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 (Delta delta phi) between the line centre and the line wing -0.12 angstrom of Fe I lambda 5324.19 caused by Faraday rotation. Grids of the longitudinal field B-z and inclination psi for intervals of 100 G and 3 degrees 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 psi. Averaging Delta delta phi in each 100-G interval of B-z and making a linear fit between <Delta delta phi > and B-z, then we obtain the correlation between the observed azimuthal difference and Bz depicted by the linear fitting formula (1), namely Delta delta phi degrees = 0.0114 vertical bar B-z vertical bar. In addition, through the simulation we also obtain the azimuthal rotation at the line centre of Fe I lambda 5324.19 described by the fitting formula (2), namely delta phi(0.00) = 0.0254 vertical bar B-z vertical bar - 3.975 x 10(-6) B-z(2). We also present a third fitting formula (3), namely Delta delta phi(t) = 0.0149 vertical bar B-z vertical bar - 1.455 x 10-6 B-z(2), which describes the azimuthal differences between the line centre and the line wing -0.12 angstrom. 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 alpha(av) calculated from the correct magnetograms are nearly equivalent to those measured at the line wing -0.12 angstrom. Furthermore, we calculate Jz 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.