VDC Calibration
The two chambers, labeled "1" and "2", are 335 mm apart and lay horizontally relative to the Hall floor but are angled at 45 degrees relative to the incoming particles. The two layers of wires in each chamber, labeled "U" and "V", are 26 mm apart and set at right angles to each other for optimal tracking.
The wires themselves are 4.24 mm apart, with a constant voltage of approximately −4 kV in a gas mixture of 62% argon and 38% ethane, which is kept in constant circulation.
For this experiment, calibration consists of determining the best t0 offset for each wire. To do this, an algorithm was used that produces a histogram for of the raw TDC timing for each wire and searches for the bin with the steepest slope, then records that bin value as a t0 offset.
For this calibration, run 2451 from Kinematic 12 was used to calibrate the left arm, while all of the hydrogen runs from kinematic 12 were used to calibrate the right arm.
The database files created as a result of this calibration can be found here: db_L.vdc.dat, db_R.vdc.dat.
Example VDC Histogram
As particles pass through the gas surrounding the sense wires, they ionize the gas and produce a shower of charged particles. These particles are either attracted or repelled by the wires and this produces a voltage response in the wires that is detected as a signal in the TDCs.
The above plot is an example of the combined signal from all the wires from the U1 layer. As is common in VDC histograms, as time advances, there is a steep rise toward a peak, which then drops to a plateau, which then eventually drops back to baseline. The peak is due to the sudden movement of charged particles close to the wires, while the plateau is due to the reaction of particles further from the wires.
The goal of this calibration is to determine the offset that will align the channel with the steepest slope from each wire.
Raw Time
The first step is to look at the raw, uncalibrated time from the TDCs. Since we are looking at calibrating these for each wire, we need to look at them as a function of the wire number.
Because the TDCs from this experiment use a common stop, the histograms are backwards in time, with the most recent events appearing last, at the highest channel.
Below are the raw times versus the wire for the layers from each arm. The plots can be clicked to view a larger image.
 LHRS U1 VDC - Raw Time vs Wire |
 LHRS V1 VDC - Raw Time vs Wire |
 LHRS U2 VDC - Raw Time vs Wire |
 LHRS V2 VDC - Raw Time vs Wire |
 RHRS U1 VDC - Raw Time vs Wire |
 RHRS V1 VDC - Raw Time vs Wire |
 RHRS U2 VDC - Raw Time vs Wire |
 RHRS V2 VDC - Raw Time vs Wire |
As can be seen, the right arm almost lines up already, but the left arm will need some work.
Calibration Code
Rather than checking the TDC plot for each individual wire, code has been written that looks for the bin with the steepest slope automatically.
The algorithm goes through each wire for each plane for each arm, and starts by creating a histogram for the raw time for that wire. To make this easier on the code, the raw time data is subtracted from 1800, to give it a look similar to that of the actual time.
The code then identifies the bin with the highest count, the maximum peak. It works its way toward the left edge of the histogram, measuring the difference in counts between each pair of adjacent bins, looking for the largest difference, which it considers the maximum slope. This is visualized in the plot below.
Once the code has determined this maximum slope, it moves on to the next wire, and ultimately exports the results to a data file, which can then be imported into the appropriate database file.
Calibration Results
Using the method described in the previous section, the calibrated VDC results are below.
 LHRS U1 VDC - Time vs Wire |
 LHRS V1 VDC - Time vs Wire |
 LHRS U2 VDC - Time vs Wire |
 LHRS V2 VDC - Time vs Wire |
 RHRS U1 VDC - Time vs Wire |
 RHRS V1 VDC - Time vs Wire |
 RHRS U2 VDC - Time vs Wire |
 RHRS V2 VDC - Time vs Wire |
There are still a few problems with the left arm, generally around wires 250, 140, and 80, and while manual corrections were made to minimize these deviations, nothing could be done to completely eliminate them.
Other Kinematics
This calibration holds up for other kinematics as well. Below are the time vs wire plots for run 2155 from Kinematic 2.
 LHRS U1 VDC - Time vs Wire |
 LHRS V1 VDC - Time vs Wire |
 LHRS U2 VDC - Time vs Wire |
 LHRS V2 VDC - Time vs Wire |
 RHRS U1 VDC - Time vs Wire |
 RHRS V1 VDC - Time vs Wire |
 RHRS U2 VDC - Time vs Wire |
 RHRS V2 VDC - Time vs Wire |