  With the advent of next generation high resolution telescopes, our
understanding of how the magnetic field is organized in the internetwork (IN)
photosphere is likely to advance.We aim to evaluate the extent to which we can
retrieve information about the magnetic vector in the IN photosphere using
inversions. We use snapshots produced from high resolution 3D
magnetohydrodynamic (MHD) simulations and employ the Stokes Inversions based on
Response functions (SIR) code to produce synthetic observables in the near
infrared spectral window observed by the GREGOR Infrared Spectrograph (GRIS),
which contains the highly magnetically sensitive photospheric Fe I line pair at
15648.52 A and 15652.87 A. We perform nearly 14 million inversions to test how
well the true MHD atmospheric parameters can be constrained. Finally, we
degrade the synthetic Stokes vectors spectrally and spatially to GREGOR
resolutions and examine how this influences observations, considering the
impact of stray light, spatial resolution and signal-to-noise (S-to-N). We find
the depth-averaged parameters can be recovered by the inversions of the
undegraded profiles, and by adding gradients to magnetic field strength,
inclination and line of sight velocity we show an improvement in the chi
squared value is achieved. We evaluate the extent to which we can constrain
these parameters at various optical depths, with the kinematic and
thermodynamic parameters sensitive deeper in the atmosphere than the magnetic
parameters. We find the S-to-N and spatial resolution play a significant role
in determining how the atmosphere appears and the magnetic and kinematic
parameters are invariant upon inclusion of unpolarized stray light. We studied
a linear polarization feature which resembles those recently observed by GRIS,
appearing as loop-like structures with similar magnetic flux density.
