Application to the VELO
1. VELO residual and the global parameters
In order to apply MILLEPEDE in the VELO context, we need first a linear relation
between the residuals and the global parameters. In the case of the VELO, where
R strips are all but linear, the situation is not evident a priori.
In fact, if we consider that the object to align is the
INDIVIDUAL SENSOR,
we are facing a huge problem. Indeed the relation between residuals and global
parameters will not be linear, and MILLEPEDE will become uneasy to apply.
This is mainly the reason why MILLEPEDE couldn't be used directly for the TestBeam
alignment. Sensors in the TestBeam are independant from each others.
On the other hand, if we consider that the object to align is the
STATION
(this assertion is justified by the fact that the to sensors are bonded together),
we have an (R,Phi) coordinate. We then could easily convert it in an (X,Y) one, ie
a linear solution.
The relations between residuals and global parameters are presented into the note on internal VELO alignment, which is available
here. The relation finally obtain is not yet fully linear, as track slopes are part of it. However, this problem could be solved by using MILLEPEDE with iterations (see the
standalone code for more information on that point).
Given these relations, you could start to use MILLEPEDE.
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