  We demonstrate a method for measuring atom-surface interactions using
transmission spectroscopy of thermal vapors confined in a wedged nano-cell. The
wedged shape of the cell allows complementary measurements of both the bulk
atomic vapor and atoms close to surfaces experiencing strong van der Waals
atom-surface interaction. These are used to tightly constrain the dipole-dipole
collisional parameters of a theoretical model for transmission spectra that
accounts for atom-surface interactions, cavity effects, collisions with the
surface of the cell and atomic motion. We illustrate this method on a cesium
vapor in a sapphire cell, find $C_3=1.3\pm0.1$\,kHz.$\mu$m$^3$ and demonstrate
that even the weakest of the van der Waals atom-surface interaction
coefficients - for ground-state alkali atom transitions - can be determined
with a very good precision. This result paves the way towards a precise
quantitative characterization of atom-surface interactions in a wide range of
atom-based nano-devices.
