Laser tracking interferometer system based on trilateration and a restriction for the position of its laser trackers

To measure three dimensional coordinate we have been developing a laser tracking interferometer system (LTS). Four laser interferometers chase the movement of a target cat's eye and measure the change in distance between them. The position of the cat's eye is determined from the measured distances based on the principle of trilateration. Taking advantage of measurement redundancy produced by the fourth tracker, the position of the trackers and the initial position of the cat's eye can be estimated by a self-calibration algorithm. A restriction on the arrangement of the laser trackers to perform the self-calibration algorithm is theoretically studied. Finally a preliminary experiment was made to show the measurement error of about 40 mu m for a 1 m measurement.