  Using the tip of a scanning probe microscope as a local electrostatic gate
gives access to real space information on electrostatics as well as charge
transport at the nanoscale, provided that the tip-induced electrostatic
potential is well known. Here, we focus on the accurate characterization of the
tip potential, in a regime where the tip locally depletes a two-dimensional
electron gas (2DEG) hosted in a semiconductor heterostructure. Scanning the tip
in the vicinity of a quantum point contact defined in the 2DEG, we observe
Fabry-P\'erot interference fringes at low temperature in maps of the device
conductance. We exploit the evolution of these fringes with the tip voltage to
measure the change in depletion radius by electron interferometry. We find that
a semi-classical finite-element self-consistent model taking into account the
conical shape of the tip reaches a faithful correspondence with the
experimental data.
