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Unfolding the Timing Resolution
To determine timing resolution of the fiber bundles, the software mean
time and the left-right timing difference must be computed. These
quantities should have constant values at any given point along the
fiber. However, there are some uncertainties associated with these
values, which arise from inherent timing resolution of PMT's involved
and photon statistics. It is easy to show that the width of the
softare mean timing peak is given by
 |
(5) |
where
is the contribution from an individual fiber PMT,
and
is the contribution from the trigger (finger)
counter, while the width of the L/R timing difference distribution is
related to the position resolution:
 |
(6) |
In the above, it has been assumed that the left and right fiber timing
resolutions are equal to one another, which is a reasonable
approximation given that the phototubes were the same model, and the
gains were approximately matched in hardware. In other words, it is
possible to determine the value of
using the above
equations in two independent ways:
 |
|
|
(7) |
Next: Attenuation Length
Up: Notes on Timing Resolution
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Web Master
2001-10-29