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Study of single tube Cherenkov distributions using cosmic data

We analyzed the single tube Cherenkov spectrum for some 1.85M cosmic data events (corresponding to about 250k tracks and 7.3M hits) taken from Jan.14 through Jan.31. We used the HitsChisq algorithm and the DcxCosmicSewer in release 7.8.2. A loose time cut of +/- 25nsec for the difference between measured and propagation corrected hit time and the most probable event time was applied. For each tube in sectors 0, 1, 9, 10, and 11 all hits were added up and the difference between the measured thetaC value and the expected (muon) thetaC value was plotted and fitted in two separate runs with either a double Gaussian or a single Gaussian plus flat background.
Preliminary results obtained with a third of the statistics and focussing on a study of swapped PMT signal cables were reported in  HN 101  and  <swapped_cables.html>. The current study is concerned with the background to signal ratio as well as the resolution and center value of the thetaC residuals.


In order to present the data sample used, Fig. 1 shows the occupancy distribution for hits with a reconstructed Cherenkov angle within 100mrad of the expected one and Figure 2 gives the column-integrated occupancy under same conditions. As usual, the hot and cold (swapped) HV groups of sector 11 are clearly visible. In addition, one recognizes the less populated light catcher (LC) free zone of rows 24-26 in sector 11 (20% fewer hits as found in a study using LED events) . The sharp drop in the occupancy fof sector 11 from row 12 to 11 is due to the fact the row 12 is the lowest row number that can be reached by any photon that is reflected off the top surface of the wedge.


Fig. 2


Background to signal ratio

The background to signal ratio (BSR), defined as the ratio of the integrals of the two fitted Gaussians, is shown in Fig. 3 (below) in a column vs. row plot where the color of each PMT location (or rather approximate location, based on Stefan's Ofb occupancy macro) is proportional to the background to signal ratio. In addition, Fig.4 presents the corresponding distribution integrated over the columns.


Fig.4 Fig.4

The BSR value rises as a function of row number (it is worthwhile to note that the worst BSR value in sector 11 does not coincide with the area of densest occupancy) and, after reaching a maximum at about row 20, drops off considerably in sector 11, rows 22-28. The interpretation of this effect is complicated by the fact that those rows are not only grouped around the three rows without light catchers (the position of the missing LC zone is indicated by the red lines in Fig. 4) but are also in a special "phase space" range: 25 is the row number that is reached when the photon is exactely parallel to the top wall of the wedge. Furthermore, while the low noise to signal ratio may be related to the absence of the light catchers in that region, an interesting high resolution phenomenon, the bluish shaded zone indicative of narrow signal widths, is observed in that region of the PMT plane. That effect will be discussed next.

Width of thetaC residuals distribution

The width of the narrow Gaussian from the double-Gaussian fit to the Cherenkov spectra is shown in Fig. 5 (below) in a column vs. row plot where the color of each PMT location is proportional to the signal width. Fig.6 gives the corresponding distribution integrated over the columns. Several interesting features stand out:

Fig. 5

Fig. 6

Fig. 7

  • On average, the signal resolution (or, more accurately, the width of the distribution of the thetaC residuals) in sector 11 is much better than in the neighboring sectors where Cherenkov photons can only end up after multiple reflections off the bar side walls. The measured reflectivity of the side walls as well as the relative damage fraction for the bars in bar box 0 is somewhat worse for side walls than the top/bottom walls.
  • The swapped HV groups in sector 11 and the damaged TDC chip group in sector 10 stand out as patterns of PMTs with poor resolution.
  • Sector 11 has two rows of tubes with extremely good signal resolution (thetaC residuals): row 0 and row 25, visible in blue in Fig. 5. and as sharp drops in Fig. 6. In fact, their resolution is close to or even below the calculated optimum single tube Cherenkov resolution which is dominated by the geometrical resolution term (7.1mrad for tubes with and 6.2mrad for tubes without light catchers) and the chromatic term (5.4mrad). Some example channels and fit results are shown in Fig. 7. We confirmed that the fitted signal width is independent of the type of fit used and the bin width and below the chromatic term.
Fig.5 also shows that the location of the "golden tubes' with sub-chromatic resolution seems to go from a row-wise pattern in sector 11 into a straight line in space in the neighboring sectors. This implies that the source for their resolution is related to the bar box geometry. In this case, the chosen projections on rows are good observables only for sector 11 (symmetric) whereas it should be rotated by +/- 30 degrees for the adjacent sectors 10,0. This was not done for Fig. 6.
We note that the two rows with the best resolution in sector 11 are both special kinematic cases (row 25 was already discussed above): row 0 can only be reached by photons that go straight down the length of the bar. Any reflections off the top/bottom walls will result in the photon ending up in a larger row number. Also, that row may be partially shaded by its location relative to the bottom of the wedge. That effect would reduce the effective radius of the photocathode and thus the geometric contribution to the resolution. We hope that Monte Carlo studies will provide the information necessary to help explaining the low background and sub-chromatic width of some residuals.

Mean value of signal residuals

Figure 8 (below) and 9 show the distribution of the mean values of the narrow Gaussians. These distributions are closely related to the graphs shown by Christophe in an earlier HN. There are (at least) three interesting observations to notice:

  • There is a bias of up to 4mrad with the tendency to larger mean values with increasing row. (This observation is discussed in more detail below.)
  • Row 25, in addition to its low BSR and signal width, breaks out of the pattern with mean values centered around zero while its neighbors have values of about +3.5mrad.
  • We find again the swapped signal cables already identified during our previous work. They have a characteristic signature of hot/cold colors indicating large positive and negative mean Cherenkov angles as expected for exchanged positions.
Fig. 8

Fig. 9


Residuals vs. dip angle

Figure 10 (below) plots in all cases the PMT row against the dip angle of the track.

  • The upper left-hand plot gives the occupancy distribution. There is an approximate one-to-one correspondence between row and dip for dip angles that deviate more than 10 degrees from orthogonality. For dip=0 degrees the photons may either exit the quartz without being reflected off the top of the wedge and hit at large row numbers (large angles)or they are reflected by the top wall of the wedge (30 degrees angle) and then scattered under smaller angles to the PMTs (center population in Fig. 10 (left-upper plot)). One notices that the two possibilities coincide for (approximately) tangential photon trajectories along the wedge ceiling at (or around) row 25 (as well as for row 0 for the bottom part of the wedge). Those tangents are only approximate since there is an step of 10mm between the upper bar face (bar thickness approx. 17mm) and the minimum wedge height of 27mm The bottom wedge surface has a positive slope of tg(6mrad).
  • The upper right-hand plot gives the mean value of the thetaC(measured) - thetaC(expected) signal. It is noticeable that the mean values for photons reflected from the upper wedge surface in the center of the plot are negative (and approximately constant) while the others follow the behavior already observed in Figs. 8/9. This misalignment is due to incorrect geometrical input into the reconstruction code. It was identified and corrected by Christophe (see his HN).
  • The lower left-hand plot (use the color table of the upper right-hand plot) shows mean of the residuals, not determined from the fit but rather as the simple mean over the total thetaC(measured) - thetaC(expected) distribution (cut at < +/-100mrad). The figure illustrates the dependence between reconstructed row and thetaC for a given polar angle of the track:
    • For 20 < abs(dip) < 40 (50 <  abs(dip) < 60), reconstructing smaller rows results in a larger Cherenkov angle and vice versa.
    • This behavior is inverted for photons that are reflected at the upper wedge surface (-15 < dip < 15).
  • The last figure (lower right-hand plot) gives the absolute deviation |thetaC(measured)-thetaC(expected)|. We again recognize the areas very of good resolution (row 0 and 25). As expected, rows away from the row-dip angle correlation axes contribute to higher background.
Fig. 10

Andreas and Joe

Last modified: Mar 29, 1999