Image analysis algorithm for the verification of hexagonal symmetry in spherical nanostructures

Verification of ordering and symmetry is essential to enhance the nanofabrication process of periodic nanostructures. In this paper, we present the open-source software HEXI, which can detect circles and distinguish between perfect hexagonal ordering and defect configurations. The proposed user-friendly image analysis software (implemented in Python) consists of several stages. First, the algorithm identifies circular structures in microscopy (e.g., scanning electron microscopy, atomic force microscopy) images using the Canny edge detector and the Hough circle transform. Then, the detected circles are categorized as hexagonally ordered or non-hexagonally ordered (defects). This classification can be achieved using three different methods: variance in brightness (global or adaptive) and distance. The software generates visual output (detected coloured circles overlaid over the original image) and quantitative data (total/defective circle count, surface coverage, histogram of size distribution). The circle detection and classification are demonstrated on real-world samples (e.g., spin-coated monolayer of polystyrene spheres, arrays of plasma etched nanospheres, holes). They verify the accuracy of the proposed algorithm, which successfully analysed circular nanostructures of various types (close-packed and non-closed packed arrays, unevenly lit large areas) with hexagonal symmetry, independently of preparation technique (nanosphere lithography, electron beam lithography). Finally, the performance and advantages of the software are discussed. [Display omitted] •Rapid qualitative image analysis of SEM, AFM images using various classifiers•Defect recognition and evaluation in hexagonal monolayers of nano/microspheres•Intuitive visual output and quantitative data (defective sphere count)•Easy to use, extensible, open source Python software HEXI