Radio pulsars scintillate because their emission travels through the ionized interstellar medium via multiple paths, which interfere with each other. It has long been realized that the scattering screens responsible for the scintillation could be used as `interstellar lenses to localize pulsar emission regions. Most scattering screens, however, only marginally resolve emission components, limiting results to statistical inferences and detections of small positional shifts. Since screens situated close to the source have better resolution, it should be easier to resolve emission regions of pulsars located in high density environments such as supernova remnants or binaries in which the pulsars companion has an ionized outflow. Here, we report events of extreme plasma lensing in the `Black Widow pulsar, PSR~B1957+20, near the phase in its 9.2 hour orbit in which its emission is eclipsed by its companions outflow. During the lensing events, the flux is enhanced by factors of up to 70--80 at specific frequencies. The strongest events clearly resolve the emission regions: they affect the narrow main pulse and parts of the wider interpulse differently. We show that the events arise naturally from density fluctuations in the outer regions of the outflow, and infer a resolution of our lenses comparable to the pulsars radius, about 10,km. Furthermore, the distinct frequency structures imparted by the lensing are reminiscent of what is observed for the repeating fast radio burst FRB 121102, providing observational support for the idea that this source is observed through, and thus at times strongly magnified by, plasma lenses.
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