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We introduce a new fluorescence microscopy technique that maps the axial position of a fluorophore with subnanometer precision. The interference of the emission of fluorophores in proximity to a reflecting surface results in fringes in the fluorescence spectrum that provide a unique signature of the axial position of the fluorophore. The nanometer sensitivity is demonstrated by measuring the height of a fluorescein monolayer covering a 12-nm step etched in silicon dioxide. In addition, the separation between fluorophores attached to the top or the bottom layer in a lipid bilayer film is determined. We further discuss extension of this microscopy technique to provide resolution of multiple layers spaced as closely as 10 nm for sparse systems.