Changeset 6635 for trunk/MagicSoft/TDAS-Extractor/Calibration.tex

Timestamp:

02/19/05 21:19:08 (20 years ago)

Author:

gaug

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• trunk/MagicSoft/TDAS-Extractor/Calibration.tex (modified) (12 diffs)

trunk/MagicSoft/TDAS-Extractor/Calibration.tex

@@ -727 +727 @@
 in order to count how many times the extractor has failed to reconstruct the correct arrival time.
 \par
-Figure~\ref{fig:time:5ledsuv} shows the number of outliers for the different time extractors, obtained with 
+Figure~\ref{fig:timeunsuit:5ledsuv} shows the number of outliers for the different time extractors, obtained with 
 a UV pulse of about 20 photo-electrons. One can see that all time extractors yield an acceptable mis-reconstruction 
 rate of about 0.5\%, except for the maximum searching spline yields three times more mis-reconstructions. 
 \par
-If one goes to very low-intensity pulses, as shown in figure~\ref{fig:time:1leduv}, obtained with on average 4 photo-electrons, 
+If one goes to very low-intensity pulses, as shown in figure~\ref{fig:timeunsuit:1leduv}, obtained with on average 4 photo-electrons, 
 the number of mis-reconstructions increases considerably up to 20\% for some extractors. We interpret this high mis-reconstruction 
 rate to the increase possibility to mis-reconstruct a pulse from the night sky background noise instead of the signal pulse from the 
@@ -737 +737 @@
 in that respect. 
 \par
-The same conclusion seems to hold for the green pulse of about 20 photo-electrons (figure~\ref{fig:time:2ledsgreen}) 
+The same conclusion seems to hold for the green pulse of about 20 photo-electrons (figure~\ref{fig:timeunsuit:2ledsgreen}) 
 where the digital filter over 6 FADC slices seems to 
 yield more stable results than the one over 4 FADC slices. The half-maximum searching spline seems to be superior to the maximum-searching 
 one. 
 \par
-In figure~\ref{fig:time:23ledsblue}, one can see the number of outliers from an intense calibration pulse of blue light yielding about 
+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
 is expected, since the low-gain pulse is wider than 4 FADC slices.
@@ -757 +757 @@
 for the outer pixels. Points 
 denote the mean of all not-excluded pixels, the error bars their RMS.}
-\label{fig:time:5ledsuv}
+\label{fig:timeunsuit:5ledsuv}
 \end{figure}
 
@@ -769 +769 @@
 for the outer pixels. Points 
 denote the mean of all not-excluded pixels, the error bars their RMS.}
-\label{fig:time:1leduv}
+\label{fig:timeunsuit:1leduv}
 \end{figure}
 
@@ -780 +780 @@
 for the outer pixels. Points 
 denote the mean of all not-excluded pixels, the error bars their RMS.}
-\label{fig:time:2ledsgreen}
+\label{fig:timeunsuit:2ledsgreen}
 \end{figure}
 
@@ -791 +791 @@
 for the outer pixels. Points 
 denote the mean of all not-excluded pixels, the error bars their RMS.}
-\label{fig:time:23ledsblue}
+\label{fig:timeunsuit:23ledsblue}
 \end{figure}
 
@@ -803 +803 @@
 
 \begin{enumerate}
-\item The intrinsic arrival time spread of the photons on the PMT. This time spread 
-can be estimated roughly by the intrinsic width $\delta t_{\mathrm{LED}}$ 
-of the calibration pulses of about 2\,ns 
-for the faster UV pulses and 3--4\,ns for the green and blue pulses. The resulting time
+\item The intrinsic arrival time spread of the photons on the PMT: This time spread 
+can be estimated roughly by the intrinsic width $\delta t_{\mathrm{IN}}$ of the 
+input light pulse.
+The resulting time
 resolution is given by:
 \begin{equation}
-\Delta t \approx \frac{\delta t_{\mathrm{LED}}}{\sqrt{Q/{\mathrm{phe}}}}
+\Delta t \approx \frac{\delta t_{\mathrm{IN}}}{\sqrt{Q/{\mathrm{phe}}}}
 \end{equation}
-
-
-For our 
-calibration LEDs this can be up to about 2 ns, for muons it is about a 
-few hundreds of ps and for hadrons a few ns. The error of the mean 
-arrival time of the total pulse is again the arrival time spread of the 
-photons divided by the number of photo electrons.
-\item The intrinsic transit time spread TTS of the PMT. It can be in the order 
-of a few hundreds of ps per single photo electron. When we reconstruct 
-the mean pulse arrival time the error of the mean is given by the time 
-spread per single photo electron dividid by the square root of number of 
-photo electrons.
-\item reconstruction error due to noise and error of the numeric fit in 
-case of the digital filter. In case of the digital filter the error for 
-the standard noise level in the MC is about 2.7 ns divided by the signal 
-in photo electrons.
+The width $\delta t_{\mathrm{LED}}$ of the calibration pulses of about 2\,ns 
+for the faster UV pulses and 3--4\,ns for the green and blue pulses, 
+for muons it is a few hundred ps, for gammas about 1\,ns and for hadrons a few ns. 
+\item The intrinsic transit time spread $\mathrm{\it TTS}$ of the photo-multiplier:
+It can be of the order of a few hundreds of ps per single photo electron, depending on the 
+wavelength of the incident light. As in the case of the photon arrival time spread, the total
+time spread scales with the inverse of the square root of the number of photo-electrons:
+\begin{equation}
+\Delta t \approx \frac{\delta t_{\mathrm{TTS}}}{\sqrt{Q/{\mathrm{phe}}}}
+\end{equation}
+\item The reconstruction error due to the background noise: This contribution is proportional to the 
+signal to square root of background light intensities.
 \end{enumerate}
 
-All this seems to quite agree with the results obtained with the MC 
-TestPulses. As 1) and 2) are proportional to one over the square root of 
-the signal and 3 is proportional to one over the signal, for small 
-pulses the noise determins the resolution, but for larger pulses the 
-intrinsic fluctuations limit the timing resolution.
-
-When we get a time resolution of about 300 ps for calibration LED pulses 
-we can not distinquish 1) and 2). Thus we have to wait for the exact 
-measurement.
-
-
-\begin{figure}[htp]
-\centering
-\includegraphics[width=0.95\linewidth]{TimeResExtractor-5LedsUV-Colour-12.eps}
+Additionally to these intrinsic and irreducible contributions to the timing resolutions, the limited precision of the 
+ extractors adds an additional time spread. In the following, we show measurements of the time resolutions at different 
+signal intensities in real conditions for the calibration pulses. These set upper limits to the time resolution for cosmics since their 
+intrinsic arrival time spread is smaller. 
+
+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 
+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 
+extraction where the 4 slices seem to yield a better resolution. This is only after excluding about 30\% of the events, as shown in 
+figure~\ref{fig:timeunsuit:23ledsblue}.
+
+\begin{figure}[htp]
+\centering
+\includegraphics[height=0.38\textheight]{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. 
@@ -853 +850 @@
 \begin{figure}[htp]
 \centering
-\includegraphics[width=0.95\linewidth]{TimeResExtractor-1LedUV-Colour-04.eps}
+\includegraphics[height=0.38\textheight]{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), 
@@ -865 +862 @@
 \begin{figure}[htp]
 \centering
-\includegraphics[width=0.95\linewidth]{TimeResExtractor-2LedsGreen-Colour-02.eps}
+\includegraphics[height=0.38\textheight]{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. 
@@ -876 +873 @@
 \begin{figure}[htp]
 \centering
-\includegraphics[width=0.95\linewidth]{TimeResExtractor-23LedsBlue-Colour-00.eps}
+\includegraphics[height=0.38\textheight]{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. 
@@ -884 +881 @@
 \label{fig:time:23ledsblue}
 \end{figure}
+
+\clearpage
 
 
@@ -904 +903 @@
 \end{figure}
 
+\subsubsection{An Upper Limit for the Average Intrinsic Time Spread of the Photo-multipliers}
+
+
 
 \begin{figure}[htp]