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As described in Section 3.4.3, the MWPC system determines the
position of the electron hit from the delay times, the time it takes the
signal to reach both ends of the delay line (see Eq. 3.4). In
addition to a hardware discrimination (via pre-amplifier threshold) against
noise in the delay signal lines, the following off-line software cut
procedure was applied in order to ensure the quality of imaging.

Since the delay lines have a fixed length, the sum of the delay times is
expected to be constant, *i.e.*, for the Z-direction,
,
where *ZL* and *ZH* are the delay time measured
at beam upstream and downstream ends of the delay lines, respectively, and
the sum is multiplied by the dispersion constant, *dispZ* with a length
dimension for convenience. In reality, however, a small but finite amount
of time is required between the ionizing electron and the current being
induced in the cathode wires, mainly due to the drift time of electrons to
the anode, which creates a distribution in *SUMZ* (and
)
reflecting the proximity of the initial hit to the
anode. There is a strong correlation between distributions of *SUMZ* and
*SUMY*, since they are due to the same physical process for both *z* and
*y* wires, *i.e.*, electron drift to the anode (*e.g.* if ionization occurs
very close to the anode, both *SUMZ* and *SUMY* are small due to a small
drift time).

Because of this correlation, the plot of *SUMZ* vs. *SUMY* for good events
occupies only a small area of two dimensional space (a long rectangular box
oriented in a diagonal direction), so making independent cuts on each
parameter *SUMZ* and *SUMY* (corresponding to accepting a large square box
on the plane) is rather inefficient in terms of noise elimination. We
therefore performed a linear transformation of the coordinate system,
introducing new uncorrelated variables,
and
.
With these coordinates, applying the cuts
becomes straightforward. *DIFSUM*, the difference in the sums, typically
had a smaller dispersion compared to that of *SUMZ* or *SUMY* and *SUMSUM*larger.
Therefore a small interval for *DIFSUM* cut (
or
mm for
this analysis) and a large interval for *SUMSUM* cut (
mm), cover
the entire parameter regions for good events, while efficiently eliminating
the noise.

Good hits in each of three MWPCs, thus passing the cut, were fitted to a
straight line with the least-squares method. Cuts in the chi-square
(**<4**) and the fit-residual for the second of three chambers (**<10** mm) for
both *z* and *y* variables, were applied to ensure a reasonable
fit.

For this analysis, all the above cut values described in this section were
taken to be relatively non-restrictive, the largest effect being about 20%
rejection due to the chi-square cut, in order to prevent biasing of the
data set and to allow for maximum statistics.

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