Index: trunk/MagicSoft/TDAS-Extractor/Changelog =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Changelog (revision 5646) +++ trunk/MagicSoft/TDAS-Extractor/Changelog (revision 5647) @@ -19,4 +19,10 @@ -*-*- END OF LINE -*-*- + +2004/12/16: Markus Gaug + * Performance.tex: included sections dealing with calibration (not yet + ready) + + 2004/12/16: Hendrik Bartko Index: trunk/MagicSoft/TDAS-Extractor/Performance.tex =================================================================== --- trunk/MagicSoft/TDAS-Extractor/Performance.tex (revision 5646) +++ trunk/MagicSoft/TDAS-Extractor/Performance.tex (revision 5647) @@ -370,4 +370,32 @@ \subsubsection{Time resolution} +The extractors \#17--32 are able to extract also the arrival time of each pulse. In the calibration, +we have a fast-rising pulse, uniform over camera also in time. 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 have an absolute measurement of the arrival time, we measure +the relative arrival time, i.e. + +\begin{equation} +\delta t_i = t_i - t_1 +\end{equation} + +where $t_i$ denotes the reconstructed arrival time of pixel number $i$ and $t_1$ the reconstructed +arrival time of pixel number 1 (software numbering). For one calibration run, one can then fill +histograms of $\delta t_i$ for each pixel which yields then a mean $<\delta t_i>$, comparable to +systematic offsets in the signal delay and a sigma $\sigma(\delta t_i)$ which is a measure of the +combined time resolutions of pixel $i$ and pixel 1. Assuming that the PMTs and readout channels are +of a same kind, we obtain an approximate absolute time resolution of pixel $i$ by: + +\begin{equation} +tres_i \approx \sigma(\delta t_i)/sqrt(2) +\end{equation} + +Figures~\ref{fig:reltimesinner10leduv} and~\ref{fig:reltimesouter10leduv} show distributions of $<\delta t_i>$ +for +one typical inner pixel and one typical outer pixel and a non-saturating calibration pulse of UV-light, +obtained with three different extractors. One can see that the first two yield a Gaussian distribution +to a good approximation, whereas the third extractor shows a three-peak structure and cannot be fitted. +We discarded that particular extractor for this reason. + \begin{figure}[htp] \centering @@ -380,5 +408,5 @@ right plot the result of the sliding window with a window size of 2 FADC slices (extractor \#17). A medium sized UV-pulse (10Leds UV) has been used which does not saturate the high-gain readout channel.} -\label{fig:reltimesinner} +\label{fig:reltimesinner10leduv} \end{figure} @@ -393,30 +421,86 @@ right plot the result of the sliding window with a window size of 2 FADC slices (extractor \#17). A medium sized UV-pulse (10Leds UV) has been used which does not saturate the high-gain readout channel.} -\label{fig:reltimesouter} -\end{figure} - -\begin{figure}[htp] -\centering -\includegraphics[width=0.45\linewidth]{RelArrTime_Pixel97_10LedBlue_Extractor32.eps} -\includegraphics[width=0.45\linewidth]{RelArrTime_Pixel97_10LedBlue_Extractor23.eps} +\label{fig:reltimesouter10leduv} +\end{figure} + +Figures~\ref{fig:reltimesinner10ledsblue} and~\ref{fig:reltimesouter10ledsblue} show distributions of +$<\delta t_i>$ for +one typical inner and one typical outer pixel and a high-gain-saturating calibration pulse of blue-light, +obtained with two different extractors. One can see that the first (extractor \#23) yields a Gaussian +distribution to a good approximation, whereas the second (extractor \#32) shows a two-peak structure +and cannot be fitted. +\par +\ldots {\it Unfortunately, this happens for all digital filter extractors in the low-gain. +The reason is not yet understood, and has to be found by Hendrik... } \ldots +\par + +\begin{figure}[htp] +\centering +\includegraphics[width=0.31\linewidth]{RelArrTime_Pixel97_10LedBlue_Extractor23.eps} +\includegraphics[width=0.31\linewidth]{RelArrTime_Pixel97_10LedBlue_Extractor32.eps} \caption{Example of a two distributions of relative arrival times of an inner pixel with respect to -the arrival time of the reference pixel Nr. 1. The left plot shows the result using the digital filter - (extractor \#32), the right plot shows the result obtained with the half-maximum of the spline. A +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 filter +(extractor \#32). A medium sized Blue-pulse (10Leds Blue) has been used which saturates the high-gain readout channel.} -\label{fig:reltimesinner} -\end{figure} - -\begin{figure}[htp] -\centering -\includegraphics[width=0.45\linewidth]{RelArrTime_Pixel400_10LedBlue_Extractor32.eps} -\includegraphics[width=0.45\linewidth]{RelArrTime_Pixel400_10LedBlue_Extractor23.eps} +\label{fig:reltimesinner10ledsblue} +\end{figure} + + + +\begin{figure}[htp] +\centering +\includegraphics[width=0.31\linewidth]{RelArrTime_Pixel400_10LedBlue_Extractor23.eps} +\includegraphics[width=0.31\linewidth]{RelArrTime_Pixel400_10LedBlue_Extractor32.eps} \caption{Example of a two distributions of relative arrival times of an outer pixel with respect to -the arrival time of the reference pixel Nr. 1. The left plot shows the result using the digital filter - (extractor \#32), the right plot shows the result obtained with the half-maximum of the spline. A +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 filter +(extractor \#32). A medium sized Blue-pulse (10Leds Blue) has been used which saturates the high-gain readout channel.} -\label{fig:reltimesouter} -\end{figure} - - +\label{fig:reltimesouter10ledsblue} +\end{figure} + +\begin{figure}[htp] +\centering +\includegraphics[width=0.95\linewidth]{TimeResExtractor-5LedsUV-Colour-12.eps} +\caption{Reconstructed arrival time resolutions from a typical, not saturating calibration pulse +of colour UV, reconstructed with each of the tested arrival time extractors. +The first plots shows the time resolutions obtained for the inner pixels, the second one +for the outer pixels. Points +denote the mean of all not-excluded pixels, the error bars their RMS.} +\label{fig:time:5ledsuv} +\end{figure} + +\begin{figure}[htp] +\centering +\includegraphics[width=0.95\linewidth]{TimeResExtractor-1LedUV-Colour-04.eps} +\caption{Reconstructed arrival time resolutions from the lowest intensity calibration pulse +of colour UV (carrying a mean number of 4 photo-electrons), +reconstructed with each of the tested arrival time extractors. +The first plots shows the time resolutions obtained for the inner pixels, the second one +for the outer pixels. Points +denote the mean of all not-excluded pixels, the error bars their RMS.} +\label{fig:time:1leduv} +\end{figure} + +\begin{figure}[htp] +\centering +\includegraphics[width=0.95\linewidth]{TimeResExtractor-2LedsGreen-Colour-02.eps} +\caption{Reconstructed arrival time resolutions from a typical, not saturating calibration pulse +of colour Green, reconstructed with each of the tested arrival time extractors. +The first plots shows the time resolutions obtained for the inner pixels, the second one +for the outer pixels. Points +denote the mean of all not-excluded pixels, the error bars their RMS.} +\label{fig:time:2ledsgreen} +\end{figure} + +\begin{figure}[htp] +\centering +\includegraphics[width=0.95\linewidth]{TimeResExtractor-23LedsBlue-Colour-00.eps} +\caption{Reconstructed arrival time resolutions from the highest intensity calibration pulse +of colour blue, reconstructed with each of the tested arrival time extractors. +The first plots shows the time resolutions obtained for the inner pixels, the second one +for the outer pixels. Points +denote the mean of all not-excluded pixels, the error bars their RMS.} +\label{fig:time:23ledsblue} +\end{figure} \clearpage