Detection of earth-size exoplanets using the astrometric signal of the host star requires sub-microarcsecond measurement precision. One major challenge in achieving this precision using a medium-size (< 2-m) space telescope is the calibration of dynamic distortions. A diffractive pupil can be used to generate polychromatic diffraction spikes in the focal plane, which encode the distortions in the optical system and may be used to calibrate astrometric measurements. The first half of this dissertation discusses the design and construction of a laboratory to test this concept. The main components of the system are a high stability star simulator, a diffraction limited off-axis optical system, and the data reduction algorithms to obtain the distortion map calibration. Currently, the laboratory is operational and first tests of distortion measurements have been done validating this concept to improve the astrometric accuracy of a telescope. The second part of this dissertation describes the use of the multi-laser guide star (LGS) system available at the 6.5 m MMT telescope to characterize GLAO performance and advance Laser Tomography Adaptive Optics (LTAO) technology. The system uses five range-gated and dynamically refocused Rayleigh laser beacons to sense the atmospheric wavefront aberration. Corrections are then applied to the wavefront using the 336-actuator adaptive secondary mirror of the telescope. So far, the system has demonstrated successful control of ground-layer aberration over a field of view (FoV) substantially wider than is delivered by conventional adaptive optics, yielding reduction in the width of the on-axis point-spread function from 1.07" to < 0.2" in H band. Both techniques can be combined to improve the astrometric accuracy of ground based telescopes, especially when using Multi-Conjugated Adaptive Optics (MCAO). A diffractive pupil can be used to calibrate the distortions induced by multiple Deformable Mirrors (DM), which is the main limitation to use this kind of AO system for high precision astrometric measurements.