- What is the problem?
- What is the cause?
- Diagnosis
- Solution
- Summary/Conclusion
- Listing of figures (with captions)

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.

- 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.

**Conclusions (prior to fixing the problem):**

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.

- Change in hit position from 1st pass to 2nd pass in 2DH.
- Digitization and resolution in the (unfixed) 2DH
- Digitization and resolution in the 1DH
- Digitization and resolution in the fixed 2DH

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