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We present a new, high-speed technique to track the three-dimensionaltranslation and rotation of non-spherical colloidal particles. We capturedigital holograms of micrometer-scale silica rods and sub-micrometer-scaleJanus particles freely diffusing in water, and then fit numerical scatteringmodels based on the discrete dipole approximation to the measured holograms.This inverse-scattering approach allows us to extract the the position andorientation of the particles as a function of time, along with staticparameters including the size, shape, and refractive index. The best-fit sizesand refractive indices of both particles agree well with expected values. Thetechnique is able to track the center of mass of the rod to a precision of 35nm and its orientation to a precision of 1.5$^\circ$, comparable to or betterthan the precision of other 3D diffusion measurements on non-sphericalparticles. Furthermore, the measured translational and rotational diffusioncoefficients for the silica rods agree with hydrodynamic predictions for aspherocylinder to within 0.3%. We also show that although the Janus particleshave only weak optical asymmetry, the technique can track their 2D translationand azimuthal rotation over a depth of field of several micrometers, yieldingindependent measurements of the effective hydrodynamic radius that agree towithin 0.2%. The internal and external consistency of these measurementsvalidate the technique. Because the discrete dipole approximation can modelscattering from arbitrarily shaped particles, our technique could be used in arange of applications, including particle tracking, microrheology, andfundamental studies of colloidal self-assembly or microbial motion.

Using the Discrete Dipole Approximation and Holographic Microscopy to Measure Rotational Dynamics of Non-spherical Colloidal Particles