  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.
