Comparing Machine Learning and Physics-Based Nanoparticle Geometry Determinations Using Far-Field Spectral Properties
Anisotropic metal nanostructures exhibit polarization-dependent light scattering, a property which has been widely studied and exploited to determine orientations of subwavelength structures using far-field microscopy. Here we explore the use of variational autoencoders (VAEs) to determine the geometries of gold nanorods (NRs) such as in-plane orientation and aspect ratio under linearly polarized dark-field illumination in an optical microscope. We enforce a shared latent space to connect two VAEs trained separately with polarized dark-field scattering spectra and electron microscopy images and achieve image prediction (shape, orientation, and size) of Au NRs using only polarized dark-field scattering spectra. We determine the geometrical parameters of orientational angle and aspect ratio quantitatively via both our dual-VAE and physics-based analysis on the input scattering spectra. We show that orientational angle prediction by dual-VAE performs well with only a small (~300 particle) training set, yielding a mean absolute error (MAE) of 14.4° and a concordance correlation coefficient (CCC) of 0.95. This performance is only marginally worse than the physics-based cos(2?) fitting approach between the scattering intensity and the polarizing angle, which achieves MAE of 8.78° and CCC of 0.99. Aspect ratio determination is also comparable for the dual-VAE and physics-based fitting comparison (MAE of 0.21 vs. 0.23 and CCC of 0.53 vs. 0.68). Here, this dual encoder-decoder architecture effectively exploits the structure-property relationships of plasmonic nanostructures to construct a cross-modal machine learning (ML) approach, providing a pathway to employ ML approaches to address other structure-property relationships in materials science.