Interferometric near-field optical microscopy achieving a resolution of 10 angstroms is demonstrated. The scattered electric field variation caused by a vibrating probe tip in close proximity to a sample surface is measured by encoding it as a modulation in the optical phase of one arm of an interferometer. Unlike in regular near-field optical microscopes, where the contrast results from a weak source (or aperture) dipole interacting with the polarizability of the sample, the present form of imaging relies on a fundamentally different contrast mechanism: sensing the dipole-dipole coupling of two externally driven dipoles (the tip and sample dipoles) as their spacing is modulated.