Statistical removal of Faraday rotation in vector magnetograms taken by filter‐type magnetographs

Based on the spectral scan data of NOAA AR 10325, 10484 and 10377 obtained with the Solar Magnetic Field Telescope at Huairou Solar Observing Station, we analyse the azimuthal differences (Δδφ) between the line centre and the line wing −0.12 Å of Fe  i λ5324.19 caused by Faraday rotation. Grids of the longitudinal field B z and inclination ψ for intervals of 100 G and 3° are made. It is found that the azimuthal rotations are of the same magnitude when B z is in a 100‐G interval. The amplitudes of azimuthal differences obviously increase with increasing B z and decrease with increasing ψ. Averaging Δδφ in each 100‐G interval of B z and making a linear fit between 〈Δδφ〉 and B z , then we obtain the correlation between the observed azimuthal difference and B z depicted by the linear fitting formula (1), namely Δδφ o = 0.0114 | B z | . In addition, through the simulation we also obtain the azimuthal rotation at the line centre of Fe  i λ5324.19 described by the fitting formula (2), namely δφ 0.00 = 0.0254 | B z | − 3.975 × 10 −6   B 2 z . We also present a third fitting formula (3), namely Δδφ t = 0.0149 | B z | − 1.455 × 10 −6   B 2 z , which describes the azimuthal differences between the line centre and the line wing −0.12 Å. Formula (3) is consistent with the observational results of the three active regions. We correct the vector magnetograms of the three active regions with formulae (1) and (3) and find that the electric current J z , the current helicity H c , and the average force‐free field factor α av calculated from the correct magnetograms are nearly equivalent to those measured at the line wing −0.12 Å. Furthermore, we calculate J z with 393 corrected vector magnetograms and find that formulae (1) and (3) can remove part of the false current whereas formula (2) can remove most of it.