Changeset 6646 for trunk

Timestamp:

02/21/05 13:31:27 (20 years ago)

Author:

hbartko

Message:

*** empty log message ***

File:

• trunk/MagicSoft/TDAS-Extractor/MonteCarlo.tex (modified) (1 diff)

trunk/MagicSoft/TDAS-Extractor/MonteCarlo.tex

@@ -187 +187 @@
 \subsection{Measurement of the Resolutions \label{sec:mc:resolutions}}
 
+In order to obtain the resolution of a given extractor, we calculated the RMS of the distribution:
+
+\begin{equation}
+R_{\mathrm{MC}} \approx RMS(\widehat{Q}_{rec} - Q_{sim})
+\end{equation}
+
+where $\widehat{Q}_{rec}$ is the reconstructed charge, calibrated to photo-electrons with the conversion factors obtained in 
+section~\ref{sec:mc:convfactors}.
+\par
+One can see that for small signals, small extracion windows yield better resolutions, but extractors which do not
+entirely cover the whole pulse, show a clear dependency of the resolution with the signal strength. In the high-gain region, 
+this is valid for all fixed window extractors up to 6~FADC slices integraion region, all sliding window extractors up to 4~FADC 
+slices and for all spline extractors and the digital filter. Among those extractors with a signal dependent resolution, the 
+digital filter with 6~FADC slices extraction window shows the smallest dependency, namely 80\% per 50 photo-electrons. This 
+finding is at first sight in contradiction with eq.~\ref{eq:of_noise} where the (theoretical) resolution depends only on the 
+noise intensity, but not on the signal strength. Here, the input light distribution of the simulated light pulse introduces the 
+amplitude dependency (the constancy is recovered for photon signals with no intrinsic input time spread). Here, the main 
+difference between the spline and digital filter extractors is found: At all intensities, but especially very low intensities, the 
+resolution of the digital filter is much better than the one for the spline.
+
 \begin{figure}[htp]
 \centering