Coordinate measurement in 2-D and 3-D geometries using frequency scanning interferometry

Frequency Scanning Interferometry (FSI) has been developed for robust precise distance measurements. We present the reconstruction of two and three dimensional geodetic grids, using simultaneous FSI measurements between grid nodes. The shape of the particle physics tracker inside the ATLAS experiment (currently under construction for the Large Hadron Collider at CERN) will be monitored using a geodetic grid of 842 remotely measured, fibre-coupled interferometers. The challenge is to make precise distance measurements in the hostile, high radiation environment and combine them to reconstruct node coordinates and hence the grid shape in quasi real time to a three dimensional precision of around 10mum. Two and three dimensional prototype grids with adjustable geometries have been measured, demonstrating shape reconstruction to a precision of around 1mum. Error propagation through these grids was studied with different reconstruction models. Grid redundancy allowed the agreement between software models and node coordinate reconstruction to be verified.