  Tailored electrostatic potentials are the foundation of scanning gate
microscopy. We present several aspects of the tip-induced potential on the
two-dimensional electron gas. First, we give methods on how to estimate the
size of the tip-induced potential. Then, a ballistic cavity is formed and
studied as a function of the bias-voltage of the metallic top gates and probed
with the tip-induced potential. It is shown how the potential of the cavity
changes by tuning the system to a regime where conductance quantization in the
constrictions formed by the tip and the top gates occurs. This conductance
quantization leads to a unprecedented rich fringe pattern over the entire
structure. Finally, the effect of electrostatic screening of the metallic top
gates is discussed.
