Holographic Tracking of Jeffery Orbits in Colloidal Dimers and Ellipsoids

An in-line hologram of a colloidal sphere can be analyzed with the Lorenz-Mie theory of light scattering to measure the sphere's three-dimensional position with nanometer-scale precision while also measuring its diameter and refractive index with part-per-thousand precision. Applying the same technique to aspherical or inhomogeneous particles yields the position, diameter and refractive index of an effective sphere that represents an average over the particle's geometry and composition. This effective-sphere interpretation has been applied successfully to a variety of asymmetric particles whose inhomogeneities appear on length scales smaller than the wavelength of light. Here, we combine numerical and experimental studies to investigate effective-sphere characterization of symmetric dimers of micrometer-scale spheres and colloidal ellipsoids. Our studies demonstrate that the effective-sphere interpretation usefully identifies dimers in holographic characterization studies of monodisperse colloidal spheres. The effective-sphere estimate for a dimer's axial position closely follows the ground truth for its center of mass. Trends in the effective-sphere diameter and refractive index, furthermore, can be used to measure a particle's three-dimensional orientation. When applied to colloidal dimers and ellipsoids transported in a Poiseuille flow, the estimated orientation distribution is consistent with expectations for Brownian particles undergoing Jeffery orbits.