  Spectropolarimetric observations used to infer the solar magnetic fields are
obtained with a limited spatial resolution. The effects of this limited
resolution on the inference of the open flux over the observed region have not
been extensively studied. We aim to characterize the biases that arise in the
inference of the mean flux density by performing an end-to-end study that
involves the generation of synthetic data, its interpretation (inversion), and
a comparison of the results with the original model. We synthesized polarized
spectra of the two magnetically sensitive lines of neutral iron around 630\,nm
from a state-of-the-art numerical simulation of the solar photosphere. We then
performed data degradation to simulate the effect of the telescope with a
limited angular resolution and interpreted (inverted) the data using a
Milne-Eddington spectropolarimetric inversion code. We then studied the
dependence of the inferred parameters on the telescope resolution. The results
show a significant decrease in the mean magnetic flux density -- related to the
open flux observed at the disk center -- with decreasing telescope resolution.
The original net magnetic field flux is fully resolved by a 1m telescope, but a
20\,cm aperture telescope yields a 30\% smaller value. Even in the fully
resolved case, the result is still biased due to the corrugation of the
photospheric surface. Even the spatially averaged quantities, such as the open
magnetic flux in the observed region, are underestimated when the magnetic
structures are unresolved. The reason for this is the presence of
nonlinearities in the magnetic field inference process. This effect might have
implications for the modeling of large-scale solar magnetic fields; for
example, those corresponding to the coronal holes, or the polar magnetic
fields, which are relevant to our understanding of the solar cycle.
