  Measuring the global magnetic field of the solar corona remains exceptionally
challenging. The fine-scale density structures observed in white light images
taken during Total Solar Eclipses (TSEs) are currently the best proxy for
inferring the magnetic field direction in the corona from the solar limb out to
several solar radii (Rs). We present, for the first time, the topology of the
coronal magnetic field continuously between 1 and 6 Rs, as quantitatively
inferred with the Rolling Hough Transform (RHT) for 14 unique eclipse coronae
that span almost two complete solar cycles. We find that the direction of the
coronal magnetic field does not become radial until at least 3 Rs, with a high
variance between 1.5 and 3 Rs at different latitudes and phases of the solar
cycle. We find that the most non-radial coronal field topologies occur above
regions with weaker magnetic field strengths in the photosphere, while stronger
photospheric fields are associated with highly radial field lines in the
corona. In addition, we find an abundance of field lines which extend
continuously from the solar surface out to several solar radii at all
latitudes, regardless of the presence of coronal holes. These results have
implications for testing and constraining coronal magnetic field models, and
for linking in situ solar wind measurements to their sources at the Sun.
