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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

\begin{displaymath}
\sigma_{MT}^2=\sigma_{L/R}^2+2\sigma_{TR}^2
\end{displaymath} (5)

where $\sigma_{L/R}$ is the contribution from an individual fiber PMT, and $\sigma_{TR}$ is the contribution from the trigger (finger) counter, while the width of the L/R timing difference distribution is related to the position resolution:
\begin{displaymath}
\sigma_{PR}^2=2\sigma_{L/R}^2
\end{displaymath} (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 $\sigma_{L/R}$ using the above equations in two independent ways:
$\displaystyle \sigma_{L/R}=\sigma_{TD}/\sqrt{2} \hspace{0.5cm} and
\hspace{0.5cm} \sigma_{L/R}=\sqrt{(\sigma_{MT}^2/2)-\sigma_{TR}^2}$     (7)


next up previous
Next: Attenuation Length Up: Notes on Timing Resolution Previous: Timing Resolution
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2001-10-29