Hi Sirvel,

Here are few comments on your chamber alignment results. I find it
interesting that we both see convergence to the 1 micron level and
yet we come up with results that differ by as much as 300 microns. It
just means that there is still a lot to do to understand plane alignments.
I will be running my code in the coming days/weeks to see if I can learn
more about this... I'm sure you will be doing that too.

Here are my comments:

1. When 4 planes are fixed to define a line for the transverse alignment,
that line is not necessarily concident with the beam direction. Due to the
fact that the DME isochrones are "highly" elliptical, the wrong point on
the ellipse will be chosen therefore resulting in a bad track fit. You therefore
need to look for the minimum of the sigma's for the tracking residuals
as you vary this "beam alignment angle". The note I first posted on plane
alignments explains this more.

2. A large number of iterations is likely needed to pin down plane positions.
Although the convergence is fast at first, it becomes painfully slow close
to the end. I found from my calculations that even after 44 iterations
there are small slopes on the convergence curves suggesting that the planes
are still moving in a specific direction (i.e. have not converged, despite the
small increments in each iteration) rather than oscillating around a specific
point as one would expect when the convergence is complete.

3. The ultimate test for alignment code is that once we claim that we
found the correct wire positions we should be able to move a bunch of
planes randomly and show that after running the alignment code we
always bring the planes back to the same position (regardless of what
planes are shifted and by how much). This test would be stronger than
Monte Carlo tests since it includes all the complications present for real
data.

4. For plane rotations, the phi of only one plane should be fixed. As I
understand  from your posting, it seems that more than one plane was fixed.
If so, this will introduce a "twist" and might explain the "relatively" big
rotations that you found in your calculations.

An interesting test is to compute the resolution with your plane shifts
and see what results I get.

Cheers,
Maher

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   Maher Quraan                            TRIUMF
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