Theory and Application of Shapelets to the Analysis of Surface Self-assembly Imaging

TL;DR

This paper introduces a shapelet-based method for quantitatively analyzing local pattern strength and defects in surface self-assembly images, demonstrating its efficiency, robustness, and broad applicability to different pattern types.

Contribution

It adapts shapelet functions from galaxy image analysis into steerable filters for surface pattern analysis, enabling defect detection in self-assembled films.

Findings

Effective distinction between defect-free and defect-containing regions.

Robustness to variations in pattern feature shape.

Applicable to both striped and hexagonal patterns.

Abstract

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.