  Non-linear force-free fields are the most general case of force-free fields,
but the hardest to model as well. There are numerous methods of computing such
fields by extrapolating vector magnetograms from the photosphere, but very few
attempts have so far made quantitative use of coronal morphology. We present a
method to make such quantitative use of X-Ray and EUV images of coronal loops.
Each individual loop is fit to a field line of a linear force-free field,
allowing the estimation of the field line's twist, three-dimensional geometry
and the field strength along it.
  We assess the validity of such a reconstruction since the actual corona is
probably not a linear force-free field and that the superposition of linear
force-free fields is generally not itself a force-free field. To do so, we
perform a series of tests on non-linear force-free fields, described in Low &
Lou (1990). For model loops we project field lines onto the photosphere. We
compare several results of the method with the original field, in particular
the three-dimensional loop shapes, local twist (coronal alpha), distribution of
twist in the model photosphere and strength of the magnetic field. We find
that, (i) for these trial fields, the method reconstructs twist with mean
absolute deviation of at most 15% of the range of photospheric twist, (ii) that
heights of the loops are reconstructed with mean absolute deviation of at most
5% of the range of trial heights and (iii) that the magnitude of non-potential
contribution to photospheric field is reconstructed with mean absolute
deviation of at most 10% of the maximal value.

Solar and Stellar Astrophysics