Transmission Microscopy with Nanometer Resolution Using a Deterministic Single Ion Source.

We realize a single particle microscope by using deterministically extracted laser-cooled ^{40}Ca^{+} ions from a Paul trap as probe particles for transmission imaging. We demonstrate focusing of the ions to a spot size of 5.8±1.0  nm and a minimum two-sample deviation of the beam position of 1.5 nm in the focal plane. The deterministic source, even when used in combination with an imperfect detector, gives rise to a fivefold increase in the signal-to-noise ratio as compared with conventional Poissonian sources. Gating of the detector signal by the extraction event suppresses dark counts by 6 orders of magnitude. We implement a Bayes experimental design approach to microscopy in order to maximize the gain in spatial information. We demonstrate this method by determining the position of a 1  μm circular hole structure to a precision of 2.7 nm using only 579 probe particles.