Changeset 5781


Ignore:
Timestamp:
01/10/05 18:14:29 (20 years ago)
Author:
gaug
Message:
*** empty log message ***
Location:
trunk/MagicSoft/TDAS-Extractor
Files:
2 edited

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  • trunk/MagicSoft/TDAS-Extractor/Changelog

    r5778 r5781  
    22222004/01/08: Markus Gaug
    2323  * Algorithms.tex: text updated and new figures
    24 
     24  * Pedestal.tex: text updated
    2525
    26262005/01/05: Hendrik Bartko

  • trunk/MagicSoft/TDAS-Extractor/Pedestal.tex

    r5718 r5781  
    2222can be completely described by the noise-autocorrelation matrix $\boldsymbol{B}$
    2323(eq.~\ref{eq:autocorr}),
    24 where the diagonal elements give what is usually denoted as the ``Pedestal RMS''. Note that
    25 in the MAGIC readout, the diagonal elements do not scale exactly with the square root of
    26 the number of slices as would be expected from pure stochasitic noise.
     24where the diagonal elements give what is usually denoted as the ``Pedestal RMS''.
    2725
    2826\par
    … …  
    4240\end{equation}
    4341
    44 has the mean $B$ and the RMS $R$
     42has the mean $B$ and the RMS $R$ defined by:
    4543
    4644\begin{eqnarray}
    … …  
    5553\end{equation}
    5654
    57 $B$ is the bias, $R$ is the RMS of the distribution of $X$ and $D$ is something
     55The parameter $B$ can be called the bias of the pedestal extractor and $R$
     56the RMS of the distribution of $X$ and $D$ is something
    5857like the (asymmetric) error of $SE$.
    5958The distribution of $X$, and thus the parameters $B$ and $R$,
    60 depend on the size of $ST$ and the size of the background fluctuations $BG$.
     59depend generally on the size of $ST$ and the size of the background fluctuations $BG$.
    6160
    6261\par
    6362
    6463For the normal image cleaning, knowledge of $B$ is sufficient and the
    65 error $R$ should be know in order to calculate a correct background probability.
    66 \par
    67 Also for the model analysis $B$ and $R$ are needed, because you want to keep small
     64error $R$ should be known in order to calculate a correct background probability.
     65
     66\par
     67\ldots {\textit{\bf THOMAS SCHWEIZER ???}}
     68\par
     69Also for the model analysis $B$ and $R$ are needed if one wants to keep small
    6870signals.
    6971\par
    … …  
    7274
    7375\begin{equation}
    74 \frac{(\Delta ST)^2}{<ST>^2} = \frac{1}{<m_{pe}>} * F^2
     76\frac{(\Delta ST)^2}{<ST>^2} = \frac{1}{<n_{phe}>} * F^2
    7577\end{equation}
    7678
    7779Here $\Delta ST$ is the fluctuation of the true signal $ST$ due to the
    7880fluctuation of the number of photo electrons. $ST$ is obtained from the
    79 measured fluctuations of $SE$  ($RMS_{SE}$) by subtracting the fluctuation of the
    80 extracted signal ($R$) due to the fluctuation of the pedestal.
    81 
    82 \begin{equation}
    83  (\Delta ST)^2 = RMS_{SE}^2 - R^2
    84 \label{eq:rmssubtraction}
    85 \end{equation}
    86 
     81measured fluctuations of $SE$  ($RMS_{SE}$) by subtracting those fluctuations of the
     82extracted signal which are due to the fluctuation of the pedestal ($R$)\footnote{%
    8783A way to check whether the right RMS has been subtracted is to make the
    8884Razmick plot
    … …  
    9995\end{equation}
    10096
    101 where $c$ is the photon/ADC conversion factor  $<ST>/<m_{pe}>$.
     97where $c$ is the photon/ADC conversion factor  $<ST>/<m_{pe}>$.}.
     98
     99\begin{equation}
     100 (\Delta ST)^2 = RMS_{SE}^2 - R^2
     101\label{eq:rmssubtraction}
     102\end{equation}
    102103
    103104\subsection{How to Retrieve Bias $B$ and Error $R$}
    … …  
    108109\par
    109110In the case of the optimum filter, $R$ is in theory independent from the
    110 signal amplitude $ST$ and depends only on the background $BG$, see eq.~\ref{of_noise}.
     111signal amplitude $ST$ and depends only on the background $BG$ (eq.~\ref{of_noise}).
    111112It can be obtained from the
    112113fitted error of the extracted signal ($\Delta(SE)_{fitted}$),
    … …  
    130131\end{enumerate}
    131132
    132 \subsubsection{ \label{sec:determiner} Determine Error $R$ by Applying the Signal Extractor to a Fixed Window
     133\subsubsection{ \label{sec:determiner} Determine $R$ by Applying the Signal Extractor to a Fixed Window
    133134of Pedestal Events}
    134135
    … …  
    136137determined the parameter $R$ for the case of no signal ($ST = 0$). In the case of
    137138all extractors using a fixed window from the beginning (extractors nr. \#1 to \#22
    138 in section~\ref{sec:algorithms}), the results were exactly the same as calculating
     139in section~\ref{sec:algorithms}), the results are thus by construction the same as calculating
    139140the mean and the RMS of a same (fixed) number of FADC slices (the conventional ``Pedestal
    140141Calculation'').
    141142
    142143\par
    143 In the case of the amplitude extracting spline (extractor nr. \#27), we took the
    144 spline value at a random place within the digitizing binning resolution (0.02 FADC slices) of
    145 one central FADC slice.
     144In the case of the amplitude extracting spline (extractor nr. \#23), we placed the
     145spline maximum value (which determines the exact extraction window) at a random place
     146within the digitizing binning resolution (0.01 FADC slices)
     147of one central FADC slice.
    146148In the case of the digital filter (extractor nr. \#28), the time shift was 
    147149randomized for each event within one central FADC slice.
    … …  
    326328%%% TeX-master: "Pedestal"
    327329%%% TeX-master: "MAGIC_signal_reco"
     330%%% TeX-master: "MAGIC_signal_reco."
    328331%%% End:
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