Aligning the CMS Muon Endcap Detector with a System of Optical Sensors

The positions and orientations of one sixth of 468 large cathode strip chambers in the endcaps of the CMS muon detector are directly monitored by several hundred sensors including 2-D optical sensors with linear CCDs illuminated by cross-hair lasers. Position measurements obtained by photogrammetry and survey under field-off conditions show that chambers in the +Z endcap have been placed on the yoke disks with an average accuracy of $\approx 1$ mm in all 3 dimensions. We reconstruct absolute Z$_{CMS}$ positions and orientations of chambers at B=0T and B=4T using data from the optical alignment system. The measured position resolution and sensitivity to relative motion is about 60 $\mu m$. The precision for measuring chamber positions taking into account mechanical tolerances is \mbox{$\approx 270 \mu m$}. Comparing reconstruction of optical alignment data and photogrammetry measurements at B=0T indicates an accuracy of $\approx$ 680 $\mu m$ currently achieved with the hardware alignment system. Optical position measurements at B=4T show significant chamber displacements of up to 13 mm due to yoke disk deformation.