The dominant paradigm of holography is best expressed through communication theoretic concepts. Ultimately, this is permitted by placing the information of interest on a spatial carrier wave. The information recorded in a 2D plane relates to a wave emanating from a 3D scattering structure. This fact has tied holography to inverse problems at frequencies for which phase information is tough to record otherwise. Emil Wolf was the first to suggest using holography to solve inverse scattering problems and Hank Carter confirmed the usefulness of his analysis. The inverse problem and its relation to holography has been largely neglected for the past three decades. This is true for both quantitative imaging of scattering obstacles and for the synthesis of scattering structures. We argue here that there are strong reasons present now, that were not present 30 years ago, to reinvigorate this connection to inverse problems. We must extend it well beyond the weak scattering case that Wolf was able to solve analytically. Strong scattering problems will always be ill-posed, meaning that solutions may not exist, or may be ambiguous or highly unstable, so exact solutions are precluded. However, good solutions can be obtained in situations where an optical readout appears to give poor results.
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