Theory and application of shapelets to the analysis of surface self-assembly imaging

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 (∝10(20)m). In this work, they are used instead to quantify the presence of translational order in surface self-assembled films (∝10(-9)m) through reformulation into "steerable" filters. The resulting method is 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-neighbor analysis to distinguish between uniform (defect-free) and nonuniform (strained, defect-containing) regions within imaged self-assembled domains, both with striped and hexagonal patterns.