One method for locating extrasolar planets is to observe the lateral movement of a star in the sky caused by a planet in orbit around it. In order to detect this displacement, the angular position of the star has to be measured with high accuracy. This technique is called astrometry. The Very Large Telescope Interferometer (VLTI) is operated by the European Southern Observatory and located at the Paranal Observatory in Chile. The purpose of the PRIMA instrument (Phase Referenced Imaging and Micro-arcsecond Astrometry) of the VLTI is to perform high-resolution astrometric measurements and high-resolution imaging of faint stars using white light interferometry, by combining the light collected by two telescopes. In order to allow the detection of extrasolar planets, the astrometric measurement has to be performed with micro-arcsecond accuracy. In astrometric mode the PRIMA instrument observes two targets at the same time: the object of scientific interest, and a bright reference star. The angular position of the science object relative to the reference star is obtained by monitoring the differential optical path travelled by the light of each object in two separate white-light interferometers. The aim of this work was to develop a high-resolution laser metrology based on superheterodyne interferometry, with an accuracy of 5 nm over a differential optical path of 100 mm. Moreover the laser source had to be stabilised on an absolute frequency reference, in order to ensure the long-term stability and calibration required to achieve the target performance. Superheterodyne interferometry allowed the direct measurement of the differential optical path using two heterodyne interferometers working with two different frequency shifts. The differential phase measurement between the two interferometers was obtained by electronic mixing of the two heterodyne signals, leading to the differential optical path needed for the astrometric measurement.