A l i g n m e n t

Last updated     by Thomas Naumann
The BST is considered as a rigid cylinder.
The positions of the Si detectors scatter around the ideal shape.
In this model the alignment consists of two steps:

 - an external alignment of the BST   in the H1  coordinate system
 - an internal alignment of the disks in the BST coordinate system .

For the internal alignment the residuals of straight line fits
in r-z and u-z are minimised by shifting each disk in r or u.

This improves the widths of the residual distributions
in r from about 60 um  to 18 um. This r resolution consists of
a Si detector and an alignment contribution.

The external position of the BST is characterized by:

 - 3 translation parameters DR, DPHI, DZ and
 - 2 rotation parameters THX and THY around the x and y axes.

It is determined from the mispointing dz of a BST track to the vertex
and checked with the difference dth of the polar angles measured by BST and BDC.

Before alignment dz and dth strongly depend on the azimuthal angle phi.
Assuming the BST gravicenter as the rotation center ZROT this is parametrized as


The 5 external alignment constants are fitted from the
3D distribution dz(phi,z). We find

  DR = 1.2 mm   DZ = 0.5 mm    THX = 1.2 mrad   THY = 0.0 mrad

After external alignment no z or theta biases and no phi dependence
of dz and dth are visible. Integrating over phi we get
the z and theta resolutions of the BST:

   z  BST - z  CT   =  0.01 +/- 0.31  mm
   th BST - th BST  =  0.07 +/- 0.43  mrad

The z and theta resolutions are also available for BST1 and BST2 separately.
dth is dominated by the BDC resolution. dz contains 2 mm z error of the CT.

The external and internal alignment of the r and u detectors is given
in the banks BSTA and BSTU .