Summary of Canadian Laserball Analyses


June 10, 2004 / updated June 17, 2004

Progress Report on Laserball Calibration Measurements taken in March, 2004, and
Search for Dependence of Tube Timing on Incident Angle of Light onto PMT (Peter):

Calibration data was taken with the laserball at z = -3m (3m below the centre of the 1 kton detector), and at +3m, +2m, +1m, 0m, -1m. Data was also available at z=-2m taken in September, 2003. At each location of the laserball, runs were taken at differing laser intensities to vary the occupancy.

Analysis

During analysis it was discovered that the data in 4 runs (613348 at -3m, 613393 at +3m, and 613396 and 613398 at +2m) showed double peaks in the timing spectra after correction for photon time of flight (TOF). This was probably caused by the fact that it was discovered that the PIN diode had not been turned on before run 613399. These four runs with the double peaks were not used in further analysis.

For each run, the raw time spectrum from each photomultiplier (PM) was corrected for TOF assuming that the laserball was at its nominal location and that the speed of light in water was 21.66 cm/ns.The data were first examined for evidence of drift in the timing by plotting the location of the timing peak (corrected for TOF and averaged over all PM's) as a function of event number
during the run. The four runs with split timing peaks showed clear evidence of jumps in timing during the run, but all others looked OK, although there appear to be timing shifts between one run and another. Figure 1 shows a profile histogram of the TOF corrected timing peak (in ns, offset by 925 ns) versus event number and the Timing distribution itself (summed over all Q and all tubes) for a 'good' run on the top and a 'bad'  run on the bottom.

t-Q correction

    The TOF-corrected time, averaged over all tubes was plotted as a function of Q, the charge (in pe) seen by the tube, to see whether the time walk correction was correct. The results for the ball at z=0 for runs at different occupancy are shown in
Figure 2. Results for other locations of the laserball are qualitatively similar. All show the following features:

  1. For Q > 5 pe, the position of the peak of the timing distribution is flat as a function of Q, but its value depends on the occupancy, always being lower for high occupancy runs.
  2. Between 5 pe and 2 pe, the location of the timing peak falls by about 2 ns, reaching a minimum between 1 and 2 pe. Its value at the minimum appears to be approximately independent of occupancy number
  3. Below 1 pe, the location of the timing peak rises again and spreads out as a function of occupancy.  Thus it would appear that the t-Q correction is not being done properly below 5 pe. The dependance on occupancy is not understood.
To reduce the Q-dependance, further analysis was carried out with cuts on Q such that only events with 1pe < Q < 3pe were used.        

Check on Vertical Position of Laserball

        The PM's were split into groups as follows:
Examples of raw and TOF-corrected timing distributions are shown in Figure 3.  The difference in the TOF-corrected timing peaks (fitted with Gaussians) between T tubes and B tubes was formed, and is shown plotted as a function of the nominal z-location of the laserball in Figure 4. At each z-location, two runs were analyzed, one called low occupancy (generally NHIT=20-40) and one called high occupancy (generally NHIT > 200). Error bars are the values given by the fit for the uncertainty in the central value of the Gaussian, but probably underestimate the true uncertainty, since the results are sensitive to the range (here 12 ns) of  timing values to which the gaussian is fit. The timing peaks in general show non-Gaussian tails which probably arise from reflected light, and the centroid can depend on how much of this tail is included in the fit.

From Figure 4, it can be seen that there is no obvious difference beween low and high occupancy runs and no obvious dependance on the z-position, but that the values are all negative with an average value of about -0.4 ns. Since the laserball position was measured from the nominal centre with an accuracy of better than 5mm, one explanation of this timing discrepancy is that the nominal centre of the 1kton is a few cm high relative to the midpoint between the top and bottom tubes.

Search for Angle Effects on Timing

In order to investigate the question of whether tha timing is affected by the angle at which light strikes a PM, the wall tubes were divided into rows all at the same vertical height, as described above. The 3 groups were chosen:
It is clear that  light from the laserball strikes any of tubes in 1 of the 3 groups at more or less the same angle, but that this angle changes drastically  going from one group to another and also as the z-position of the laserball is changed . Typical raw and TOF corrected time spectra for one group at one z-position of the laserball are shown in Figure 5. The TOF-corrected distributions were fitted with gaussians. To reduce the dependancy on drift from run to run, the mean of the T and B TOF-corrected times, (T+B)/2, for the run in question  was then subtracted. The mean of T and B has no angular dependance and should not depend on the z-position of the laserball. The central values of the fits after subtracting (T+B)/2 are shown plotted as a function of the z-position of the laserball for each of the 3 groups in Figure 6 for low-occupancy runs and Figure 7 for high occupancy.  There is no obvious dependancy on either the group or the z-position, both of which change the angle at which the light strikes the tubes.  Hence we can conclude that this angle does not affect the timing, at least at the 0.5 ns level



Reconstruction Biases on Laserball Position (Frank/Scott):

Method:  Time histograms are created from each run for each PMT.  A +-5nsec window is slid across each timing histogram to find the location that maximizes the number of counts inside the sliding window.  The centroid of all the times inside this window is assigned as the mean time for the tube for that run.  No charge cuts are applied.  A simple time fitter is used to determine the position of the ball for the run.  So one fit is done per run---we are not fitting individual events here.  The fitter is a chi^2 fitter that accounts just for time of flight.  No charge data is included in the fit.  The standard kiloton time calibration and time vs. q correction have been applied.  All tubes with physically reasonable data are used in the fit, including the wall, top, and bottom.

(Reconstructed - True) X-position as a function of true Z position of ball
(Reconstructed - True) Y-position as a function of true Z position of ball
(Reconstructed - True) Z-position as a function of true Z position of ball

Black points are low occupancy runs (average NHIT<110).  Red points are medium occupancy (110<NHIT<390).  Blue points are high occupancy runs (390<NHIT).  High, medium, and low occupancy runs at each position were taken at the same time without moving the ball.

The reconstructed position shows a serious bias in Z.  Low occupancy runs are pulled up by ~+10cm, while medium and high ocupancy runs show an unexpected slope.  If only low charge hits are included in the time histogram (q<1pe), then the high occupancy runs reconstruct similarly to the low occupancy runs.  We suspect an error in the time calibration as a function of charge.  Even though most of the hits are single pe hits, the fraction of multi-pe hits is higher for tubes closer to the ball.  If the t vs. q correction doesn't work well as a function of charge, then there may be a differential bias in timing between the higher and lower occupancy sections of the detector.  When the occupancy is decreased to very low levels (black points), then these multi-pe differential effects would go away, so the slope goes away.  But this does not explain why the fitted positions are still shifted by 10cm for high occupancy runs.

From the above plots we see no evidence for a bias in X.  For Y, there does seem to be some slope between the top and bottom of the tank, although the bias is not large.  If I've understood the coordinate systems, then the Y direction in the kiloton coordinate system is in the upstream-downstream direction (Y in kiloton coordinate system = Z in the beam coordinate system).  It may be possible that we are seeing some timing effect here associated with the MRD.  There has been speculation that the magnetic fields at the top of the tank could be different due to the proximity of the MRD.  This might change the timing of the tubes more on the downstream region than on the upstream region at the top of the tank, and perhaps could cause a small bias in Y.  This is speculation at this point, not proof.


Stability of the Trigger Time for the Laserball (Frank)

A few early laserball runs (notably 613348,613393,613396,613398) show a double-peaked structure in their timing histograms.  We subsequently discovered that prior to Run 613398, the voltage for the laser photodiode was not hooked up.  The photodiode will still put out a signal that is large enough to trigger the detector even with the voltage off, but we became worried that the trigger time of the photodiode was perhaps not stable.  To check this, Frank produced a Trigger Timing Plot.  The top plot is most interesting---it is the mean TOF-corrected time for all hits in the run, as a function of run number.  As can be seen, the time offset was not stable before Run 613399, but was quite stable after this time, once the photodiode voltage was hooked on. The middle plot shows the RMS of the TOF-corrected times, while the bottom plot shows the mean width of the timing peak for all tubes.  There is some structure in this plot, but we have not associated this structure with any pathologies.

It is not a problem if the timing offset changes from run to run, but it is a problem if it changes within a run, since we form the time histograms we use in the fits by integrating over an entire run.  We suspect that this was what happened in the double-peaked runs.  One solution to this problem would be to abandon run-by-run fitting (averaging the arrival time over all events), and instead to reconstruct each event separately.  Thomas Kutter is pursuing an event-by-event fitter for the laserball analysis.


Tests of Reconstruction on Monte Carlo Runs (Shaomin/Scott/Frank)

We have modified Asia's laserbeam Monte Carlo to produce an isotropic point source of light.  We have been using this to produce fake data sets that we can test the reconstruction routine on.  Monte Carlo runs have been generated at 5 positions: z=0, z=+-150cm, and z=+-300cm.  Runs have been simulated with three different scattering settings.  First, scattering was turned off (ARAS=AMIS=0.0).  Then we used a non-zero scattering (ARAS=AMIS=0.5).  Finally, the scattering was increased by a factor of five to ARAS=AMIS=2.5.  The following plots show the reconstruction bias in the X, Y, and Z coordinates as a function of ball position.  Black points are with no scattering,  red points have ARAS=AMIS=0.5, and blue points have ARAS=AMIS=2.5.

MC: (Reconstructed - True) X-position as a function of true Z position of ball
MC: (Reconstructed - True)Y-position as a function of true Z position of ball
MC: (Reconstructed - True) Z-position as a function of true Z position of ball

No reconstruction bias is seen in the X or Y coordinates.  For the Z coordinate, there is a slope that increases with scattering.  The significance of the slope in the ARAS=AMIS=0.5 simulation is 2.67 sigma, but for the higher scattering setting the slope is quite significant. Asia's studies favor a setting of ARAS=0.7, and I'm not sure what AMIS setting is appropriate.  But it looks likely now that more reasonable levels of scattering will not produce a large bias.

There is a natural explanation of how scattering could produce a bias.  When we assign times to each PMT, we take the centroid of the time within a +-5nsec window around the timing peak.  If there is a significant scattering peak, that would pull the centroid to slightly later times.  Because the size of the scattering tail relative to the main (direct light) peak varies with tube position, the amount of this timing pull would be different for different tubes.  The direction of the resulting pull matches the small slope seen  in the z-coordinate.


Studies of Reflection Peaks (Scott)

The time histograms show secondary peaks roughly ~30nsec and ~100nsec after the main peak from direct light.  These peaks are well outside the timing window used for the laserbll reconstruction studies, and so should not affect the laserball reconstruction results here.  But it is maybe interesting to understand their origins nonetheless, since they can affect neutrino event reconstruction.

For this study, we used three runs (613350, at z=-300cm, 613417, at z=0cm, and 613374, at z=+300cm).  All are low occupancy runs.  We restricted the analysis to strips (rows) of PMT on the wall at z=+385cm, z=-385cm, and z=+-35cm (the two middle rows, which were binned together).  Time histograms were accumulated for all three strips of PMTs for each run, subtracting an offet for each run so that the main timing peak appeared at t=0. 

A collection of reflection peaks may be seen here.

The first plot shows the timing distributions for tubes at +385cm, +-35cm, and -385cm ,when the ball is at +300cm.  All histograms have been normalized to unit area.  The reflection peaks in the 25-35nsec ranges are obvious, and shift with position.  A possible origin of these peaks may be reflection off the far wall, as illustrated in this diagram:

Direct and reflected light paths to selected PMTS

Reflection paths

In this diagram the solid lines indicate the paths that direct light would take to the PMTs, while the dashed lines indicate the paths taken by light that reflects cleanly off the far wall once before hitting the tube.  The dotted line indicates an example of a path that reflects twice before hitting a PMT.

It's easy to calculate analytically the difference in transit time between the direct light paths and the single-reflection paths just from geometry, using 21.66cm/nsec for the speed of light of laserball light (390nm) in water.  This can be used to predict where the first reflection peak should occur relative to the direct light peak.  This table shows the results:

                                         Comparison of Predicted and Measured First Reflection
                      Peak Location, with Laserball at +300cm
Tube Location
 Predicted Peak Position
 Fitted Peak Position
 Difference
z=+385
 39.5 nsec
 36.3 nsec
 3.2 nsec
z=0
 37.1 nsec
 34.5 nsec
 2.6 nsec
z=-385cm
 30.8 nsec
 26.9 nsec
 3.9 nsec

The analytic calculation reproduces the trend in the data, although the absolute peak positions seem to be shifted by ~3nsec earlier than expected.  The origin of this 3nsec discrepancy is not understood.

It also should be noted from this first plot that the amplitude of the reflection peak relative to the direct light peak increases when the tube is farther from the ball.

The second plot shows the time distributions for the three strips of tubes when the ball is at z=0cm.  The reflection peak for z=+385cm seems a bit wider than the peak for the tubes at z=-385cm.  However, the fitted locations of the peaks agree, and again the analytic model predicts the peak positions, except for the same ~3nsec overall shift



                                         Comparison of Predicted and Measured First Reflection
                      Peak Location, with Laserball at +0cm
Tube Location
 Predicted Peak Position
 Fitted Peak Position
 Difference
z=+385
 35.8 nsec
 33.3 nsec
 2.5 nsec
z=0
 39.7 nsec
 36.5 nsec
 3.2 nsec
z=-385cm
 35.8 nsec
 33.9 nsec
 1.9 nsec

The third plot shows the time distributions for the three strips of tubes when the ball is at z=-300cm.  This should be symmetric with the first plot, but swapping the


                                         Comparison of Predicted and Measured First Reflection
                      Peak Location, with Laserball at -300cm
Tube Location
 Predicted Peak Position
 Fitted Peak Position
 Difference
z=+385
 30.8 nsec
 25.4 nsec
 5.4 nsec
z=0
 37.1 nsec
 34.8 nsec
 2.3 nsec
z=-385cm
 39.5 nsec 36.5 nsec
 3.0 nsec

Again the same general trend is seen ... the variation of the peak position with the tube location is generally good, but a overall offset of the measured peaks to earlier times by ~3nsec is seen.

The last three plots show the same data, this time comparing the peak positions and amplitudes for the same set of tubes as the ball is moved. 

I note that there appears to be a much smaller secondary peak at ~105nsec.  The location of this peak is approximately what would be expected for a ray that bounced twice off of the wall before reaching the PMT (see dotted line in the above figure), but as the peak location is then not as sensitive to the ball location, it is not easy to confirm this suggestion.


Results from an event-by-event laserball fitter (Thomas):

Rather than simply calculating the average of the timing peak over the run for each tube, we plan to write an event-by-event laserball position fitter.  This is not ready yet.

Time Residuals of Laserball vs. position (Frank, June 15, 2004)


The time residual for each tube in each run was calculated by comparing the centroid of that tube's time for the run to the expected time with the ball at its nominal position.  Frank cut out all overly large residuals (<2 ns in code). The tube number correspond to wall, top, or bottom as follows:
  • WALL:    PMT# < 456
  • TOP:     456 < PMT# < 568
  • BOTTOM: 568 < PMT# < 680
Mean time residuals are also calculated for each row (plotted vs. z) and for each radial ring on the top and bottom of the detector.

The mean charge for each PMT was calculated cutting events with charge less than 0 or greater than 2.


Run
 Laserball position
 Approximate NHIT
 Time residual vs. tube position
 Average charge vs. tube position
613393
 z=+300cm
 25
 Time residual plot
 Charge plot
613401
 z=+200cm
 30
 Time residual plot Charge plot
613402
 z=+200cm, ball rotated in phi by 180 degrees
 30
 Time residual plot Charge plot
613417
 z=0cm
 25
 Time residual plot Charge plot
613425
 z=-100cm
 25
 Time residual plot Charge plot