# 3D spherical-cap fitting procedure for (truncated) sessile nano- and micro-droplets & -bubbles

## TL;DR

This paper introduces a comprehensive 3D spherical-cap fitting procedure for analyzing nanostructures from AFM images, providing more accurate and consistent morphological parameters than traditional 2D methods.

## Contribution

A novel 3D fitting algorithm that automatically extracts nanostructure geometry from AFM images, improving accuracy over existing 2D cross-sectional methods.

## Key findings

- 3D-SCFP yields consistent and accurate morphological parameters.
- Compared to 2D fitting, 3D method uses all valid data points for higher fidelity.
- The procedure is applicable to both complete and truncated spherical caps.

## Abstract

In the study of nanobubbles, nanodroplets or nanolenses immobilised on a substrate, a cross-section of a spherical-cap is widely applied to extract geometrical information from atomic force microscopy (AFM) topographic images. In this paper, we have developed a comprehensive 3D spherical cap fitting procedure (3D-SCFP) to extract morphologic characteristics of complete or truncated spherical caps from AFM images. Our procedure integrates several advanced digital image analysis techniques to construct a 3D spherical cap model, from which the geometrical parameters of the nanostructures are extracted automatically by a simple algorithm. The procedure takes into account all valid data points in the construction of the 3D spherical cap model to achieve high fidelity in morphology analysis. We compare our 3D fitting procedure with the commonly used 2D cross-sectional profile fitting method to determine the contact angle of a complete spherical cap and a truncated spherical cap. The results from 3D-SCFP are consistent and accurate, while 2D fitting is unavoidably arbitrary in selection of the cross-section and has a much lower number of data points on which the fitting can be based, which in addition is biased to the top of the spherical cap. We expect that the developed 3D spherical-cap fitting procedure will find many applications in imaging analysis.