  Early magnetographic observations indicated that magnetic field in the solar
photosphere has unresolved small-scale structure. Near-infrared and optical
data with extremely high spatial resolution show that these structures have
scales of few tens of kilometres, which are not resolved in the majority of
solar observations. The goal of this study is to establish the effect of
unresolved photospheric magnetic field structure on Stokes profiles observed
with relatively low spatial resolution. Ultimately, we aim to develop methods
for fast estimation of the photospheric magnetic filling factor and
line-of-sight gradient of the photospheric magnetic field, which can be applied
to large observational data sets. We exploit 3D MHD models of
magneto-convection developed using MURAM code. Corresponding profiles of Fe I
6301.5 and 6302.5 $\mathrm{\AA}$ spectral lines are calculated using NICOLE
radiative transfer code. The resulting I and V Stokes [x,y,$\lambda$] cubes
with reduced spatial resolution of 150 km are used to calculate magnetic field
values as they would be obtained in observations with Hinode/SOT or SDO/HMI.
Three different methods of the magnetic filling factor estimation are
considered: the magnetic line ratio method, Stokes V width method and a simple
statistical method. We find that the statistical method and the Stokes V width
method are sufficiently reliable for fast filling factor estimations.
Furthermore, we find that Stokes $I\pm V$ bisector splitting gradient can be
used for fast estimation of line-of-sight gradient of the photospheric magnetic
field.
