Theory and Computation of Mask-Aided Phase Retrieval

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X-ray crystallography is the gold standard for determining molecular structures such as DNAs and proteins. However, the trouble of growing crystals for macromolecules has become the main bottleneck in crystallography. An alternative technology called X-ray coherent diffraction imaging (CDI) has the potential of determining noncrystalline structures of single macromolecules. An essential part of CDI is to solve the mathematical problem called phase retrieval for noncrystalline structures, in order to recover the phase information destroyed by the photon detection process. The investigator studies the random mask method as a way to recover this information. Because detection and reconstruction of an optical signal after it has propagated some distance is a basic procedure in optical communication and information processing, effective and efficient phase retrieval for noncrystalline structures can affect not only the development of CDI but also progress on some of the National Research Council Grand Challenge Questions raised in the 2012 report "Optics and Photonics: Essential Technologies for Our Nation." Graduate students are trained in the course of this project. This project focuses on developing the mathematical foundation and numerical schemes for the random mask method (RMM) to enhance the performance of current CDI. RMM is a quantitative coded-aperture imaging technique that employs a random mask in photon detection and exploits the mask effect in reconstruction. The investigator and his colleagues study RMM's potential for significant performance gains in the following aspects: accurate reconstruction, efficient computation, improved data quality, and reduction of demand for data and prior knowledge, all of central importance to the ultimate impact of CDI.