A generalized shapelet-based method for analysis of nanostructured surface imaging.

The determination of quantitative structure-property relations is a vital but challenging task for nanostructured materials research due to the presence of large-scale spatially varying patterns resulting from nanoscale processes such as self-assembly and nano-lithography. Focusing on nanostructured surfaces, recent advances have been made in automated quantification methods for orientational and translational order using shapelet functions, originally developed for analysis of images of galaxies, as a reduced-basis for surface pattern structure. In this work, a method combining shapelet functions and machine learning is developed and applied to a representative set of images of self-assembled surfaces from experimental characterization techniques including scanning electron miscroscopy, atomic force microscopy and transmission electron microscopy. The method is shown to be computationally efficient and able to quantify salient pattern features including deformation, defects, and grain boundaries from a broad range of patterns typical of self-assembly processes.