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.
Occupancy
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 columnintegrated 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 2426 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.1
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.3
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 2228. 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 doubleGaussian 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 subchromatic
resolution seems to go from a rowwise 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 subchromatic
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 lefthand plot gives the occupancy distribution. There is an
approximate onetoone 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 (leftupper
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 righthand 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 lefthand plot (use the color table of the upper righthand 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 righthand 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 rowdip angle correlation axes contribute
to higher background.
Fig.
10
Andreas and Joe
Last modified: Mar 29, 1999
