Metrology of convex-shaped nanoparticles via soft classification machine learning of TEM images

The shape of nanoparticles is a key performance parameter for many applications, ranging from nanophotonics to nanomedicines. However, the unavoidable shape variations, which occur even in precision-controlled laboratory synthesis, can significantly impact on the interpretation and reproducibility of nanoparticle performance. Here we have developed an unsupervised, soft classification machine learning method to perform metrology of convex-shaped nanoparticles from transmission electron microscopy images. Unlike the existing methods, which are based on hard classification, soft classification provides significantly greater flexibility in being able to classify both distinct shapes, as well as non-distinct shapes where hard classification fails to provide meaningful results. We demonstrate the robustness of our method on a range of nanoparticle systems, from laboratory-scale to mass-produced synthesis. Our results establish that the method can provide quantitative, accurate, and meaningful metrology of nanoparticle ensembles, even for ensembles entailing a continuum of (possibly irregular) shapes. Such information is critical for achieving particle synthesis control, and, more importantly, for gaining deeper understanding of shape-dependent nanoscale phenomena. Lastly, we also present a method, which we coin the "binary DoG", which achieves significant progress on the challenging problem of identifying the shapes of aggregated nanoparticles.