Microwave tomography of solar magnetic fields

We present a new technique for the measurement of magnetic fields in the solar chromosphere - corona through observations of its free-free microwave emission in intensity and polarization. We derive the decoupled radiation transfer equations for Stoke's parameters of I and Sr for circular polarized emission in plane-layer inhomogeneous atmospheres and present a model solutions of inversion problem. We discuss the discrimination between contributions from the corona and the chromosphere to the observed brightness spectra from the quiet Sun and plage regions and propose a practical method of magnetic field estimates, which was used both with single frequency (the Nobeyama Radioheliograph at 17 GHz) and multi frequency (RATAN at 1 - 16 GHz) observations and discuss the preliminary results. The proposed techniques may be useful as microwave magnetography at the corona base and for checks and improvements in the current problem of extrapolating magnetic fields from photosphere to corona.