Index: trunk/MagicSoft/TDAS-Extractor/Criteria.tex
===================================================================
--- trunk/MagicSoft/TDAS-Extractor/Criteria.tex	(revision 6577)
+++ trunk/MagicSoft/TDAS-Extractor/Criteria.tex	(revision 6578)
@@ -7,14 +7,19 @@
 in the signal extraction algorithms and the subsequent image cleaning. 
 \par
-In the image analysis, one takes the decision whether the extracted signal of a certain pixel is considered as signal or background. 
+In the traditional image analysis, one takes the decision whether the extracted signal of a certain pixel is considered as signal or background. 
 Those considered as signal are further used to compute the image parameters while the background ones are simply rejected. The calculation 
-of the second moments of the image ``ellipse'' usually fails when applied to un-cleaned images, therefore the decision is yes or no. Moreover,
+of the second moments of the image ``ellipse'' usually fails when applied to un-cleaned images, therefore the decision is yes or 
+no\footnote{This restriction is not necessary any more in all advanced analyses using likelihood fits to the images or fourier transforms}. 
+Moreover,
 already low contributions of mis-estimated background can degrade the resolution of the image parameters considerably. If one wants to 
 lower the threshold for signal recognition, it is therefore mandatory to increase the efficiency with which the background is recognized as 
 such. If the background resolution is bad, the signal threshold goes up and vice versa.
 \par
-The algorithm must be stable with respect to changes 
-in observation conditions and background levels and between signals induced from gamma or hadronic showers or from muons. 
-The reconstructed signal shall be proportional to the total integrated charge in the FADCs due to the PMT pulse from the Cherenkov signal.
+One cuts on the probability that the reconstructed charge is due to background. This yields a lower reconstructed signal limit for an event 
+being considered as signal at all. The lower the limit (keeping constant the background probability), the lower the analyzed energy 
+threshold.
+\par
+Furthermore, the algorithm must be stable with respect to changes 
+in observation conditions and background levels and between signals obtained from gamma or hadronic showers or from muons. 
 
 Also the needed computing time is of concern.
@@ -30,5 +35,5 @@
 \end{equation}
 
-has the mean $B$ and the Variance $MSE$ defined as:
+has the mean $B$ and the Variance $R$ defined as:
 
 \begin{eqnarray}
@@ -51,12 +56,36 @@
 
 \subsection{Linearity}
-\ldots {\textit The Nuria plots ... }
+
+The reconstructed signal should be proportional to the total integrated charge in the FADCs 
+due to the PMT pulse from the Cherenkov signal.  A deviation from linearity is usually obtained in the following cases:
+
+\begin{itemize}
+\item At very low signals, the bias causes as too high reconstructed signal (positive $X$).
+\item At very high signals, the FADC system goes into saturation and the reconstructed signal becomes too low (negative $X$).
+\item Any error in the inter-calibration between the high- and low-gain acquisition channels yield an effective deviation from 
+linearity.
+\end{itemize}
+
+The linearity is very important for the reconstruction of the shower energy and further the obtained energy spectra from the 
+observed sources. 
 
 \subsection{Low Gain Extraction}
-\ldots {\textit The stability of the low-gain extraction w.r.t. the high-gain extraction}
+
+Because of the peculiarities of the MAGIC data acquisition system, the extraction of the low-gain pulse is somewhat critical:
+The low-gain pulse shape differs significantly from the high-gain shape. Due to the analogue delay line, the low-gain pulse is 
+wider and the integral charge is distributed over a longer time window.
+
+The time delay between high-gain 
+and low-gain pulse is small, thus for large pulses, 
+mis-interpretations between the tails of the high-gain pulse and the low-gain pulse might occur. Moreover, the total recorded time window 
+is relatively small and at late high-gain pulses, parts of the low-gain pulse might already reach out of the recorded FADC window. 
+A good extractor must be 
+stably extracting the low-gain pulse without being confused by the above points. This is especially important since the low-gain 
+pulses are due to the large signals with a big impact on the image parameters, especially the size parameter.
+
+\subsection{Stability}
 
 
-\subsection{Stability}
-\ldots {\textit The stability of an extractor to slightly varying pulse shapes is examined. }
+