We investigate the detection of single molecules on an organic surface using a scanning molecular exciton microscope in the collection mode. To that end we present a theoretical framework to determine the detected intensity in dependence on the wavelength of the incident electric field and the distance between tip and sample. The tip and sample are treated quantum mechanically and are modeled as an ensemble of organic molecules with a single resonant energy level and a transition dipole moment. The electronic excitations are described by Frenkel excitons. Dipole-dipole interaction causes the energy transport via exciton transfer. The electromagnetic field is described by the classical Maxwell equations. Using a self-consistent solution of the Schrodinger equation and the Maxwell equations we calculate the induced polarization in the tip molecule and from this the intensity which is observed in the far field. By means of numerical investigations we are able to explain the realization of the contrast in the x-y scans. Outside the resonance regimes there is a uniform contrast for each distance between the tip and the sample and the resolution decreases with increasing distance. In the range of resonance, contrast and resolution depend sensitively on the distance.