  We examine whether or not it is possible to derive the field strength
distribution of quiet Sun internetwork regions from very high spatial
resolution polarimetric observations in the visible. In particular, we consider
the case of the spectropolarimeter attached to the Solar Optical Telescope
aboard Hinode. Radiative magneto-convection simulations are used to synthesize
the four Stokes profiles of the \ion{Fe}{1} 630.2 nm lines. Once the profiles
are degraded to a spatial resolution of 0\farcs32 and added noise, we infer the
atmospheric parameters by means of Milne-Eddington inversions. The comparison
of the derived values with the real ones indicates that the visible lines yield
correct internetwork field strengths and magnetic fluxes, with uncertainties
smaller than $\sim$150 G, when a stray light contamination factor is included
in the inversion. Contrary to the results of ground-based observations at
1\arcsec, weak fields are retrieved wherever the field is weak in the
simulation.
