Index: /trunk/MagicSoft/TDAS-Extractor/Calibration.tex =================================================================== --- /trunk/MagicSoft/TDAS-Extractor/Calibration.tex (revision 6438) +++ /trunk/MagicSoft/TDAS-Extractor/Calibration.tex (revision 6439) @@ -400,5 +400,5 @@ \begin{equation} -c_{phe} =\ / <\widehat{S}> +c_{phe} =\ / <\widehat{S}> \end{equation} @@ -406,11 +406,12 @@ 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. +linearity region. \par 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 shown in a -separate TDAS~\cite{tdas-calibration}. +per FADC counts over the tested intensity region. This test includes all systematic uncertainties +in the calculation of the number of photo-electrons and the computation of the mean signal. +A more detailed investigation on the linearity will be shown in a +separate TDAS~\cite{tdas-calibration}, although there, the number of photo-electrons will be calculated +in a more direct way. \par @@ -418,13 +419,26 @@ obtained for different light intensities and colours for three exemplary inner and three exemplary outer pixels using a fixed window on -8 FADC slices. Some of the pixels show a difference +8 FADC slices. The conversion factor seem to be linear to a good approximation, +except for two cases: +\begin{itemize} +\item The green pulses yield systematically low conversion factors +\item Some of the pixels show a difference between the high-gain ($<$100\ phes for the inner, $<$300\ phes for the outer pixels) and the low-gain ($>$100\ phes for the inner, $>$300\ phes for the outer pixels) region and a rather good stability of $c_{phe}$ for each region separately. -We conclude that the fixed window extractor \#4 is a linear extractor -for both high-gain and low-gain regions, separately. -\par - -\begin{figure}[htp] +\end{itemize} + +We conclude that, apart from the two reasons above, +the fixed window extractor \#4 is a linear extractor for both high-gain +and low-gain regions, separately. +\par + +Figures~\ref{fig:linear:phevscharge9} and~\ref{fig:linear:phevscharge15} show the conversion factors +using an integrated spline and a fixed window with global peak search, respectively, over +an extraction window of 8 FADC slices. The same behaviour is obtained as before. These extractors are +linear to a good approximation, except for the two cases mentionned above. +\par + +\begin{figure}[h!] \centering \includegraphics[width=0.99\linewidth]{PheVsCharge-9.eps} @@ -436,11 +450,5 @@ \end{figure} -Figures~\ref{fig:linear:phevscharge9} and~\ref{fig:linear:phevscharge15} shows the conversion factors -using an integrated spline and a fixed window with global peak search, respectively, over -an extraction window of 8 FADC slices. The same behaviour as before is obtained. These extractors are -thus linear to good approximation, for the two amplification regions, separately. -\par - -\begin{figure}[htp] +\begin{figure}[h!] \centering \includegraphics[width=0.99\linewidth]{PheVsCharge-15.eps} @@ -452,5 +460,10 @@ \end{figure} -\begin{figure}[htp] +Figure~\ref{fig:linear:phevscharge20} shows the conversion factors using a sliding window of 6 FADC slices. +The linearity is maintained like in the previous examples, except for the smallest signals the effect +of the bias is already visible. +\par + +\begin{figure}[h!] \centering \includegraphics[width=0.99\linewidth]{PheVsCharge-20.eps} @@ -462,10 +475,15 @@ \end{figure} -Figure~\ref{fig:linear:phevscharge20} shows the conversion factors using a sliding window of 6 FADC slices. -The linearity is maintained like in the previous examples, except for the smallest signals where the effect -of the bias is already visible. -\par - -\begin{figure}[htp] +Figure~\ref{fig:linear:phevscharge23} shows the conversion factors using the amplitude-extracting spline +(extractor \#23). +Here, the linearity is worse than in the previous samples. A very clear difference between high-gain and +low-gain regions can be seen as well as a bigger general spread in conversion factors. In order to investigate +if there is a common, systematic effect of the extractor, we show the averaged conversion factors over all +inner and outer pixels in figure~\ref{fig:linear:phevschargearea23}. Both characteristics are maintained, +there. Although the differences between high-gain and low-gain can be easily corrected for, we conclude +that extractor \#23 is still unstable against the linearity tests. +\par + +\begin{figure}[h!] \centering \includegraphics[width=0.99\linewidth]{PheVsCharge-23.eps} @@ -482,5 +500,15 @@ \end{figure} -\begin{figure}[htp] +Figure~\ref{fig:linear:phevscharge24} shows the conversion factors using a spline integrating over +one effective FADC slice in the high-gain and 1.5 effective FADC slices in the low-gain (extractor \#24). +The same problems are found as with extractor \#23, however to a much lower extent. +The difference between high-gain and low-gain regions is less pronounced and the spread +in conversion factors is smaller. +Figure~\ref{fig:linear:phevschargearea24} shows already rather good stability except for the two +lowest intensity pulses in green and blue. We conclude that extractor \#24 is still not too stable, but +preferable to amplitude extractor. +\par + +\begin{figure}[h!] \centering \includegraphics[width=0.99\linewidth]{PheVsCharge-24.eps} @@ -499,4 +527,13 @@ \end{figure} +Looking at figure~\ref{fig:linear:phevscharge25}, one can see that raising the integration window by +to two effective FADC slices in the high-gain and three effective FADC slices in the low-gain +(extractor \#25), the stability is completely resumed, except for that +there seems to be a small systematic increase of the conversion factor in the low-gain range. This effect +is not significant in figure~\ref{fig:linear:phevschargearea25}, however it can be seen in five out of the +six tested channels of figure~\ref{fig:linear:phevscharge25}. We conclude that extractor \#25 is +almost as stable as the fixed window extractors. +\par + \begin{figure}[htp] \centering @@ -516,16 +553,15 @@ \end{figure} -Figure~\ref{fig:linear:phevscharge25} shows the conversion factors using a spline -extractor with an integration window of 2 FADC slices in the high-gain and 3 FADC slices in the -low-gain. There seems to be a systematic -increase in the conversion factor in the low-gain range. In order to see if this effect is systematic, -we calculated the average of all conversion factors over the camera, separated for inner and outer -pixels (figure~\ref{fig:linear:phevschargearea25}). - - -If one uses this extractor, probably this effect will have to be corrected for. - -\par - +Figure~\ref{fig:linear:phevscharge30} shows the conversion factors using a digital filter, +applied on 6 FADC slices with weights calculated from the UV-calibration pulse. +One can see that many blue and green calibration pulses at low and intermediate intensity fall +out of the linear region, moreover there is also a systematic offset between high-gain and low-gain region. +It seems that the digital filter does not pass this test if the pulse form changes slightly from the +expected one. The effect is not as problematic as it may appear here, because the actual calibration +will not calculate the number of photo-electrons (with the F-Factor method) for every signal intensity. +Thus, one possible reason for the instability falls away in the cosmics analysis. However, the limits +of this extraction are clearly visible here and have to be monitored further. + +\par \begin{figure}[htp] @@ -546,12 +582,4 @@ \end{figure} -Figure~\ref{fig:linear:phevscharge30} shows the conversion factors using a digital filter applied on 6 FADC slices with weights calculated from -the UV-calibration pulse. -One can see that all calibration blue and green calibration pulses at low and intermediate intensity fall - out of the linear region, moreover there seems to be -a systematic offset between high-gain and low-gain. These offsets have to corrected for in any way, however the loss of stability against the -exact pulse form in the high-gain is more problematic. - -\par \begin{figure}[htp] @@ -576,6 +604,6 @@ \subsection{Time Resolution} -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. +The extractors \#17--39 are able to compute the arrival time of each pulse. The calibration LEDs +deliver a fast-rising pulses, 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 @@ -588,10 +616,10 @@ where $t_i$ denotes the reconstructed arrival time of pixel number $i$ and $t_1$ the reconstructed -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 +arrival time of the reference pixel nr. 1 (software numbering). In one calibration run, one can then fill +histograms of $\delta t_i$ 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 +systematic delays in the signal travel time, 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: +of a same kind, we obtain an approximate time resolution of pixel $i$: \begin{equation}