Index: trunk/MagicSoft/TDAS-Extractor/Performance.tex
===================================================================
--- trunk/MagicSoft/TDAS-Extractor/Performance.tex	(revision 5882)
+++ trunk/MagicSoft/TDAS-Extractor/Performance.tex	(revision 5884)
@@ -353,5 +353,5 @@
 \par
 Moreover, one can see that the extractors applying a small fixed window do not get the ratio of 
-photo-electrons from outer to inner pixels correctly for the green and blue pulses. 
+photo-electrons correctly between outer to inner pixels for the green and blue pulses. 
 \par
 The extractor MExtractTimeAndChargeDigitalFilter seems to be stable against modifications in the 
@@ -360,28 +360,31 @@
 hold any more for the low-gain, as can be seen in figure~\ref{fig:phe:23ledsblue}. There, the application 
 of high-gain weights to the low-gain signal (extractors \#30--31) produces a too low number of photo-electrons
-and also a too low ratio of outer per inner pixels.
+and also a too low ratio of outer vs. inner pixels.
 \par
 All sliding window and spline algorithms yield a stable ratio of outer vs. inner pixels in the low-gain, 
 however the effect of raising the number of photo-electrons with the extraction window is very pronounced. 
-Note that in figure~\ref{fig:phe:23ledsblue}, the number of photo-electrons raises by about a factor 1.4, 
+Note that in figure~\ref{fig:phe:23ledsblue}, the number of photo-electrons rises by about a factor 1.4, 
 which is slightly higher than in the case of the high-gain channel (figure~\ref{fig:phe:2ledsgreen}). 
 \par
-Concluding, there is now fixed window extractor yielding the correct number of photo-electrons 
+Concluding, there is no fixed window extractor yielding the correct number of photo-electrons 
 for the low-gain, except for the largest extraction window of 10 low-gain slices. 
 Either the number of photo-electrons itself is wrong or the ratio of outer vs. inner pixels is 
 not correct. All sliding window algorithms seem to reproduce the correct numbers if one takes into 
-account the after-pulse behaviour of the light pulser itself. The digital filter seems to be not 
-stable against exchanging the pulse form to match the slimmer high-gain pulses, though.
+account the after-pulse behaviour of the light pulser itself. The digital filter seems to be 
+unstable against exchanging the pulse form to match the slimmer high-gain pulses, though.
 
 
 \subsubsection{Linearity Tests}
 
-In this section, we test the lineary of the extractors. As the photo-multiplier is a linear device over a 
+In this section, we test the lineary of the extractors. As the photo-multiplier and the subsequent 
+optical transmission devices~\cite{david} is a linear device over a 
 wide dynamic range, the number of photo-electrons per charge has to remain constant over the tested 
 linearity region. We will show here only examples of extractors which were not already excluded in the 
 previous section.
 \par
-A first test concerns the stability of the conversion factor photo-electrons per FADC counts over the 
-tested intensity region.
+A first test concerns the stability of the conversion factor: mean number of averaged photo-electrons 
+per FADC counts over the 
+tested intensity region. A much more detailed investigation on the linearity will be shwon in a 
+separate TDAS~\cite{tdas-calibration}.
 
 
@@ -459,9 +462,10 @@
 \subsubsection{Time Resolution}
 
-The extractors \#17--32 are able to extract also the arrival time of each pulse. In the calibration, 
-we have a fast-rising pulse, uniform over camera also in time. We estimate the time-uniformity to better 
+The extractors \#17--32 are able to extract also the arrival time of each pulse. The calibration
+delivers a fast-rising pulse, uniform over the camera in signal size and time. 
+We estimate the time-uniformity to better 
 than 300\,ps, a limit due to the different travel times of the light between inner and outer parts of the
-camera. Since the calibraion does not have an absolute measurement of the arrival time, we measure 
-the relative arrival time, i.e. 
+camera. Since the calibraion does not permit a precise measurement of the absolute arrival time, we measure 
+the relative arrival time for every channel with respect to a reference channel (usually pixel Nr.\,1):
 
 \begin{equation}
@@ -470,15 +474,16 @@
 
 where $t_i$ denotes the reconstructed arrival time of pixel number $i$ and $t_1$ the reconstructed 
-arrival time of pixel number 1 (software numbering). For one calibration run, one can then fill 
-histograms of $\delta t_i$ for each pixel which yields then a mean $<\delta t_i>$, comparable to 
-systematic offsets in the signal delay and a sigma $\sigma(\delta t_i)$ which is a measure of the 
+arrival time of the reference pixel nr. 1 (software numbering). For one calibration run, one can then fill 
+histograms of $\delta t_i$ for each pixel and fit them to the expected Gaussian distribution. The fits 
+yield a mean $\mu(\delta t_i)$, comparable to 
+systematic offsets in the signal delay, and a sigma $\sigma(\delta t_i)$, a measure of the 
 combined time resolutions of pixel $i$ and pixel 1. Assuming that the PMTs and readout channels are 
 of a same kind, we obtain an approximate absolute time resolution of pixel $i$ by:
 
 \begin{equation}
-tres_i \approx \sigma(\delta t_i)/sqrt(2)
+t^{res}_i \approx \sigma(\delta t_i)/sqrt(2)
 \end{equation}
 
-Figures~\ref{fig:reltimesinner10leduv} and~\ref{fig:reltimesouter10leduv} show distributions of $<\delta t_i>$ 
+Figures~\ref{fig:reltimesinner10leduv} and~\ref{fig:reltimesouter10leduv} show distributions of $\delta t_i$ 
 for 
 one typical inner pixel and one typical outer pixel and a non-saturating calibration pulse of UV-light,