A Classic Thesis Style - Johannes Gutenberg-Universität Mainz

54 detection efficiencies and data analysis
3.2.2 Cluster analysis
For single hit events, a well defined peak like cluster will populate
several ADC channels in both coordinate directions. As the FWHM
of the distribution of the induced charge is known to be nearly equal
to twice the anode-to-cathode gap, clusters of 3-5 read-out strips are
expected for the signals. The position of the center-of-charge of the
ion avalanche along the anode wires does in principle provide, for
this simple case, a good measurement of the actual coordinates of
the intersection point of the particle track with the grid plane 1 . For
higher multiplicities, the situation is substantially more complicated:
Noisy channels, multiple hits on the chamber, induced signals in
the electronic chain and drifting charges will in general result in a
complex spectrum where it will be far from obvious how to define
a single cluster. Clearly, the charge centroid, simply evaluated from
the measured charges on all cathode channels, will not correspond
to the trajectory position. Therefore, it is of practical importance to
find an algorithm which gives the best position resolution and highest
efficiency, using a limited number of cathode strips of selected clusters.
A careful study of signals phenomenology performed by Professor
Achenbach ended up in an algorithm whose implementation resulted
in a substantial improvement of the tracking system. We quote it here
for completeness but we refer to [66] for further details:
Peak positions are determined by calculating the centre-of-charge
from a restricted number of cathode channels forming a cluster. Clusters
are defined by neighboring cathode strips with ADC values above
a given threshold. A cluster must consist of at least 2 ADC channels
and can include a maximum of 1 ADC channel with a value below
threshold. Each cluster is further analysis for its internal structure
to identify possible peak positions as follows: A truncated cluster is
created around the channel with the charge maximum. It extends
to the left and to the right for 2 channels, if the charge values for
these channels are below a minimum of 90% of the charge in xmax.
The truncated cluster extends at most up to the limits of the original
cluster or up to a channel with only a minimum of charge. For clusters
that reach the 8-bit maximum of the ADC the counting of channels
starts at the left and right limits of the saturation plateau. If no such
structure is found the cluster is discarded. This procedure ensured
that a truncated cluster corresponds to a peak-like structure. Next, the
summed charge in the truncated cluster is compared to the charge
outside the peak region. If the latter is larger than 30% in the x-planes
of the MWPC or larger than 1% in the y-planes of the MWPC and the
outside region is wider than the required minimum for a cluster, a
1 Note that, altought measured signals are induced and read out from the cathode
planes, the actual hit position is located in the grid plane since the avalanche starts
there and drifts towards the anode perpendicularly to all planes thus conserving the
coordinates value.