We consider scanning gate conductance microscopy of an open quantum dot that is connected to the conducting channel using the wave function description of the quantum transport and a finite difference approach. We discuss the information contained in conductance (G) maps. We demonstrate that the maps for a delta-like potential perturbation exactly reproduce the local density of states for a quantum dot that is weakly coupled to the channel, i.e. when the connection of the channel to the dot transmits a single transport mode only. We explain this finding in terms of the Lippmann–Schwinger perturbation theory. We demonstrate that the signature of the weak coupling conditions is the conductance, which for P subbands at the Fermi level varies between and P in units of . For stronger coupling of the quantum dot to the channel, the G maps resolve the local density of states only for very specific work points, with the Fermi energy coinciding with quasi-bound energy levels.