  We experimentally demonstrate nanoscopic transmission microscopy relying on a
deterministic single particle source. This increases the signal-to-noise ratio
with respect to conventional microscopy methods, which employ Poissonian
particle sources. We use laser-cooled ions extracted from a Paul trap, and
demonstrate remote imaging of transmissive objects with a resolution of 8.6
$\pm$ 2.0nm and a minimum two-sample deviation of the beam position of 1.5nm.
Detector dark counts can be suppressed by 6 orders of magnitudes through gating
by the extraction event. The deterministic nature of our source enables an
information-gain driven approach to imaging. We demonstrate this by performing
efficient beam characterization based on a Bayes experiment design method.
