Zeeman-Doppler-Imaging (ZDI) is a technique for the diagnosis of stellar magnetic fields from observations of circularly polarized light, based on the weak-field approximation. This approach has proved adequate in numerous studies of the magnetic fields of solar-type stars. To improve the signal-tonoise ratio, one can add the contributions of different lines to the polarization signature. However, this multi-line extension has been limited by a number of assumptions (e.g., the weak-field approximation). Here we present a novel approach. We created a database of synthetic polarized spectra for different combinations of magnetic-field intensities and orientations. Principal Components Analysis was used to compress the database, so that only few Principal Components are needed to represent all the calculated spectra.
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