Implicit and Explicit Codes For Diffraction Tomography

Diffraction tomography is the attempt to estimate the scattering density of an object from measurements of a scattered coherent field. This work moves to overcome many of the constraints and limitations of the current state of the art. In general, these constraints present themselves as physical and cost limitations. The limitations ``encode" the data, giving rise to the title of this dissertation. Implicit coding is the encoding of the data by the acquisition system. For instance, coherent scatter is bound to be sampled on specific arcs in the Fourier space of the scattering density. Explicit coding is the choice of how the data is sampled within the implicit coding limitations. The beam patterns of an antenna may be optimized to better detect certain types of targets, or datasets may be subsampled if prior knowledge of the scene is introduced in some way.

We investigate both of these types of data coding, introduce a method for sampling a particular type of scene with high efficiency, and present strategies for overcoming a specific type of implicit data encoding which is detrimental to ``pure" image estimation known as speckle. The final chapter of this dissertation incorporates both implicit and explicit coding strategies, to demonstrate the importance of taking both into account for a new paradigm in diffraction tomography known as frequency diversity imaging. Frequency diversity imaging explicitly encodes coherent fields on the illumination wavelength. Combining this paradigm with speckle estimation requires a new way to evaluate the quality of explicit codes.