A scanning optical microscope whose active element (the tip) consists of a crystal containing impurity ions or color centers, which are excited by laser radiation, is proposed. The excitation energy from a single impurity center located at the point of the tip is transferred to the fluorescence centers of the experimental sample by the mechanism of resonant dipole-dipole exchange. It is shown that this approach can give nanometer spatial resolution with high sensitivity, which in many cases is much higher than the sensitivity of the ''standard'' near-field fluorescence microscopy. (C) 1996 American Institute of Physics.