  Much of our understanding of the state of coronal plasmas comes from
observations that are optically thin. This means that light travels freely
through the corona without being materially affected by it, which allows it to
be easily seen through, but also results in a line-of-sight degeneracy which
has previously thwarted attempts to recover the three-dimensional structure of
the coronal plasma. However, although the corona is disorganized in the
line-of-sight direction, it is highly organized in the field-aligned direction.
This paper demonstrates how to exploit this organization to resolve the
line-of-sight degeneracy in the plasma properties using a suitable magnetic
field structure. A preliminary investigation with a potential field is shown,
finding a solution which clearly resembles the real solar data, even with a
single perspective. The results indicate that there is ample information in the
resulting residuals that can be used to refine the magnetic field structure,
allowing, for the first time, the optically thin plasma observations to speak
directly to the magnetic field extrapolations.
