Fluorescence nanotomography is a newly developed experimental technique enabling determination of the molecular distributions with Angstrom resolution in complex structures such as soft solids, porous materials, and biomacromolecules. In this approach to structural sensing, Forster resonance energy transfer is used as the mechanism of detection of molecular separations, and fluorescence decay measurements with nanosecond resolution are used for determination of the molecular distribution function. Unlike the traditional Forster-type approach, wherein a model fluorescence decay function is derived for an assumed donor-acceptor distribution and then fitted to the experimental decay, returning the values of the parameters of assumed distribution, fluorescence nanotomography makes no a priori assumptions regarding the distribution function. In this paper we present the theoretical background of the method and demonstrate its applicability to various molecular systems by testing the method on artificial fluorescence decay data, generated for specific molecular structures.