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I discuss a series of advancements I have made towards making digital holographic microscopy into a useful tool for experimental scientists in soft-matter physics and biophysics. Digital holograms can be recorded with simple hardware at high speed to capture three-dimensional information about the dynamics of aqueous suspensions of colloidal particles, cells, viruses or other microscopic objects.

The challenge of working with holograms is that they map information about the objects non-locally onto an interference pattern. Therefore, post processing is needed to extract the information from a hologram. Traditionally this has been done by reconstructions, effectively shining light back through the hologram to obtain a representation of the recorded objects. More recently Ovryn and Izen (JOSA A 2000) and Lee, Grier and coworkers (Opt. Express 2012) have shown that more precise information can be recovered by physically modelling the light scattering that creates the hologram and solving a constrained inverse-scattering problem to obtain information about the scatterers such as their position or size. This technique gives precise results but requires a scattering model for the objects under observation. It therefore requires significant expertise to set up and implement.

In this dissertation I present several advances that improve upon this
state-of-the art. First, I present a simple, inexpensive, portable,
battery-powered holographic microscope that is suitable for imaging
biological samples inside an incubator. Next, I describe a method
using a general scattering model called the discrete dipole
approximation to analyze holograms of non-spherical particles. Because
this analysis is computationally expensive, I present a new method
based on analyzing a random subset of the pixels of a hologram. This
method, which significantly speeds up computation, is the basis for a
framework based on Bayesian inference that gives a more intuitive and
rigorous way of specifying prior information and presenting
uncertainty in results, which I present at the end.

The motivating thread through this thesis is building tools to enable new experiments using holography and making it easier for scientists who are not experts in holography and light scattering to use holography as a tool to do the science that interests them. In support of these goals, I have implemented all of the computational techniques and physical models in an open source library, HoloPy, to make it as easy as possible for other scientists to use them.
