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Interaction-free measurement (IFM) has been proposed as a means ofhigh-resolution, low-damage imaging of radiation-sensitive samples, such asbiomolecules and proteins. The basic setup for IFM is a Mach-Zehnderinterferometer, and recent progress in nanofabricated electron diffractiongratings has made it possible to incorporate a Mach-Zehnder interferometer in atransmission-electron microscope (TEM). Therefore, the limits of performance ofIFM with such an interferometer and a shot-noise limited electron source (suchas that in a TEM) are of interest. In this work, we compared the errorprobability and sample damage for ideal IFM and classical imaging schemes,through theoretical analysis and numerical simulation. We considered a samplethat is either completely transparent or completely opaque at each pixel. Inour analysis, we also evaluated the impact of an additional detector forscattered electrons. The additional detector resulted in reduction of error byup to an order of magnitude, for both IFM and classical schemes. We alsoinvestigated a sample re-illumination scheme based on updating priors aftereach round of illumination and found that this scheme further reduced error bya factor of two. Implementation of these methods is likely achievable withexisting instrumentation and would result in improved resolution in low-doseelectron microscopy.

Reduced damage in electron microscopy by using interaction-free measurement and conditional re-illumination