Panel a: Galactic free–free EM map obtained by the Planck Collaboration (Planck Collaboration X 2016). The other figures show the amplitude fields of the different reconstructions, which were supposed to capture the amplitude variations of the Faraday sky. Panel b: exponentiated amplitude field ρ of the reconstruction II, defined in Eq. (8). This field is not constrained by free–free data. Panel c: exponentiated ɛ field definedin Eq. (18). This field is part of the revised Faraday map resulting from reconstruction I and the denoised free–free sky. A logarithmic version of this plot is shown in Fig. 10a. Panel d: full Faraday amplitude field of reconstruction I, defined in Eq. (20). This field is part of the result of the model in Eq. (20). A logarithmic version of this plot is shown in Fig. 10d.