  In extreme scattering events, the brightness of a compact radio source drops
significantly, as light is refracted out of the line of sight by foreground
plasma lenses. Despite recent efforts, the nature of these lenses has remained
a puzzle, because any roughly round lens would be so highly overpressurized
relative to the interstellar medium that it could only exist for about a year.
This, combined with a lack of constraints on distances and velocities, has led
to a plethora of theoretical models. We present observations of a dramatic
double-lensing event in pulsar PSR~B0834+06 and use a novel phase-retrieval
technique to show that the data can be reproduced remarkably well with a
two-screen model: one screen with many small lenses and another with a single,
strong one. We further show that the latter lens is so strong that it would
inevitably cause extreme scattering events. Our observations show that the lens
moves slowly and is highly elongated on the sky. If similarly elongated along
the line of sight, as would arise naturally from a sheet of plasma viewed
nearly edge-on, no large over-pressure is required and hence the lens could be
long-lived. Our new technique opens up the possibility of probing interstellar
plasma structures in detail, leading to understanding crucial for
high-precision pulsar timing and the subsequent detection of gravitational
waves.
