The problem of spatial digitization in 2DH
Suggestion: Go directly to the conclusions and list of figures
At the July collaboration meeting, the point was made by several people,
notably the SUNY crowd, that the hit position coming from the 2D hitfinder
is "discrete" in y. That is, it is clustered about the center of the
time bucket position. This presents a problem in making t0 tables from
the data, and in topological searches. It has also been known that the
resolution (as measured by RMS of xdev_fit and ydev_fit) is worse for
2DH than for 1DH.
As is well known, in 2DH we make 2 passes at the data. In the first
pass, the position of the hit is guessed at, and in the second, that guess
may be refined, and the dE is calculated using information
from the tracker.
- In our current default settings (H2D_SW.NOFIT_ISOLATED=1),
there is no refinement of hit position for isolated hits, so the initial
guess is the final hit position.
- Also, for those hits who come from
clusters too crowded to be deconvolved (decided by H2D_SW.MAX_PEAKS_FIT=3),
there is no refitting done, so the initial guess is the final position.
- Finally, for those hits that do go through full refitting in the second
pass, the hit position may not change too much.
Here are some plots showing
how much the x and y position changes for those hits that are refit.
Basically, y can shift around on the order of a time bucket, and x shifts
around very little.
The upshot is that if our initial guess has "digitization" in it, then the
final positions will be digitized as well.
In 2DH, the initial guess at position (in 1st pass) was just the weighted
mean in pad and time of the "peak pixel" and its 8 closest neighbors in 2
dimensions. This led to digitization in x and y, but mostly in y.
- Look here for plots showing the
digitization and resolution with the 2DH (before the fix we discuss here).
- For comparison, see how the 1DH does
at digitization and resolution on the same event.
These plots were made with a 2 A GeV event.
Conclusions (prior to fixing the problem):
2DH+BTF uses about 15% more hits in this event than 1DH+BTF. This is
consistent with previous studies.
2DH gives about 10% better resolution in x than 1DH.
2DH gives about 25% worst resolution in y than 1DH.
Both 2DH and 1DH show significant digitization in x, of very different
structure.
2DH has much worse digitization in y than 1DH.
The initial guess has been made a little
more sophisticated, so that a
3-point fit to the y-projection is made, using the shaper response function
P(t) = ((t-t0)/tau)**N * exp(-(t-t0)/tau)
where N=4 for E895.
Also, a 3-point fit to a Gaussian is made to the x-projection. This gives
just about the same result as a weighted mean.
Especially the first change makes a *big* difference. See the
plots here. Again, you may want to compare
with how the 1DH does.
Conclusions
- X digitization
- Fixed 2DH is probably a little better than original 2DH.
- Fixed 2DH looks better than 1DH.
- Y digitization
- Fixed 2DH is lots better than original 2DH.
- Fixed 2DH is about the same as 1DH, maybe a little better (?).
- X resolution RMS (Gaussian sigma), in microns
Code | RMS (micron) | Gassian sigma (micron)
|
---|
Original 2DH | 1080 | 758
|
Fixed 2DH | 1060 | 721
|
1DH | 1145 | 855
|
- Fixed 2DH is 10% better than 1DH.
- Y resolution RMS (Gaussian sigma), in microns
Code | RMS (micron) | Gassian sigma (micron)
|
---|
Original 2DH | 2044 | 1937
|
Fixed 2DH | 1853 | 1683
|
1DH | 1704 | 1540
|
- Fixed 2DH is 10% worse than 1DH. Unclear whether this is due to 2DH using
15% more hits.
The spatial digitization problem in 2DH has been fixed.
Using 1DH as a benchmark:
- 2DH now gives better performance in terms of x-digitization
- 2DH now gives same performance in terms of y-digitization
- 2DH now gives 10% better x-resolution
- 2DH now gives 10% worse y-resolution
- 2DH uses 10-15% more hits, consistent with previous studies.
The worse y-resolution as compared to 1DH will be studied more (it may be due to using
more hits). But my conclusion is that the code is fixed enough to say it is "ready."
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