  We present a new, high-speed technique to track the three-dimensional
translation and rotation of non-spherical colloidal particles. We capture
digital holograms of micrometer-scale silica rods and sub-micrometer-scale
Janus particles freely diffusing in water, and then fit numerical scattering
models based on the discrete dipole approximation to the measured holograms.
This inverse-scattering approach allows us to extract the the position and
orientation of the particles as a function of time, along with static
parameters including the size, shape, and refractive index. The best-fit sizes
and refractive indices of both particles agree well with expected values. The
technique is able to track the center of mass of the rod to a precision of 35
nm and its orientation to a precision of 1.5$^\circ$, comparable to or better
than the precision of other 3D diffusion measurements on non-spherical
particles. Furthermore, the measured translational and rotational diffusion
coefficients for the silica rods agree with hydrodynamic predictions for a
spherocylinder to within 0.3%. We also show that although the Janus particles
have only weak optical asymmetry, the technique can track their 2D translation
and azimuthal rotation over a depth of field of several micrometers, yielding
independent measurements of the effective hydrodynamic radius that agree to
within 0.2%. The internal and external consistency of these measurements
validate the technique. Because the discrete dipole approximation can model
scattering from arbitrarily shaped particles, our technique could be used in a
range of applications, including particle tracking, microrheology, and
fundamental studies of colloidal self-assembly or microbial motion.
