  In a focused ion beam (FIB) microscope, source particles interact with a
small volume of a sample to generate secondary electrons that are detected,
pixel by pixel, to produce a micrograph. Randomness of the number of incident
particles causes excess variation in the micrograph, beyond the variation in
the underlying particle-sample interaction. We recently demonstrated that joint
processing of multiple time-resolved measurements from a single pixel can
mitigate this effect of source shot noise in helium ion microscopy. This paper
is focused on establishing a rigorous framework for understanding the potential
for this approach. It introduces idealized continuous- and discrete-time
abstractions of FIB microscopy with direct electron detection and
estimation-theoretic limits of imaging performance under these measurement
models. Novel estimators for use with continuous-time measurements are
introduced and analyzed, and estimators for use with discrete-time measurements
are analyzed and shown to approach their continuous-time counterparts as time
resolution is increased. Simulated FIB microscopy results are consistent with
theoretical analyses and demonstrate that substantial improvements over
conventional FIB microscopy image formation are made possible by time-resolved
measurement.
