  Emission profiles of the resonantly scattered OII~83.4~nm triplet can in
principle be used to estimate \(\mathrm{O}^+\) density profiles in the F2
region of the ionosphere. Given the emission source profile, solution of this
inverse problem is possible, but requires significant computation. The
traditional Feautrier solution to the radiative transfer problem requires many
iterations to converge, making it time-consuming to compute. A Markov chain
approach to the problem produces similar results by directly constructing a
matrix that maps the source emission rate to an effective emission rate which
includes scattering to all orders. The Markov chain approach presented here
yields faster results and therefore can be used to perform the \(\mathrm{O}^+\)
density retrieval with higher resolution than would otherwise be possible.
