  An open resonator fabricated in a two-dimensional electron gas is used to
explore the transition from strongly invasive scanning gate microscopy to the
perturbative regime of weak tip-induced potentials. With the help of numerical
simulations that faithfully reproduce the main experimental findings, we
quantify the extent of the perturbative regime in which the tip-induced
conductance change is unambiguously determined by properties of the unperturbed
system. The correspondence between the experimental and numerical results is
established by analyzing the characteristic length scale and the amplitude
modulation of the conductance change. In the perturbative regime, the former is
shown to assume a disorder-dependent maximum value, while the latter linearly
increases with the strength of a weak tip potential.
