Theory and Application of Shapelets to the Analysis of Surface Self-assembly Imaging
This provides a tool for researchers in materials science to analyze defects in self-assembled films, though it is incremental as it adapts an existing method to a new domain.
The authors tackled the problem of quantitatively analyzing local pattern strength and defects in surface self-assembly imaging by applying shapelet functions, originally used for galaxy analysis, to nanoscale films, resulting in a computationally efficient and robust method applicable to various pattern types like stripes and hexagons.
A method for quantitative analysis of local pattern strength and defects in surface self-assembly imaging is presented and applied to images of stripe and hexagonal ordered domains. The presented method uses "shapelet" functions which were originally developed for quantitative analysis of images of galaxies ($\propto 10^{20}\mathrm{m}$). In this work, they are used instead to quantify the presence of translational order in surface self-assembled films ($\propto 10^{-9}\mathrm{m}$) through reformulation into "steerable" filters. The resulting method is both computationally efficient (with respect to the number of filter evaluations), robust to variation in pattern feature shape, and, unlike previous approaches, is applicable to a wide variety of pattern types. An application of the method is presented which uses a nearest-neighbour analysis to distinguish between uniform (defect-free) and non-uniform (strained, defect-containing) regions within imaged self-assembled domains, both with striped and hexagonal patterns.