Inverse scattering theory for optical coherence tomography (OCT) is developed. The results are used to produce algorithms to resolve three-dimensional object structure, taking into account the finite beam width, diffraction, and defocusing effects. The resolution normally achieved only in the focal plane of the OCT system is shown to be available for all illuminated depths in the object without moving the focal plane. Spatially invariant resolution is verified with numerical simulations and indicates an improvement of the high-resolution crosssectional imaging capabilities of OCT.