Abstract
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.
Highlights
T HE ability to image the structure of a sample at nanoscale resolution using microscopes that scan samples with a focused beam of particles is critical in material science and the life sciences
We establish an abstract framework for TR measurement in focused ion beam (FIB) microscopy with direct electron detection
Through estimation-theoretic analyses, analyses of estimators, and Monte Carlo FIB imaging simulations, we show the extent to which source shot noise can be mitigated by TR
Summary
T HE ability to image the structure of a sample at nanoscale resolution using microscopes that scan samples with a focused beam of particles is critical in material science and the life sciences. The vastly greater mass of ions compared to electrons (by a factor of 7.3 × 103 for helium or 1.3 × 105 for gallium) makes sputtering much more significant for FIB microscopy than for SEM. Experiments with HIM data demonstrated mean-squared error (MSE) improvement by about a factor of 4 at doses of 1.0 and 2.5 incident ions per pixel This use of time resolution is entirely for the purpose of making the measurements more informative without increasing the total dose. It is not for imaging of dynamic samples and not comparable to any previous use of time resolution in microscopy.
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