Figure 3 shows TDC comparisons. The peaks appear in positions that are in agreement between the two sets of measurements, dependant somewhat on the geometrical alignment. These spectra were fitted by Gaussian distributions to extract their means in order to calculate the TDC conversion factor and the index of refraction of the scintillating fibers.
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The differences in distance and in TDC peak centroid were calculated
for all pairs of points in Table 2. These were then
used to calculate the speed of light in the Kuraray and Pol.Hi.Tech.
single-clad fiber bundles respectively. The resultant values were
18.780.63 and 18.53
1.27 cm/ns, which correspond to an index
of refraction around 1.60. This result is near those found by
KLOE [4] which ranged between 1.74 and 1.80.
Next, the fitted TDC peak location was plotted versus the distance
from each PMT. The slopes and y-intercepts of these plots were
(0.264, 37.6), (0.257, 98.4), (0.270, 36.9) and (0.259, 100.4) for
PMT1 and PMT2 from the Kuraray and single-clad Pol.Hi.Tech.
measurements, respectively. These slopes are in agreement with the
expected number of
, as
presented in equation (4). The slope of each graph,
once multiplied by the TDC conversion factor, is equal to the inverse
of the speed of light in the fibers, following
equations (3) and (4). The extracted
values were consistent with an index of refraction of 1.60 once again,
using the conversion factor of 200 ps/channel.
The summation of the left and right PMT TDC values corresponds to the mean time of the two ends and should be a constant. Indeed, both Kurary and Pol.Hi.Tech. data exhibit an approximately flat behaviour as a function of position, averaging at 210 and 215 channels, respectively. If the functional dependence of the TDC peak on position for each PMT shown above is added, the total TDC offset is obtained. If these numbers are in turn substracted from the the mean-time values, and then multiplied by the TDC conversion factor of 200 ps/channel and the calculated speed of light, the total length of each fiber bundle is calculated: 284.4 cm and 299.8 cm, respectively. These numbers are in agreement with the measured lengths of approximately 284 cm and 291 cm. Note that the measured lengths were approximate only because they were taken when the fibers were already in the black tubing, and thus it was not possible to ensure that each fiber was stretched out completely.