The Fe XIII 10747 and 10798 Å lines observed in the solar corona are sensitive to the coronal magnetic field in such a way that, in principle, the full vector field at a point on the line of sight can be inferred from their combined polarization signals. This paper presents analytical inversion formulae for the field parameters and analyzes the uncertainty of magnetic field measurements made from such observations, assuming emission dominated by a single region along the line of sight. We consider the case of the current Coronal Multi-channel Polarimeter (CoMP) instrument as well as the future Coronal Solar Magnetism Observatory (COSMO) and Advanced Technology Solar Telescope (ATST) instruments. Uncertainties are estimated with a direct analytic inverse and with a Markov Chain Monte Carlo algorithm. We find that (in effect) two components of the vector field can be recovered with CoMP, and well recovered with COSMO or ATST, but that the third component can only be recovered when the solar magnetic field is strong and optimally oriented.
