Andrei's recipe for BCAL Timing Calibration

Here is an e-mail that Andrei Semenov sent around to a select group on Mar. 18, 2013 describing a plan for timing calibration of the BCAL.

Will:

The following is the time-walk correction procedure that I prefer.

You have the times (TDC values) from upstream and downstream (t_up, t_do)
as well as correspondent amplitudes (ADC values) a_up and a_do.

1. On event-by-event basis, you form the difference dt0=(t_up-t_do), fill
1-dim histograms with dt0 for the slices (intervals) on a_up, calculate
mean values (with uncertainties) for these histograms, plot these mean
values as a function of a_up, and fit the data points with the function
f1(a_up).

2. On event-by-event basis, you form the corrected difference
dt1 = (t_up-t_do) - f1(a_up), fill 1-dim histograms with dt1 for the
slices (intervals) on a_do, calculate mean values (with uncertainties) for
these histograms, plot these mean values as a function of a_do, and fit
the data points with the function f2(a_do).

3. (Optional step but it helps sometimes.) On event-by-event basis, you
form the corrected difference dt2 = (t_up-t_do)-f1(a_up)-f2(a_do), fill
1-dim histograms with dt2 for the slices (intervals) on r=(a_up/a_do),
calculate mean values (with uncertainties) for these histograms, plot
these mean values as a function of r, and fit the data points with the
function f3(r).

4. The corrected difference dt3=(t_up-t_do)-f1(a_up)-f2(a_do)-f3(r) is the
corrected time difference you want for the z-position calculation (surely,
you should add to this value the "correct" constant time shift for the
position in the calorimeter you working with). To improve the result, I
would suggest to process the corrected dt3 through the steps 1-3 again (so
in the end you'll have dt6=(t_up-t_do)-f1-f2-f3-f4-f5-f6).

I would strongly recommend to work directly with the value of interest
(viz., dt=t_up-t_do) instead of correcting the artificial difference of
the "registered signal" and the "first energy deposition time" because the
later will be not available in the real data. (Surely, the smaller range
of time-walk correction required for the difference will also help.)

David:  Can we put into our simulation data the real coordinates of the
shower from the simulation (to be able to compare the positions
reconstructed from the time with the "real" values that will be an
estimation of our position resolution).

For the mean time (viz., (t_up+t_do)/2 ), I would propose to perform
indipendent correction.

Some information on this time-walk procedure can be found in the report
GlueX-doc-1221-v4 and in my talk
https://halldweb.jlab.org/wiki/images/a/a5/Meet121113.pdf

Hope it will help,
Andrei