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Attenuation Length
To evaluate the attenuation length of the various fibers tested, it is
necessary to evaluate first the ratio of the means of the left and
right PMT ADC values at each position along the beam. To understand
this, consider that the attenuation of light as it travels along the
fiber is given by
 |
(8) |
where
is the distance from the point of impact of the beam along
the fiber to the appropriate PMT,
is the attenuation length,
and
is the amount of light produced at the interaction point.
Figure 2:
ADC spectra for fiber PMT's
|
In practice, it is found that the amount of light produced at the
interaction point is a function of
, as can be seen in
Fig. 2, where the three ADC spectra are from the TRIUMF
data taken at 90 cm, 150 cm, and 210 cm with respect to the left fiber
end PMT. Consequently, the ADC values for the two PMT's in question
may be expressed as
 |
(9) |
where
is the geometric mean calculated from
 |
(10) |
Thus, a reliable method to extract the attenuation length value is to
take the ratio between the two ADC values above:
 |
(11) |
Plotting the ADC ratio values at different positions on a semi-log
scale results in a straight line with a slope of
.
Next: Fiber Bundle Preparations
Up: Notes on Timing Resolution
Previous: Unfolding the Timing Resolution
Web Master
2001-10-29