Detection of planets by virtue of their gravitational perturbations of nearby visible stars generally requires relative astrometric accuracies of ~ 3 × 10−4 arc sec for Jovian planets and ~ 3 × 10−7 arc sec for terrestrial planets. Two-color optical astrometric interferometers on earth should be capable of ~ 10−4 arc sec rms accuracy for stars brighter than magnitude 7–10, while small one-color space systems should achieve at least ~ 10−5 arc sec. Two-color systems permit correction every few milliseconds for the random wavefront tilt due to atmospheric turbulence; the correction is based on the observed offset between the red and blue fringes, and the known atmospheric dispersion. A 3.4-meter baseline interferometer on Mount Wilson has demonstrated ~ 0.02 arc sec rms fluctuations for 1-second samples.