Compact radio sources sometimes exhibit intervals of large, rapid changes in their flux-density, due to lensing by interstellar plasma crossing the line-of-sight. A novel survey program has made it possible to discover these Extreme Scattering Events (ESEs) in real time, resulting in a high-quality dynamic spectrum of an ESE observed in PKS 1939-315. Here we present a method for determining the column-density profile of a plasma lens, given only the dynamic radio spectrum of the lensed source, under the assumption that the lens is either axisymmetric or totally anisotropic. Our technique relies on the known, strong frequency dependence of the plasma refractive index in order to determine how points in the dynamic spectrum map to positions on the lens. We apply our method to high-frequency (4.2-10.8 GHz) data from the Australia Telescope Compact Array of the PKS 1939-315 ESE. The derived electron column-density profiles are very similar for the two geometries we consider, and both yield a good visual match to the data. However, the fit residuals are substantially above the noise level, and deficiencies are evident when we compare the predictions of our model to lower-frequency (1.6-3.1 GHz) data on the same ESE, thus motivating future development of more sophisticated inversion techniques.
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