| Summary: | Interaction-free measurement (IFM) has been proposed as a means of high-resolution, low-damage imaging of radiation-sensitive samples, such as biomolecules and proteins. The basic setup for IFM is a Mach-Zehnder interferometer, and recent progress in nanofabricated electron-diffraction gratings has made it possible to incorporate a Mach-Zehnder interferometer in a transmission electron microscope (TEM). Therefore, the limits of performance of IFM with such an interferometer and a shot-noise limited electron source (such as that in a TEM) are of interest. In this paper, we compare the error probability and sample damage for ideal IFM and classical imaging schemes, through theoretical analysis and numerical simulation. We consider a sample that is either completely transparent or completely opaque at each pixel. In our analysis, we also evaluate the impact of an additional detector for scattered electrons. Inclusion of the scattering detector results in reduction of error by up to an order of magnitude, for both IFM and classical schemes. We also investigate a sample reillumination scheme based on updating priors after each round of illumination and find that this scheme further reduces error. Implementation of these methods is likely achievable with existing instrumentation and would result in improved resolution in low-dose electron microscopy.
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