Absolute multilateration-based coordinate measurement system using retroreflecting glass spheres

We have measured the three-dimensional coordinates of retroreflecting glass spheres using a multilateration technique. To this end, the distances between each target and our measurement heads have been determined by an in-house prototype of electro-optical absolute distance meter. The used targets are spheres of glass refractive index n = 2 and of diameter 14.2 mm. They offer a much larger aperture than corner cubes and a lower cost, but they present a low reflectivity. However, this paper shows that with a proper collimation of the laser beams it is possible to reach a range of operation of 20 m. The standard uncertainty on such distances is better than 11 μm, including the mechanical errors of the gimbal mechanisms of our aiming systems. This uncertainty has been validated thanks to a comparison with an interferometric bench. In addition, the measurement of the coordinates of 16 glass spheres using a self-calibration multilateration algorithm has also confirmed the performances of the developed system: the standard deviation on the position errors has been estimated to about 10 μm.