Changeset 6439 for trunk/MagicSoft
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- 02/13/05 21:58:11 (20 years ago)
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trunk/MagicSoft/TDAS-Extractor/Calibration.tex (modified) (12 diffs)
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trunk/MagicSoft/TDAS-Extractor/Calibration.tex
r6437 r6439 400 400 401 401 \begin{equation} 402 c_{phe} =\ < Phe> / <\widehat{S}>402 c_{phe} =\ <N_{phe}> / <\widehat{S}> 403 403 \end{equation} 404 404 … … 406 406 optical transmission devices~\cite{david} is a linear device over a 407 407 wide dynamic range, the number of photo-electrons per charge has to remain constant over the tested 408 linearity region. We will show here only examples of extractors which were not already excluded in the 409 previous section. 408 linearity region. 410 409 \par 411 410 A first test concerns the stability of the conversion factor: mean number of averaged photo-electrons 412 per FADC counts over the 413 tested intensity region. A much more detailed investigation on the linearity will be shown in a 414 separate TDAS~\cite{tdas-calibration}. 411 per FADC counts over the tested intensity region. This test includes all systematic uncertainties 412 in the calculation of the number of photo-electrons and the computation of the mean signal. 413 A more detailed investigation on the linearity will be shown in a 414 separate TDAS~\cite{tdas-calibration}, although there, the number of photo-electrons will be calculated 415 in a more direct way. 415 416 416 417 \par … … 418 419 obtained for different light intensities 419 420 and colours for three exemplary inner and three exemplary outer pixels using a fixed window on 420 8 FADC slices. Some of the pixels show a difference 421 8 FADC slices. The conversion factor seem to be linear to a good approximation, 422 except for two cases: 423 \begin{itemize} 424 \item The green pulses yield systematically low conversion factors 425 \item Some of the pixels show a difference 421 426 between the high-gain ($<$100\ phes for the inner, $<$300\ phes for the outer pixels) and the low-gain 422 427 ($>$100\ phes for the inner, $>$300\ phes for the outer pixels) region and 423 428 a rather good stability of $c_{phe}$ for each region separately. 424 We conclude that the fixed window extractor \#4 is a linear extractor 425 for both high-gain and low-gain regions, separately. 426 \par 427 428 \begin{figure}[htp] 429 \end{itemize} 430 431 We conclude that, apart from the two reasons above, 432 the fixed window extractor \#4 is a linear extractor for both high-gain 433 and low-gain regions, separately. 434 \par 435 436 Figures~\ref{fig:linear:phevscharge9} and~\ref{fig:linear:phevscharge15} show the conversion factors 437 using an integrated spline and a fixed window with global peak search, respectively, over 438 an extraction window of 8 FADC slices. The same behaviour is obtained as before. These extractors are 439 linear to a good approximation, except for the two cases mentionned above. 440 \par 441 442 \begin{figure}[h!] 429 443 \centering 430 444 \includegraphics[width=0.99\linewidth]{PheVsCharge-9.eps} … … 436 450 \end{figure} 437 451 438 Figures~\ref{fig:linear:phevscharge9} and~\ref{fig:linear:phevscharge15} shows the conversion factors 439 using an integrated spline and a fixed window with global peak search, respectively, over 440 an extraction window of 8 FADC slices. The same behaviour as before is obtained. These extractors are 441 thus linear to good approximation, for the two amplification regions, separately. 442 \par 443 444 \begin{figure}[htp] 452 \begin{figure}[h!] 445 453 \centering 446 454 \includegraphics[width=0.99\linewidth]{PheVsCharge-15.eps} … … 452 460 \end{figure} 453 461 454 \begin{figure}[htp] 462 Figure~\ref{fig:linear:phevscharge20} shows the conversion factors using a sliding window of 6 FADC slices. 463 The linearity is maintained like in the previous examples, except for the smallest signals the effect 464 of the bias is already visible. 465 \par 466 467 \begin{figure}[h!] 455 468 \centering 456 469 \includegraphics[width=0.99\linewidth]{PheVsCharge-20.eps} … … 462 475 \end{figure} 463 476 464 Figure~\ref{fig:linear:phevscharge20} shows the conversion factors using a sliding window of 6 FADC slices. 465 The linearity is maintained like in the previous examples, except for the smallest signals where the effect 466 of the bias is already visible. 467 \par 468 469 \begin{figure}[htp] 477 Figure~\ref{fig:linear:phevscharge23} shows the conversion factors using the amplitude-extracting spline 478 (extractor \#23). 479 Here, the linearity is worse than in the previous samples. A very clear difference between high-gain and 480 low-gain regions can be seen as well as a bigger general spread in conversion factors. In order to investigate 481 if there is a common, systematic effect of the extractor, we show the averaged conversion factors over all 482 inner and outer pixels in figure~\ref{fig:linear:phevschargearea23}. Both characteristics are maintained, 483 there. Although the differences between high-gain and low-gain can be easily corrected for, we conclude 484 that extractor \#23 is still unstable against the linearity tests. 485 \par 486 487 \begin{figure}[h!] 470 488 \centering 471 489 \includegraphics[width=0.99\linewidth]{PheVsCharge-23.eps} … … 482 500 \end{figure} 483 501 484 \begin{figure}[htp] 502 Figure~\ref{fig:linear:phevscharge24} shows the conversion factors using a spline integrating over 503 one effective FADC slice in the high-gain and 1.5 effective FADC slices in the low-gain (extractor \#24). 504 The same problems are found as with extractor \#23, however to a much lower extent. 505 The difference between high-gain and low-gain regions is less pronounced and the spread 506 in conversion factors is smaller. 507 Figure~\ref{fig:linear:phevschargearea24} shows already rather good stability except for the two 508 lowest intensity pulses in green and blue. We conclude that extractor \#24 is still not too stable, but 509 preferable to amplitude extractor. 510 \par 511 512 \begin{figure}[h!] 485 513 \centering 486 514 \includegraphics[width=0.99\linewidth]{PheVsCharge-24.eps} … … 499 527 \end{figure} 500 528 529 Looking at figure~\ref{fig:linear:phevscharge25}, one can see that raising the integration window by 530 to two effective FADC slices in the high-gain and three effective FADC slices in the low-gain 531 (extractor \#25), the stability is completely resumed, except for that 532 there seems to be a small systematic increase of the conversion factor in the low-gain range. This effect 533 is not significant in figure~\ref{fig:linear:phevschargearea25}, however it can be seen in five out of the 534 six tested channels of figure~\ref{fig:linear:phevscharge25}. We conclude that extractor \#25 is 535 almost as stable as the fixed window extractors. 536 \par 537 501 538 \begin{figure}[htp] 502 539 \centering … … 516 553 \end{figure} 517 554 518 Figure~\ref{fig:linear:phevscharge25} shows the conversion factors using a spline 519 extractor with an integration window of 2 FADC slices in the high-gain and 3 FADC slices in the 520 low-gain. There seems to be a systematic 521 increase in the conversion factor in the low-gain range. In order to see if this effect is systematic, 522 we calculated the average of all conversion factors over the camera, separated for inner and outer 523 pixels (figure~\ref{fig:linear:phevschargearea25}). 524 525 526 If one uses this extractor, probably this effect will have to be corrected for. 527 528 \par 529 555 Figure~\ref{fig:linear:phevscharge30} shows the conversion factors using a digital filter, 556 applied on 6 FADC slices with weights calculated from the UV-calibration pulse. 557 One can see that many blue and green calibration pulses at low and intermediate intensity fall 558 out of the linear region, moreover there is also a systematic offset between high-gain and low-gain region. 559 It seems that the digital filter does not pass this test if the pulse form changes slightly from the 560 expected one. The effect is not as problematic as it may appear here, because the actual calibration 561 will not calculate the number of photo-electrons (with the F-Factor method) for every signal intensity. 562 Thus, one possible reason for the instability falls away in the cosmics analysis. However, the limits 563 of this extraction are clearly visible here and have to be monitored further. 564 565 \par 530 566 531 567 \begin{figure}[htp] … … 546 582 \end{figure} 547 583 548 Figure~\ref{fig:linear:phevscharge30} shows the conversion factors using a digital filter applied on 6 FADC slices with weights calculated from549 the UV-calibration pulse.550 One can see that all calibration blue and green calibration pulses at low and intermediate intensity fall551 out of the linear region, moreover there seems to be552 a systematic offset between high-gain and low-gain. These offsets have to corrected for in any way, however the loss of stability against the553 exact pulse form in the high-gain is more problematic.554 555 \par556 584 557 585 \begin{figure}[htp] … … 576 604 \subsection{Time Resolution} 577 605 578 The extractors \#17--3 2 are able to extract also the arrival time of each pulse. The calibration579 deliver s a fast-rising pulse, uniform over the camera in signal size and time.606 The extractors \#17--39 are able to compute the arrival time of each pulse. The calibration LEDs 607 deliver a fast-rising pulses, uniform over the camera in signal size and time. 580 608 We estimate the time-uniformity to better 581 609 than 300\,ps, a limit due to the different travel times of the light between inner and outer parts of the … … 588 616 589 617 where $t_i$ denotes the reconstructed arrival time of pixel number $i$ and $t_1$ the reconstructed 590 arrival time of the reference pixel nr. 1 (software numbering). Forone calibration run, one can then fill591 histograms of $\delta t_i$ for each pixeland fit them to the expected Gaussian distribution. The fits618 arrival time of the reference pixel nr. 1 (software numbering). In one calibration run, one can then fill 619 histograms of $\delta t_i$ and fit them to the expected Gaussian distribution. The fits 592 620 yield a mean $\mu(\delta t_i)$, comparable to 593 systematic offsets in the signal delay, and a sigma $\sigma(\delta t_i)$, a measure of the621 systematic delays in the signal travel time, and a sigma $\sigma(\delta t_i)$, a measure of the 594 622 combined time resolutions of pixel $i$ and pixel 1. Assuming that the PMTs and readout channels are 595 of a same kind, we obtain an approximate absolute time resolution of pixel $i$ by:623 of a same kind, we obtain an approximate time resolution of pixel $i$: 596 624 597 625 \begin{equation}
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