Light scattering patterns of triaxial ellipsoidal drops and their use in inferring drops’ shapes, aided by deep learning

Nonspherical liquid drops are commonly encountered in atmospheric optics, multiphase flows, and chemical engineering, where accurate determination of their shape and size is essential for both fundamental research and practical applications. However, resolving the true three-dimensional (3D) geometry of nonspherical drops remains a significant challenge for conventional measurement techniques, which typically rely on multi-view imaging. In contrast, a single light scattering pattern intrinsically encodes the geometrical features of a drop, offering a promising alternative for 3D shape inference. While prior studies have primarily addressed spheroidal drops with rotational symmetry, the scattering characteristics of more general nonspherical drops remain largely unexplored. In this work, we extend the vectorial complex ray model for 3D scattering (VCRM3D) to investigate the light scattering by triaxial ellipsoidal drops. The simulation results were validated against multilevel fast multipole algorithm (MLFMA) solutions over a broad range of axial ratios. Leveraging the efficiency of VCRM3D, we established and released the first database of light scattering patterns for ellipsoidal drops. As a proof of principle, we trained a convolutional neural network on this synthetic database to retrieve drop shape parameters, achieving mean relative errors below 1.5<i>%</i> on simulated scattering patterns. Compared to conventional methods that rely on costly and complex multi-view imaging, the proposed approach requires only a single light scattering pattern to reconstruct the drop's 3D shape. Beyond uncovering the light scattering characteristics of triaxial ellipsoidal drops, this work demonstrates a promising path toward advanced yet cost-effective optical diagnostics for nonspherical drops.