The uncertainty in the mean, specified in Equation 3, arises from uncorrelated as well as correlated uncertainties in the ADC sums (due again to white and ``filtered'' noise). These may be expressed as [9]

where is just , and . The overall uncertainty is then estimated as

Values of the uncorrelated and correlated noise for use in Equations10 and 11 are estimated as

where is the number of pads that contributed nonzero ADC values to the time bucket of the time projection.

(Of course, since in calculating the mean with finite sums instead of integrals in Equation 3, we have an additional error , where is the width of a time bucket, and the shaper response g(t) is given in 4. We ignore this here, as the effect of time bucket width, when 512 buckets are used, has been seen to be small [11].

As with the uncertainty along the padrow, Equation 12 estimates the uncertainty in time (z-position) only for =0 tracks. A non-zero crossing angle will degrade the spatial resolution in z. We follow Equation 9 in parametrizing the time resolution.

As with the resolution along the padrow, the constants and must be determined empirically. See Section 6.3.2.

Again, for the uncertainty in the time (z) direction, only an estimate of the first term in Equation 15 is provided by the cluster/hitfinder and stored in TPHIT.DZ. Tracking software, which has a hypothesis of the crossing angle , must update this uncertainty.

Tue Feb 6 15:49:35 EST 1996