Time of each RS TDC hit in E949 is recorded in TDC counts. After that all these count have to be calculated with respect to BS signal. So by definition BS arrives at t = 0 and the rest of the signals are calculated with respect to it. As RS TDC by itself can not provide information of Z origin of the hit (coordinate along RS module), time of the hit t is calculated as if the track crossed the RS module in the middle.
So time of hit t related to TDC counts T by (rd_unptdc.F):
t = 0.5*(BS-T) - t0 - twalk(E),where
twalk (E) = A/(Euse+B) - C, Euse = Max( Min(E,Emax), Emin)5 constants that describe twalk are assumed to be equal for all RS modules and are stored in $CAL_DB/rd_twk.????? file. Based on cosmic triggers data twalk = 87 / (7.4 + Euse) -1.04 . For energy boundaries we used Emin=0 and Emax=2000. Choice of constant C is absoultely arbitrary as t0 can compensate for it. I've chosen C=+1.04 so that average value of twalk correction over typical kmu21 sample is equal to 0 average(twalk)=0 .
t(DS) = 0.5*(BS-DS) - t0(DS) t(RS) = 0.5*(BS-RS) - t0(RS) - twalk(E)The calibration constant t0(DS) is extracted from (BS-DS) distribution, knowing that -t(DS) should have an exponential distribution starting at t=0 and smeared with a gaussian. This study was done by Dima Vavilov and he concluded that t0(DS) = -42.96 Results of similar study are shown here: PS , we showd bug Dima to document his studies.
Then assuming infinite speed of particles (so much for special relativity heh :) t(DS) = t(RS) then
t0(RS) = 0.5*(DS-RS) - t0(RS) - twalk(E)So procedure pretty much boils down to histogramming the right-hand-side of above equation.
We have to select tracks that pass through the middle of the RS TDC. To do that calibrated ADC amplitudes from both ends were required to be equal to each other within 10%. All necessary routins are located at the source directory.
Calibration constants were calculated basd on 4 runs with about 100k kmu21 events. To extract t0(RS) RHS was simply averaged. More sophisiticated procedure would requre gaussian fit of RHS distribution, but given good quality of the data it is not going to improve fit by a lot.
To verify procedure special test program developed by Dima Vavilov was used. First muon track was reconstructed in RS system using RS TDC signals as input (rd_trk.F). After that track time was computed as an average (with some weights) of individual RS TDC times of each module in the track ( trktim_rd.F). At last track time was compared to DS ( PS ). Track average time minus DS is refered to as "track resolution" and it is dominated by error on DS calibration (or so we hope).
Preliminary RS TDC constants were calculated based on 100k kmu21 triggers. They give "track resolution" ( PS ) about 0.6 nsec and are adequate for preliminary studies. Calibration constants were saved in file rd_tof.00001 and put in CFM database on September 11, 2001.
As the next step we would like to improve on "track resolution" by at least a factor of 2. We want to drop assumption on infinite particle speed, and also get Z coordinate of the track from UTC detectors.