For each event, four data words per chamber are read out: the TDC's of the
two ends of the anode delay lines, the TDC of the O+E signal and the O-E
ADC. From this information, the anode wire nearest the path of the charged
particle can be determined. In addition, the distance to the nearest anode
wire (the drift distance) and the side of the anode wire on which lies the
particle's trajectory can be found. The anode wire number 
is obtained
from the difference in the arrival times 
and 
of the signals from
the two ends of the delay lines:
where N=73 is the total number of wires and 
is the delay
per wire spacing.
Figure: Calibration of the drift chambers. At the
top left is the histogram of the
positions of the anode wires. The top right shows the drift time obtained from the arrival
times of the anode and O+E signals with respect to the time of the trigger. The drift
distance (bottom left) is calculated from the drift times and look-up files. The left-right
side identification is shown on the bottom right (O-E ADC). Because the electronics can only
accept negative pulses, a gain offset is applied in the O/E amplifiers. This is compensated
for in the calibration by the identification of the valley in the O-E ADC spectrum as the
zero point, i.e., the divide between the left and right sides of the anode wire where the
original particle's trajectory lies.
Due to non-linear effects in the long delay lines, the corrected position of the anode wire is written as:
where m depends of the delay line. The coefficient 
's are obtained
by minimizing the function 
. The truncated anode position 
is a multiple of the wire spacing g:
The drift distance d is obtained from the drift time 
which is
determined from a comparison between of arrival times (TDC's) of the anode
and O+E signals with that of the trigger. Figure 
shows the anode position
and the drift time. The side of the anode wire on which lies the original
particle's path is inferred from the O-E ADC signal also shown in figure
The ADC spectrum of the O-E signals shows two low gain peaks separated by a
valley which is the divide between O>E (the left side of the anode wire)
and E>O (the right side of the anode wire). The valley is therefore the
origin point 0.0 for the calibration. The coordinate of the charged
particle in the chamber is given as:
with n being the wire number.
A precise and fast way to check the chamber
alignment is the calculation of the residuals which are the deviations of
the best straight line fit to the measured coordinates in two chambers
and 
from the measured coordinate in the third
chamber 
. The spectrum of the residuals is expected to be a very
sharp peak centered at channel zero as shown in figure . Once
the chambers are calibrated, checks and cuts can be applied to the data to
obtain a clean sample of events. The residuals and the checksums (the sums
the delay line end times) provide good basis for eliminating ``bad''
events.
Figure: The residuals obtained as the deviations of the best line fits
to the coordinates of the central and bottom chambers from the coordinates
of the top chamber. The FWHM's are 
and
for the x and y coordinates respectively. The 1.2 cm
plateau contains the events with incorrect left-right identification,
and/or with large scattering angles.
