  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 work, we compared the error
probability and sample damage for ideal IFM and classical imaging schemes,
through theoretical analysis and numerical simulation. We considered a sample
that is either completely transparent or completely opaque at each pixel. In
our analysis, we also evaluated the impact of an additional detector for
scattered electrons. The additional detector resulted in reduction of error by
up to an order of magnitude, for both IFM and classical schemes. We also
investigated a sample re-illumination scheme based on updating priors after
each round of illumination and found that this scheme further reduced error by
a factor of two. Implementation of these methods is likely achievable with
existing instrumentation and would result in improved resolution in low-dose
electron microscopy.
