The problem of increasing the quality of the image created by a scanning near field optical micro scope with the Förster Resonance Energy Transfer (FRET) module is discussed. The possibility of improving the resolution of the near field optical microscope due to the FRET effect is analyzed, as is the formation of high quality images of nanoobjects on the basis of signals of increased intensity obtained by means of plas mon resonance in specially formed metal nanostructures (the plasmon resonance antennas). Research results for the nonradiative transfer of the electron exitation energy between the molecules placed near the planar surface of a conductor or a metal nanocylinder of the nanometer radius, as well as around a spherical nano particle, are presented. In the simplest model, the influence of the conducting phase boundary is taken into account by introducing an effective dipole image. If the antenna is a sphertical nanoparticle, then multipole polarization formalism is a more adequate representation of the responce.