  We simulate scanning probe imaging of the local density of states related to
scattering Fermi level wave functions inside a resonant cavity. We calculate
potential landscape within the cavity taking into account the Coulomb charge of
the probe and its screening by deformation of the two-dimensional electron gas
using the local density approximation. Approximation of the tip potential by a
Lorentz function is discussed. The electron transfer problem is solved with a
finite difference approach. We look for stable work points for the extraction
of the local density of states from conductance maps. We find that conductance
maps are highly correlated with the local density of states when the Fermi
energy level enters into Fano resonance with states localized within the
cavity. Generally outside resonances the correlation between the local density
of states and conductance maps is low.
