Radiation damage has long been a problem for electron microscopy. (A nice overview can be found in the papers from my November 2013 posting on ‘Protecting two-dimensional materials during TEM’.
In what he admits to be a long shot research program, Hiroshi Okamoto-san at Akita Prefectural University is attempting to reduce the electron dose required for TEM imaging by several orders of magnitude. His proposal is to use entangled electrons in order to enhance the sensitivity to electron phase in the detection process.
So far, the work is purely theoretical. Major technological hurdles remain, but Okamoto-san quite sensibly is first addressing the fundamental principles.
“Entanglement-assisted electron microscopy based on a flux qubit”, arXiv:1311.2377
“Measurement errors in entanglement-assisted electron microscopy”, arXiv:1401.7410
Okamoto-san’s Google site