  Brownian motion in confinement and at interfaces is a canonical situation,
encountered from fundamental biophysics to nanoscale engineering. Using the
Lorenz-Mie framework, we optically record the thermally-induced tridimensional
trajectories of individual microparticles, within salty aqueous solutions, in
the vicinity of a rigid wall, and in the presence of surface charges. We
construct the time-dependent position and displacement probability density
functions, and study the non-Gaussian character of the latter which is a direct
signature of the hindered mobility near the wall. Based on these distributions,
we implement a novel, robust and self-calibrated multifitting method, allowing
for the thermal-noise-limited inference of diffusion coefficients
spatially-resolved at the nanoscale, equilibrium potentials, and forces at the
femtoNewton resolution.
