  Properties of magnetic field in the internetwork regions are still fairly
unknown due to rather weak spectropolarimetric signals. We address the matter
by using the 2D inversion code that is able to retrieve the information on
smallest spatial scales, up to the diffraction limit, while being less
susceptible to noise than most of the previous methods used. Performance of the
code and the impact of the various effects on the retrieved field distribution
is tested first on the realistic MHD simulations. The best inversion scenario
is then applied to the real Hinode/SP data. Tests on simulations show: (1) the
best choice of node position ensures a decent retrieval of all parameters, (2)
code performs well for different configurations of magnetic field, (3) slightly
different noise level or slightly different defocus included in the spatial PSF
produces no significant effect on the results and (4) temporal integration
shifts the field distribution to the stronger, more horizontally inclined
field. Although the contribution of the weak field is slightly overestimated
due to noise, the 2D inversions are able to recover well the overall
distribution of the magnetic field strength. Application of the 2D inversion
code on the Hinode/SP internetwork observations reveals a monotonic field
strength distribution. The mean field strength at optical depth unity is $\sim
130$~G. At the higher layers, field strength drops as the field becomes more
horizontal. Regarding the distribution of the field inclination, tests show
that we cannot directly retrieve it with the observations/tools at hand,
however the obtained distributions are consistent with those expected from
simulations with a quasi-isotropic field inclination after accounting for
observational effects.
