  Extrapolations of solar photospheric vector magnetograms into
three-dimensional magnetic fields in the chromosphere and corona are usually
done under the assumption that the fields are force-free. The field
calculations can be improved by preprocessing the photospheric magnetograms. We
compare two preprocessing methods presently in use, namely the methods of
Wiegelmann et al. (2006) and Fuhrmann et al. (2007). The two preprocessing
methods were applied to a recently observed vector magnetogram. We examine the
changes in the magnetogram effected by the two preprocessing algorithms.
Furthermore, the original magnetogram and the two preprocessed magnetograms
were each used as input data for nonlinear force-free field extrapolations by
means of two different methods, and we analyze the resulting fields. Both
preprocessing methods managed to significantly decrease the magnetic forces and
magnetic torques that act through the magnetogram area and that can cause
incompatibilities with the assumption of force-freeness in the solution domain.
Both methods also reduced the amount of small-scale irregularities in the
observed photospheric field, which can sharply worsen the quality of the
solutions. For the chosen parameter set, the Wiegelmann et al. method led to
greater changes in strong-field areas, leaving weak-field areas mostly
unchanged, and thus providing an approximation of the magnetic field vector in
the chromosphere, while the Fuhrmann et al. method weakly changed the whole
magnetogram, thereby better preserving patterns present in the original
magnetogram. Both preprocessing methods raised the magnetic energy content of
the extrapolated fields to values above the minimum energy, corresponding to
the potential field. Also, the fields calculated from the preprocessed
magnetograms fulfill the solenoidal condition better than those calculated
without preprocessing.
