ATLAS is the largest particle detector under construction at CERN Geneva. Frequency scanning interferometry (FSI), also known as absolute distance interferometry, will be used to monitor shape changes of the SCT (semiconductor tracker), a particle tracker in the inaccessible, high radiation environment at the centre of ATLAS. Geodetic grids with several hundred fibre-coupled interferometers (30 mm to 1.5 m long) will be measured simultaneously. These lengths will be measured by tuning two lasers and comparing the resulting phase shifts in grid line interferometers (GLIs) with phase shifts in a reference interferometer. The novel inexpensive GLI design uses diverging beams to reduce sensitivity to misalignment, albeit with weaker signals. One micrometre precision length measurements of grid lines will allow 10 µm precision tracker shape corrections to be fed into ATLAS particle tracking analysis. The technique was demonstrated by measuring a 400 mm interferometer to better than 400 nm and a 1195 mm interferometer to better than 250 nm. Precise measurements were possible, even with poor quality signals, using numerical analysis of thousands of intensity samples. Errors due to drifts in interferometer length were substantially reduced using two lasers tuned in opposite directions and the precision was further improved by linking measurements made at widely separated laser frequencies.