  Digital holographic microscopy is a fast three-dimensional (3D) imaging tool
with many applications in soft matter physics. Recent studies have shown that
electromagnetic scattering solutions can be fit to digital holograms to obtain
the 3D positions of isolated colloidal spheres with nanometer precision and
millisecond temporal resolution. Here we describe the results of new techniques
that extend the range of systems that can be studied with fitting. We show that
an exact multisphere superposition scattering solution can be used to fit
holograms of colloidal clusters containing up to six spheres. We also introduce
an approximate and computationally simpler solution, Mie superposition, that is
valid for multiple spheres spaced several wavelengths or more from one another.
We show that this method can be used to fit holograms of several spheres on an
emulsion droplet, and we give a quantitative criterion for assessing its
validity.
