| 1 | \section{Results \label{sec:results}}
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| 2 |
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| 3 | Based on the previous investigations, we summarize the obtained results in table~\ref{tab:result}. The following criteria
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| 4 | have been used to compare the extractors:
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| 5 |
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| 6 | \begin{itemize}
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| 7 | \item Stability of the reconstructed charge in the calibration. Extractors with more than 5\% of the pixels excluded from the
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| 8 | calibration with any colour or intensity are considered as too unstable. Also extractors yielding more than 0.1\% mis-reconstructed
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| 9 | events are excluded. Moreover, the correct number of photo-electrons should be reconstructed at least for the standard calibration
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| 10 | pulses (10\,LEDs\,UV).
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| 11 | \item The extractor should yield stable results against slight modifications of the pulse shape.
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| 12 | \item The extractor must also yield the correct charges for the low-gain pulses on average.
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| 13 | \item The reconstructed charge must be linear to the input signal charge for all signals above the image cleaning level and below
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| 14 | the low-gain saturation level.
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| 15 | \item The resolution of the reconstructed charge should not depend significantly on the signal amplitude, especially should never
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| 16 | become comparable to the intrinsic Poissonian signal fluctuations.
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| 17 | \item The resolution of the reconstructed charge should not exceed twice the resolution of the best extractor.
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| 18 | \item The extractor should not have a charge bias bigger than its charge resolution.
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| 19 | \item The time resolution should not be worse than twice the one obtainable with the best extractor.
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| 20 | \item The number of mis-reconstructed times should not exceed 1\% on average (including the FADC jumps).
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| 21 | \item The needed CPU-time should not exceed the one required for reading the data into memory and writing it to disk.
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| 22 | \end{itemize}
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| 23 |
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| 24 | Table~\ref{tab:result} shows which extractors fulfill the above criteria. One can see that there are a handful extractors which
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| 25 | are excluded by only one criterion:
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| 26 |
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| 27 | \begin{itemize}
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| 28 | \item The sliding window extracting 8 slices in high- and low-gain which is only excluded by the poor resolution at very low intensities.
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| 29 |
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| 30 | \item The integrating spline over 2 FADC slices which still needs to be optimized somewhat for speed.
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| 31 | \end{itemize}
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| 32 |
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| 33 | The digital filter passes all tests, where the extraction over 4 FADC slices yields still superior resolutions compared to the one
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| 34 | over 6~FADC slices.
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| 35 |
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| 36 |
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| 37 | \newcommand{\no}{\textcolor{red}{\bf NO\xspace}}
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| 38 | \newcommand{\nt}{\textcolor[rgb]{0.9,0.75,0.}{\scriptsize NOT\xspace}}
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| 39 | \newcommand{\test}{\textcolor[rgb]{0.9,0.75,0.}{\scriptsize TESTED\xspace}}
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| 40 | \newcommand{\ok}{\textcolor[rgb]{0.,.7,0.}{OK\xspace}}
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| 41 | \newcommand{\best}{\textcolor[rgb]{0.,.4,0.}{\bf BEST\xspace}}
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| 42 |
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| 43 | \begin{table}[htp]
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| 44 | \small{%
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| 45 | \rotatebox{90}{%
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| 46 | \centering
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| 47 | \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
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| 48 | \hline
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| 49 | \hline
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| 50 | \multicolumn{12}{|c|}{\large Tested Characteristics} \rule{0mm}{6mm} \rule[-2mm]{0mm}{6mm} \hspace{-3mm}\\
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| 51 | \hline
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| 52 | \hline
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| 53 | Nr. & Name &Stab. &Stab. & Stab. &Lin. & Res. & Res. & Bias & Res. & Stab. & Speed \\
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| 54 | & &$\widehat{S}$&pulse & low- &$\widehat{S}$&$\widehat{S}$&$\widehat{S}$& $\widehat{S}$&$\widehat{T}$& $\widehat{T}$ & \\
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| 55 | & &calib. &shape & gain & size & const. & & & & & \\
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| 56 | \hline
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| 57 | \hline
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| 58 | 1 & Fix Win. (4,4) & \no & \no & \no & \no & \no & \no & -- & n/a & n/a &\best\\
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| 59 | 2 & Fix Win. (4,6) & \no & \no & \no & \no & \no & \no & -- & n/a & n/a &\best\\
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| 60 | 3 & Fix Win. (6.6) & \ok & \ok & \no & \ok & \ok & \ok & -- & n/a & n/a & \ok \\
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| 61 | 4 & Fix Win. (8,8) & \no & \ok & \ok &\best& \no & \ok & -- & n/a & n/a & \ok \\
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| 62 | 5 & Fix W. (14,10) & \no & \ok & \ok &\best& \no & \ok & -- & n/a & n/a & \ok \\
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| 63 | \hline
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| 64 | 6 & FW. Spl. (4,4) & \ok & \no & \no & \no & \ok & \no & -- & n/a & n/a & \ok \\
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| 65 | 7 & FW. Spl. (4,6) & \ok & \no & \no & \no & \ok & \no & -- & n/a & n/a & \ok \\
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| 66 | 8 & FW. Spl. (6.6) & \no & \ok & \no & \no & \ok & \ok & -- & n/a & n/a & \ok \\
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| 67 | 9 & FW. Spl. (8,8) & \no & \ok & \ok & \ok & \no & \ok & -- & n/a & n/a & \ok \\
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| 68 | 10 & FW. Spl (14,10) & \no & \ok & \ok & \ok & \no & \ok & -- & n/a & n/a & \ok \\
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| 69 | \hline
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| 70 | 11 & FW. Pk S. (2,2) & \no & \no & \no & \no & \no & \no & -- & n/a & n/a & \ok \\
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| 71 | 12 & FW. Pk S. (4,4) & \ok & \no & \no & \no & \no & \no & -- & n/a & n/a & \ok \\
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| 72 | 13 & FW. Pk S. (4.6) & \ok & \no & \no & \no & \no & \no & -- & n/a & n/a & \ok \\
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| 73 | 14 & FW. Pk S. (6,6) & \ok & \ok & \no & \no & \ok & \ok & -- & n/a & n/a & \ok \\
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| 74 | 15 & FW. Pk S. (8,8) & \no & \ok & \ok & \ok & \no & \ok & -- & n/a & n/a & \ok \\
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| 75 | 16 & FW Pk S (14,10) & \no & \ok & \ok & \ok & \no & \ok & -- & n/a & n/a & \ok \\
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| 76 | \hline
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| 77 | 17 & Slid. W. (2,2) & \ok & \no & \no & \no & \ok & \no & \ok & \no & \no & \ok \\
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| 78 | 18 & Slid. W. (4,4) & \ok & \ok & \ok & \no & \ok & \ok & \ok & \no & \no & \ok \\
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| 79 | 19 & Slid. W. (4.6) & \ok & \ok & \ok & \ok & \ok & \ok & \ok & \ok & \no & \ok \\
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| 80 | 20 & Slid. W. (6,6) & \ok & \ok & \ok & \ok & \no & \ok & \ok & \no & \ok &\best\\
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| 81 | 21 & Slid. W. (8,8) & \ok & \ok & \ok & \ok & \no & \ok & \ok & \ok & \ok &\best\\
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| 82 | 22 & Slid. W. (14,10) & \no & \ok & \ok & \ok & \no & \no & \ok & \no & \ok &\best\\
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| 83 | \hline
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| 84 | 23 & Spline Ampl. & \no &\nt & \ok & \no & \no & \no & \no &\ok & \no & \ok \\
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| 85 | & & &\test& & & & & & & & \\
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| 86 | 24 & Splne Int. (1,1.5) & \ok &\nt & \ok & \no & \no & \no & \ok &\best& \ok & \ok \\
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| 87 | & & &\test& & & & & & & & \\
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| 88 | 25 & Spline Int. (2,3) &\best&\nt & \ok & \ok & \ok & \ok & \ok &\best& \ok & \no \\
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| 89 | & & &\test& & & & & & & & \\
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| 90 | 26 & Spline Int. (4,6) & \ok &\ok & \ok & \ok & \ok & \ok & \ok &\best& \ok & \no \\
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| 91 | 27 & Spline Int. (6,9) & \ok &\ok & \ok & \ok & \no & \ok &\best&\best& \ok & \no \\
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| 92 | \hline
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| 93 | 28 & Dig. Filt. (6,6) & \ok &\ok & \ok & \ok & \ok & \ok & \ok &\ok & \ok & \ok \\
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| 94 | 29 & Dig. Filt. (4,4) & \ok &\ok & \ok & \ok & \ok &\best& \ok &\best& \ok & \ok \\
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| 95 | \hline
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| 96 | \hline
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| 97 | \end{tabular}
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| 98 | }
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| 99 | \caption{The tested characteristics for every extractor: Bias, Resolution (``Res.''), stability (``Stab.''), linearity (``Lin.'') for both
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| 100 | charge signal $\widehat{S}$ and time $\widehat{T}$, and speed. \ok\ means that the extractor has passed the
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| 101 | test, without being among the best. \no\ means that the extractor has severely failed the test and should
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| 102 | not be taken because of that reason. \best\ means that the extractor(s) have come out as best of the particular test.}
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| 103 | \label{tab:result}
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| 104 | }
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| 105 | \end{table}
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| 106 |
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| 107 |
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| 108 |
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| 109 | %%% Local Variables:
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| 110 | %%% mode: latex
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| 111 | %%% TeX-master: "MAGIC_signal_reco"
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| 112 | %%% TeX-master: "MAGIC_signal_reco"
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| 113 | %%% End:
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