We have started a systematic study of the field topologies of magnetic single and accreting white dwarfs using Zeeman tomography. Here we report on our analysis of phase-resolved flux and circular polarization spectra of the magnetic cataclysmic variables BL Hyi and MR Ser obtained with FORS1 at the ESO VLT. For both systems we find that the field topologies are more complex than a dipole or an offset dipole and require at least multipole expansions up to order l = 3 to adequately describe the observed Zeeman features and their variations with rotational phase. Overall our model fits are in excellent agreement with observations. Remaining residuals indicate that the field topologies might even be more complex. It is, however, assuring that the global characteristics of our solutions are consistent with the average effective field strengths and the halo field strengths derived from intensity spectra in the past.
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