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Timing Resolution
Both the cosmic ray and TRIUMF
measurements were
accomplished by sandwiching the fiber bundles between two scintillator
counters in coincidence mode, definining the event trigger. The
setups involved at least four PMT's arranged as shown in
Figure 1.
Figure 1:
Schematic diagram of experimental setup used for both
cosmics and TRIUMF runs. Additional counters, used in some of the
measurements, are not shown here.
|
It can be easily shown that the time difference between the fiber left and
right PMT's is given by the equation:
![\begin{displaymath}
\Delta T = \eta \left[ \frac{n}{c} ( 2 d_1 - L_{fiber} ) +
T_{CONSTANT}\right],
\end{displaymath}](img8.gif) |
(1) |
where
is the distance from one of the PMT's,
is the
total length of the fiber,
is the speed of light,
is the index
of refraction of the fibers, and
is the TDC conversion factor
in channels/ns.
Therefore, a plot of
vs.
(measured in cm) will result
in a straight line, with the slope of the line being given by
 |
(2) |
For the Lecroy TDC that was used for the cosmic ray runs, the
conversion factor was 200 ps/channel, therefore,
.
Thus:
![\begin{displaymath}
m_{\Delta T} = \frac {2 \cdot [5~channels/ns] \cdot n}{30~cm/ns} = \frac{n}{3} [channels/cm].
\end{displaymath}](img17.gif) |
(3) |
Given that
[4], it is expected that
. Likewise, simply plotting the TDC peak location
vs. position for each PMT should result in a slope:
 |
(4) |
and therefore a predicted value of
.
Next: Unfolding the Timing Resolution
Up: Notes on Timing Resolution
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Web Master
2001-10-29