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TDC Information

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.

Figure 3: Comparison of TDC spectra for the three fiber bundles for PMT1 (FL) on the left and PMT2 (FR) on the right. The curves from left to right for PMT1 and right to left for PMT2 correspond to the distances in Table 2.
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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 18.78$\pm$0.63 and 18.53$\pm$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 $m_{single} \approx 0.285~channels/cm$, 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.


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Next: ADC Information Up: Measurements and Results Previous: Measurements and Results
Web Master
2001-10-29