Doppler Imaging of stellar magnetic fields

We describe our latest Magnetic Doppler Imaging (MDI) code capable of simultaneously reconstructing the magnetic field vector and chemical composition distribution over the stellar surface. Input data consists of polarization measurements in the line profiles and the reconstruction is performed by solving the regularized inverse problem. The code incorporates the latest developments in the radiative transfer, the optimization and parallel computing techniques. We have also developed a new regularization method that allows application of our MDI code to incomplete data sets (e.g. only intensity and circular polarization) by restricting possible configurations of the field. Numerical experiments to be presented in a forthcoming paper demonstrate what can be achieved with MDI and allow studying of systematic errors that can cause serious distortions of the maps.