[d2n-analysis-talk] Scintillator Studies: A Possible Solution

Sat Dec 4 18:15:04 EST 2010

Hi all,

Since our last meeting, I've been working through the 'original'
procedure.  Here are the steps and their results:

1. Choose an S2m paddle as the 'reference' paddle and align all other
paddles to that one.

The results to this are seen in my most recent status report talk.  See
plot 1.

2. Construct the time difference s1_raw[k] - s2m_cor[j] for each
combination of k and j

S2m Times (corrected):

S2mRMean[0]: 61.336
S2mRMean[1]: 61.3055
S2mRMean[2]: 61.3105
S2mRMean[3]: 61.3396
S2mRMean[4]: 61.3093
S2mRMean[5]: 61.3222
S2mRMean[6]: 61.3022
S2mRMean[7]: 61.3138
S2mRMean[8]: 61.3174
S2mRMean[9]: 61.3111
S2mRMean[10]: 61.3187
S2mRMean[11]: 61.3201
S2mRMean[12]: 61.3155
S2mRMean[13]: 61.3603
S2mRMean[14]: 61.3638
S2mRMean[15]: 61.2838

S1 Times (raw):

S1RMean[0]: 68.9786
S1RMean[1]: 70.1427
S1RMean[2]: 78.1951
S1RMean[3]: 78.2402
S1RMean[4]: 79.3335
S1RMean[5]: 82.1707

Each time difference is (first index is for S1, second for S2m; all S1
paddles were shifted to times smaller than those seen in S2m before this
calculation):

Delta[0][0]: 12.3575
Delta[0][1]: 12.327
Delta[0][2]: 12.3319
Delta[1][3]: 11.1969
Delta[1][4]: 11.1666
Delta[1][5]: 11.1795
Delta[2][5]: 3.12705
Delta[2][6]: 3.10713
Delta[2][7]: 3.11872
Delta[3][8]: 3.07719
Delta[3][9]: 3.07092
Delta[3][10]: 3.07849
Delta[4][10]: 1.98521
Delta[4][11]: 1.98665
Delta[4][12]: 1.98208
Delta[5][13]: -0.810443
Delta[5][14]: -0.806909
Delta[5][15]: -0.886927

3. From this time difference, determine the time offset for each s1 paddle
-- that is, consider the average of the time differences in step 2
particular to each paddle s1.

Average Delta, for application as S1 offset (shown in units of nanoseconds
below):

S1DeltaAvg[0]: 12.3388
S1DeltaAvg[1]: 11.181
S1DeltaAvg[2]: 3.11763
S1DeltaAvg[3]: 3.07553
S1DeltaAvg[4]: 1.98465
S1DeltaAvg[5]: -0.83476

The result of this method is shown in the next two plots.  The first of
these is the raw S1 times, while the second is the corrected S1 times. 
There is still the jitter seen in S1 time vs. track-x.

I have also tried a different method.  This time, I consider
event-by-event corrections, based upon which S2m paddle took the trigger
time.  The method is as follows:

1. Going event by event, I see which S2m paddle took the trigger time
(i.e., the event has a time in the self-timing peak in S2m paddle j).

2. For this event, I then scan through the S1 paddles to see which paddle
it fired.  Call this paddle k.

3. For each combination of S2m paddle j and S1 paddle k, there is a
certain time offset that should be applied to the S1 time in order to
account for the unaligned <raw> s2m paddle times, causing the stops to be
different for a given track in S1 paddle k compared to another track of
the same S1 paddle k with a  <different> S2m paddle of index j.  This
corresponds to a 6 by 16 matrix of time offsets.  Of the 96 possible
elements, only 18 have been assigned values based upon the mapping of S1
to S2m paddles.  All others are set to zero.

For each identified event of S1 paddle k corresponding to S2m paddle j (in
the self-timing peak), the correction is applied as follows:

L_s1_rt_my_cor[k] = fTDCRes*L_s1_rt[k] + fTrigOff[k][j];

Where the units of my corrected variable is nanoseconds.

4.  After we are satisfied with the results of this correction, we can
then apply a time offset for each S1 paddle, so that each S1 paddle lines
up:

L_s1_rt_my_cor[k] = fTDCRes*L_s1_rt[k] + fTrigOff[k][j] +
S1PaddleOffset[k];

The results of this study are shown in the last two plots.

This method does a pretty good job of fixing the issue of the jitter in S1
vs. track-x.  There are some cases in these plots where it's not quite
perfect.  These regions are where neighboring paddles in S1 see the <same>
paddle in S2m... this takes a lot of juggling with some of these
coefficients I've come up with to get them to work, and the process is
very 'touchy'.

An example of this is at x = 0.20m, where S1 paddle 3 and 4 map to S2m
paddle 10.  So, with some more patience, I think it's possible to clean
that up a little bit better; although, I haven't had any luck today with
this.  These sections where we see jitter remaining may be due to overlap
regions in the S1 paddles.  I haven't verified this yet, but would be
interesting to look at.  In which case, I'll have to think some more about
how a correction may be correctly applied to such a situation.

I have also considered the time difference between S2m and S1.  If we look
at the last plot, we can see that the time difference has a tiny spike at
zero.  These events are clearly due to the S1 time matching that of the
S2m time.  The shape of the main peak is <mostly> gaussian, and it's clear
that the tail on the lower times is due to the jitter that has remained
after my correction.

If this were to be implemented into the database, this would warrant
changing the THaScintillator class...  I'm not quite sure how that would
work at the moment (concerning steps 1 and 2 above).

Overall, I think this is a nice method to clean up the jitter in S1 timing.

-------------------------------------------------
David Flay
Physics Department
Temple University
Philadelphia, PA 19122

office: Barton Hall, BA319
phone: (215) 204-1331

e-mail: flay at jlab.org
            flay at temple.edu

website: http://www.jlab.org/~flay
              http://quarks.temple.edu
-------------------------------------------------

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