 6 FADC slices. (This behaviour @@ -622,5 +622,5 @@ vs. a reference extractor (sliding window over 8 high-gain and 8 low-gain FADC slices, extractor \#21). The tested extractors are: top left: integrating spline over 0.5 FADC slices left from maximum and 1.5 -FADC slice right from maximum (extrator \#25), top right: integrating spline over 1.5 FADC slices left +FADC slice right from maximum (extractor \#25), top right: integrating spline over 1.5 FADC slices left from maximum and 4.5 FADC slices right from maximum (extractor \#27), bottom left: digital filter fitting cosmics pulses over 6 FADC slices, bottom left: digital filter fitting a blue calibration pulse over @@ -702,5 +702,5 @@ to miss the exact arrival time in some events. Only the position of the half-maximum gives the expected result of a single Gaussian distribution. -A similiar problem occurs in the case of the digital filter: If one takes the correct weights +A similar problem occurs in the case of the digital filter: If one takes the correct weights (fig.~\ref{fig:reltimesinnerledblue2} bottom), the distribution is perfectly Gaussian and the resolution good, however a rather slight change from the blue calibration pulse weights to cosmics pulses weights (top) @@ -800,5 +800,5 @@ \par In figure~\ref{fig:timeunsuit:23ledsblue}, one can see the number of outliers from an intense calibration pulse of blue light yielding about -600 photo-electrons per inner pixel. All extractors seem to be stable, except for the digital filter with weigths over 4 FADC slices. This +600 photo-electrons per inner pixel. All extractors seem to be stable, except for the digital filter with weights over 4 FADC slices. This is expected, since the low-gain pulse is wider than 4 FADC slices. \par @@ -895,5 +895,5 @@ Figures~\ref{fig:time:5ledsuv} through~\ref{fig:time:23ledsblue} show the measured time resolutions for very different calibration -pulse intensities and colours. One can see that the sliding window resolutions are always worse than the spline and digital filter +pulse intensities and colors. One can see that the sliding window resolutions are always worse than the spline and digital filter algorithms. Moreover, the half-maximum position search by the spline is always slightly better than the maximum position search. The digital filter does not show notable differences with respect to the pulse form or the extraction window size, except for the low-gain @@ -948,6 +948,6 @@ \clearpage -The following figure~\ref{fig:time:dep} shows the time resolution for various calibration runs taken with different colours -and light intensities as a funcion of the mean number of photo-electrons -- +The following figure~\ref{fig:time:dep} shows the time resolution for various calibration runs taken with different colors +and light intensities as a function of the mean number of photo-electrons -- reconstructed with the F-Factor method -- for four different time extractors. The dependencies have been fit to the following empirical relation: @@ -982,6 +982,6 @@ \end{tabular} \caption{The fit results obtained from the fit of equation~\ref{eq:time:fit} to the time resolutions obtained for various -intensities and colours. The fit probabilities are very small mainly because of the different intrinsic arrival time spreads of -the photon pulses from different colours. } +intensities and colors. The fit probabilities are very small mainly because of the different intrinsic arrival time spreads of +the photon pulses from different colors. } \label{tab:time:fitresults}. } @@ -989,6 +989,6 @@ The low fit probabilities are partly due to the systematic differences in the pulse forms in intrinsic arrival time spreads between -pulses of different LED colours. Nevertheless, we had to include all colours in the fit to cover the full dynamic range. In general, -one can see that the time resolutions for the UV pulses are systematically better than for the other colours which we attribute to the fact +pulses of different LED colors. Nevertheless, we had to include all colors in the fit to cover the full dynamic range. In general, +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 the these pulses have a smaller intrinsic pulse width -- which is very close to pulses from cosmics. Moreover, there are clear differences visible between different time extractors, especially the sliding window extractor yields poor resolutions. The other three extractors are @@ -1020,8 +1020,8 @@ the half-maximum searching spline (extractor~\#25, top right), the digital filter with correct pulse weights over 6 slices (extractor~\#30 and~\#32, bottom left) -and the digital filter with UV calibration-pulse weights over 4 slices (extractor~\#31 and~\#33, bottom rigth). +and the digital filter with UV calibration-pulse weights over 4 slices (extractor~\#31 and~\#33, bottom right). Error bars denote the spread (RMS) of time resolutions of the investigated channels. -The marker colours show the applied -pulser colour, except for the last (green) point where all three colours were used.} +The marker colors show the applied +pulser colour, except for the last (green) point where all three colors were used.} \label{fig:time:dep} \end{figure} Index: /trunk/MagicSoft/TDAS-Extractor/Criteria.tex =================================================================== --- /trunk/MagicSoft/TDAS-Extractor/Criteria.tex (revision 6746) +++ /trunk/MagicSoft/TDAS-Extractor/Criteria.tex (revision 6747) @@ -3,5 +3,5 @@ The goal for the optimal signal reconstruction algorithm is to compute an unbiased estimate of the strength and arrival time of the Cherenkov signal with the highest possible resolution for all signal intensities. The MAGIC telescope has been optimized to -lower the energy treshold of observation in any respect. Particularly the choice for an FADC system has been made with an eye on the +lower the energy threshold of observation in any respect. Particularly the choice for an FADC system has been made with an eye on the possibility to extract the smallest possible signals from air showers. It would be inconsequent not to continue the optimization procedure in the signal extraction algorithms and the subsequent image cleaning. @@ -82,5 +82,5 @@ Because of the peculiarities of the MAGIC data acquisition system, the extraction of the low-gain pulse is somewhat critical: -The low-gain pulse shape differs significantly from the high-gain shape. Due to the analogue delay line, the low-gain pulse is +The low-gain pulse shape differs significantly from the high-gain shape. Due to the analog delay line, the low-gain pulse is wider and the integral charge is distributed over a longer time window. @@ -121,5 +121,5 @@ non-trivial for extractors searching the signal in a sliding window. \item As the calibration pulses are slightly wider than the cosmics pulses, the obtained conversion factors must not be affected by -the difference in pulse shape. This puts severe contraints on all extractors which do not integrate the whole pulse or take the pulse +the difference in pulse shape. This puts severe constraints on all extractors which do not integrate the whole pulse or take the pulse shape into account. \end{enumerate} Index: /trunk/MagicSoft/TDAS-Extractor/Introduction.tex =================================================================== --- /trunk/MagicSoft/TDAS-Extractor/Introduction.tex (revision 6746) +++ /trunk/MagicSoft/TDAS-Extractor/Introduction.tex (revision 6747) @@ -13,5 +13,5 @@ 1.0 - 1.2 ns and rise and fall times of 600 and 700\,ps correspondingly~\cite{Magic-PMT}. By modulating vertical-cavity surface-emitting laser (VCSEL) -type laser diodes in amplitude, the fast analogue signals from the PMTs are transferred via 162\,m long, +type laser diodes in amplitude, the fast analog signals from the PMTs are transferred via 162\,m long, 50/125\,$\mu$m diameter optical fibers to the counting house \cite{MAGIC-analog-link-2}. After transforming the light back to an electrical signal, the original PMT pulse has a FWHM of about 2.2 ns and rise and fall @@ -82,15 +82,15 @@ \item Size: The outer pixels have a factor four bigger area then the inner pixels~\cite{MAGIC-design}. Their (quantum-efficiency convoluted) effective area is about a factor 2.6 higher. -\item Gain: The camera is flat-fielded in order to yield a similiar reconstructed charge signal for the same photon illumination intensity. +\item Gain: The camera is flat-fielded in order to yield a similar reconstructed charge signal for the same photon illumination intensity. In order to achieve this, the gain of the inner pixels has been adjusted to about a factor 2.6 higher than the outer ones~\cite{tdas-calibration}. This results in lower effective noise charge from the night sky background for the outer pixels. \item Delay: The signal of the outer pixels is delayed by about 1.5\,ns with respect to the inner ones. \end{enumerate} -\item[Clock noise:\xspace] The MAGIC 300\,MHz FADCs have an intrinsic clock noise of a few LSBs occurring with a frequency of 150\,MHz. +\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. This clock noise results in a superimposed AB-pattern for the read-out pedestals. In the standard analysis, the amplitude of this clock noise gets measured in the pedestal extraction algorithms and further corrected for by all signal extractors. \item[Trigger Jitter:\xspace] The FADC clock is not synchronized with the trigger. Therefore, the relative position of the recorded -signal samples varies uniformely by one FADC slice with respect to the position of the signal shape by one FADC slice from event to event. +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. \item[DAQ jumps:\xspace] Unfortunately, the position of the signal pulse with respect to the first recorded FADC sample is not constant. It varies randomly by an integer number of FADC slices -- typically two -- in about 1\% of the channels per event. Index: /trunk/MagicSoft/TDAS-Extractor/Pedestal.tex =================================================================== --- /trunk/MagicSoft/TDAS-Extractor/Pedestal.tex (revision 6746) +++ /trunk/MagicSoft/TDAS-Extractor/Pedestal.tex (revision 6747) @@ -83,6 +83,6 @@ \item Determine $B$ and $MSE$ from MC events with added noise. % Assuming that $MSE$ and $B$ are negligible for the events without noise, one can - With this method, one can get a dependence of both values on the size of the signal, - although the MC might contain systematic differences with respect to the real data. + With this method, one can get a dependence of both values on the size of the signal, + although the MC might contain systematic differences with respect to the real data. \item Determine $MSE$ from the error retrieved from the fit results of $\widehat{S}$, which is possible for the fit and the digital filter (eq.~\ref{eq:of_noise}). @@ -190,5 +190,5 @@ and for the different levels of (night-sky) background applied to 1000 pedestal events. One can see that the bias vanishes to an accuracy of better than 2\% of a photo-electron -makefor the extractors which are used in this TDAS. +for the extractors which are used in this TDAS. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1 @@ -564,5 +564,5 @@ applied on a sliding window of different sizes. In the top plot, a pedestal run with extra-galactic star background has been taken and in the bottom, -a galatic star background. An exemplary pixel (Nr. 100) has been used. +a galactic star background. An exemplary pixel (Nr. 100) has been used. Above, a rate of 0.08 phe/ns and below, a rate of 0.1 phe/ns has been obtained.} \label{fig:df:ratiofit} @@ -613,3 +613,4 @@ %%% TeX-master: "MAGIC_signal_reco" %%% TeX-master: "MAGIC_signal_reco" +%%% TeX-master: "MAGIC_signal_reco" %%% End: Index: /trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex =================================================================== --- /trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex (revision 6746) +++ /trunk/MagicSoft/TDAS-Extractor/Reconstruction.tex (revision 6747) @@ -25,5 +25,5 @@ -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). +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). @@ -60,5 +60,5 @@ % while the FWHM of the average reconstructed low gain pulse shape is % 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. -It has a FWHM of about 10 ns. +It has a FWHM of about 10\,ns.