  We propose a procedure for extraction of the Fermi surface for a
two-dimensional electron gas with a strong Rashba spin-orbit coupling from
conductance microscopy. Due to the interplay between the effective spin-orbit
magnetic field and the external one within the plane of confinement, the
backscattering induced by a charged tip of an atomic force microscope located
above the sample, leads to the spin precession, and thus to the spin mixing of
the incident and reflected modes. This mixing leads to a characteristic
angle-dependent beating pattern visible in the conductance maps. We show that
the structure of the Fermi level, bearing signatures of the spin-orbit
coupling, can be extracted from the Fourier transform of the interference
fringes in the conductance maps as a function of the magnetic field direction.
We propose a simple analytical model which can be used to fit the experimental
data in order to obtain the spin-orbit coupling constant.
