Sub-nanometer 3D morphometric precision of polarisation-resolved wide-field optical extinction microscopy determines the roundness of individual gold nanospheres.

Quantitative polarisation-resolved optical extinction microscopy of individual plasmonic nanoparticles has recently been introduced as a powerful approach to characterise the nanoparticle's morphology with a precision comparable to that of electron microscopy, while using a simple optical microscope [L. M. Payne, W. Albrecht, W. Langbein and P. Borri, Nanoscale, 2020, 12, 16215-16228]. Here we provide a step change by adding measurements for radial polarisation in the condenser back focal plane, probing plasmonic resonances polarised in the axial direction. The combined linear and radial polarisation measurements provide a significantly enhanced precision of the retrieved 3D morphology, as we show on defect-free ultra-uniform gold nanospheres of 30 nm nominal diameter characterised by transmission electron microscopy. The measured cross-sections are modelled for an ellipsoidal particle, determining the three semi-axes and rotation angles by fitting the measurements. The material permittivity and surface damping providing the best fit are found. The particle aspect ratio is determined with a precision better than 5%, and the size with an impressive precision of 0.1 nm. Notably, corrections to the Rayleigh-Gans ellipsoid model due to retardation are significant even though the particle diameters are more than an order of magnitude smaller than the wavelength in the medium, and taking them into account reduces the systematic error in the retrieved diameters from 2 nm to below 1 nm. The accuracy of size and shape determination is limited by the remaining systematic errors in modelling.