ADC spectra

As a follow up to our discussion at the previous meeting, ADC distributions are shown for different LED thresholds and trigger sconfigurations. They are for the Left channel of the long TOF paddle which has the weakest-gain PMT. In the first 2 plots below, this channel was part of the trigger at 60mV(left) and 120mV(right) LED threshold. Note that TDC threshold is 30mV lower than trigger threshold in both cases due to the way JLAB-LED works. Trigger paddles are under 90 degrees to the long TOF paddle.
In the next 2 plots, this channel was not in the trigger. The right plot is for the case of 90-degree angle between the TOF and trigger paddles. About 85% of events do not have a TDC hit (i.e., they are useless for time-walk corrections) and contribute only to a huge pedestal peak.
In the left plot, all 3 paddles were parallel to each other. This plot nicely explains the origin of background underneath Landau peak in the first 3 plots. With 90-degree rotation, there is a significant number of cosmic rays that went through the top and bottom trigger paddles but only scratched the edge of the long TOF paddle. This cannot happen in the parallel configuration and, therefore, the background is gone in this case.

Time-walk corrections

Different variations of Elton's suggested time-walk corrections were tried with cosmic data from the 90-degree rotated setup. Three different functional forms have been tried. In some fits, ADC pedestals were treated as parameters to fit. Most important variation was the quantity to be minimized. Two Elton's approaches have been tried: 1) fitting ADC vs t' for each channel individually; 2) minimizing Sum[(tH-tV)2]. The results mostly looked similar. However, minimizing Sum[(tV-tVavg)2 + (tH-tHavg)2] gave a slightly better timing resolution than other approaches. Scatter plots below show the ADC vs t' dependence before and after time walk corrections for Left TOF channel.
There is a noticable difference with Elton's Monte Carlo, however. After correction, his resolution for (t'L+t'R)/2 became 80ps - the intrinsic resolution of TOF he put into MC. In my cosmic data, the resolution impoves only slightly as seen on the plots below from 10.54 to 10.03 TDC counts, or from 265ps to 250ps. Perhaps, variation in the angle of cosmic rays accounts for that: there may be a few centimeter variations in path lengths, accounting for a few hundred ps variation in time. Note that when time-walk parameters are used with parallel-setup data, Gilles method gives about 130ps resolution. Resolution was 110ps under similar conditions with CFD which means that there should be some room to improve "LED+time-walk" resolution.