  We discuss the effect of semitransparency in a quantum-Zeno-like
interaction-free measurement setup, a quantum-physics based approach that might
significantly reduce sample damage in imaging and microscopy. With an emphasis
on applications in electron microscopy, we simulate the behavior of probe
particles in an interaction-free measurement setup with semitransparent
samples, and we show that the transparency of a sample can be measured in such
a setup. However, such a measurement is not possible without losing (i.e.,
absorbing or scattering) probe particles in general, which causes sample
damage. We show how the amount of lost particles can be minimized by adjusting
the number of round trips through the setup, and we explicitly calculate the
amount of lost particles in measurements which either aim at distinguishing two
transparencies or at measuring an unknown transparency precisely. We also
discuss the effect of the sample causing phase shifts in interaction-free
measurements. Comparing the resulting loss of probe particles with a classical
measurement of transparency, we find that interaction-free measurements only
provide a benefit in two cases: first, if two semitransparent samples with a
high contrast are to be distinguished, interaction-free measurements lose less
particles than classical measurements by a factor that increases with the
contrast. This implies that interaction-free measurements with zero loss are
possible if one of the samples is perfectly transparent. A second case where
interaction-free measurements outperform classical measurements is if three
conditions are met: the particle source exhibits Poissonian number statistics,
the number of lost particles cannot be measured, and the transparency is larger
than approximately 1/2. In all other cases, interaction-free measurements lose
as many probe particles as classical measurements or more.
