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.