%!TEX root = ../dissertation.tex
\chapter{Conclusion}
\label{conclusion}

This thesis shows a number of advances that should help holography to be useful to many more scientists working on many more problems. In Chapter~\ref{chap:simple-dhm} I demonstrated a simple, inexpensive, self-contained holographic microscope suitable for portable use and inside environments such as cell incubators. In Chapter~\ref{chap:dda} I showed how to use the discrete dipole approximation to analyze holograms of non-spherical scatterers, a previously inaccessible regime. In Chapter~\ref{chap:random-subset} I showed an elegant technique for reducing the computation time required for analysis of holograms to a much more manageable duration. Finally, in Chapter~\ref{chap:bayesian} I introduced a Bayesian analysis paradigm which more naturally handles known prior information, allows marginalizing out nuisance parameters, and eliminates the need for manual initial guesses for parameter inference. Taken together, the advances in this thesis and my open source implementations of them in the software package HoloPy should allow a broader range of scientists to use high precision holographic measurements on a broader range of problems.

There is still work to be done in this field. Our scattering models still include a nuisance parameter, $\alpha$, which should be replaced with physically motivated parameters obtained from a proper analysis of the holographic imaging system. Our ability to parameterize shapes still limits the objects we can analyze even with the DDA. My work with Ana Carpio and coworkers on topological techniques offers one route forward in this space~\cite{carpio_noninvasive_2016}, but this is still an open problem.

The DDA works well for small objects, but computation becomes prohibitive for larger objects. In order to work with holograms of objects the size of mammalian cells we will need another scattering theory, perhaps one based on Rayleigh-Gans or other models.

Shot noise from the reference wave also limits our ability to take holograms of small, weakly scattering objects. This situation can be improved by reducing the intensity of the reference wave relative to the scattered field from the object of interest. This can be done by introducing an attenuation filter that selectively attenuates the reference field~\cite{pham_digital_2012, goto_three-dimensional_2015} or by using the reflection from a coverglass as the reference~\cite{jacobsen_interferometric_2006, ortega-arroyo_interferometric_2012, piliarik_direct_2014, kukura_high-speed_2009, goldfain_dynamic_2016}. In some cases it also may be possible to increase the scattering signal of small objects by attaching dyes to the object whose resonant effect with incident light yields a signal out of proportion to their size. My colleague Aaron Goldfain is working on these approaches.

Holography works without any labeling of samples, giving contrast to refractive index differences similar to differential interference contrast. This is an advantage of holography over other three-dimensional imaging techniques like confocal microscopy that require labels. However, it is also a disadvantage because selective labeling of structures of interest is an extremely powerful tool for many investigations. Nonetheless, it may be possible to use labels in a two-color holographic instrument and see refractive or absorptive effects from attached dyes. If the dyes and wavelengths of incident light overlap, a dye should have a strong signal in only one channel~\cite{nadeau_use_2015}.

Holography also is difficult to use on optically thick samples where very large amounts of light are scattered. Switching to an off axis-geometry may help, though at the cost of increased resolution requirements. For scenes without too much multiple scattering it might still be possible to model and infer parameters, but that will require efficient parameterizations, efficient scattering models, significant advances in available computing power, and probably new, more efficient inference techniques.

In spite of these limitations, holography has the potential to become an increasingly useful imaging and measurement tool. It is already useful for many problems, particularly tracking three-dimensional dynamics at high speed. Additionally, because holography uses simple hardware and moves most of image formation and measurement into post-processing in software, it can easily benefit from advances in computing, and new techniques and improvements can be readily adopted.
