Date: Fri, 03 Apr 2015 12:04:37 -0400
From: Mark Ito <marki@jlab.org>
To: Kei Moriya <kmoriya@jlab.org>
CC: Beni Zihlmann <zihlmann@jlab.org>
Subject: tof calibration
Kei,
Talked to Nathan and he told me you were out of town. Maybe we can talk
when you get back. Beni is also interested. But here is the basic idea:
- pretend all counters are double ended
- only consider two-ended counter hits for everything below (when we say
a counter is hit, we mean both ends always)
Mean time offsets
- pick a horizontal counter
- look for coincidences between vertical counters and the special
horizontal counter
- histogram the mean time difference: t_mean,v - t_mean,h for each
vertical counter
- process the information from these histograms
- pick a vertical counter
- define its mean time offset, t_off,m to be zero
- note the average value of t_mean,v - t_mean,h for this counter,
call it dt_m0
- calculate a mean time offset t_off,m for all of the other vertical
counters such that
the average of t_mean,v - t_mean,h - dt_m0 + t_off,m = 0
- this gives mean time offsets for all vertical counters, where the
special vertical counter has an offset of 0 by definition.
- now do the same thing exchanging vertical for horizontal
Time difference offsets
- pick a horizontal counter
- look for coincidences between vertical counters and the special
horizontal counter
- histogram the end-to-end time differences: t_2 - t_1 for each vertical
counter
- process the information from these histograms
- pick a vertical counter
- define its time difference offset, t_off,d to be zero
- note the value of the average end-to-end time difference for this
counter, call it dt_d0
- calculate a time difference offset t_off,d for all of the other
vertical counters such that
the average of t_2 - t_1 - dt_d0 + t_off,d = 0
- this gives time difference offsets for all vertical counters, where
the special vertical counter has an offset of 0 by definition.
- now do the same thing exchanging vertical for horizontal
Transform to the single end basis:
For each counter, we have a t_off,m and a t_off,d
When we apply t_off,m to the mean time we get a corrected mean time,
t_corr,m
(t_1 + t_2)/2 + t_off,m = t_corr,m
and we want individual end offsets, t_off,1 and t_off,2, to do the same
thing, i. e.,
[(t_1 + t_off,1) + (t_2 + t_off,2)]/2 = t_corr,m
so
t_off,m = (1/2)(t_off,1 + t_off,2)
When we apply t_off,d to the time difference we get a corrected time
difference, t_corr,d
t_2 - t_1 + t_off,d = t_corr,d
and we want individual end offsets, to do the same thing, i. e.,
(t_2 + t_off,2) - (t_1 + t_off,1) - t_corr,d
so
t_off,d = t_off,2 - t_off,1
and solving for t_off,1 and t_off,2 gives
t_off,1 = t_off,m - (1/2)t_off,d
t_off,2 = t_off,m + (1/2)t_off,d
What we end up with is a vertical plane that is calibrated to itself in
time and calibrated to itself in vertical location. We also have a
horizontal plane that is calibrated to itself in time and calibrated to
itself in horizontal position. So there are still four global constants
to fix to bring the TOF into registration with the rest of the detector.
You can think of the planes as floating around in this four-dimensional
space. We have to use outside information to attach the TOF to the rest
of the detector. For time the FCAL would be good. For position, charged
tracks.
Right?
-- Mark