Theory and Computation of Mask-Aided Phase Retrieval

X射线晶体学是确定DNA和蛋白质等分子结构的黄金标准。 然而，大分子晶体生长的困难已成为晶体学研究的主要瓶颈。 另一种称为X射线相干衍射成像（CDI）的技术有可能确定单个大分子的非晶体结构。 CDI的一个重要组成部分是解决称为非晶体结构相位恢复的数学问题，以恢复被光子探测过程破坏的相位信息。 研究者研究随机掩码方法作为恢复该信息的一种方式。 由于光信号传播一定距离后的检测和重建是光通信和信息处理中的基本程序，因此有效和高效的非晶体结构相位恢复不仅可以影响CDI的发展，还可以影响2012年报告“光学和光子学：我们国家的基本技术”中提出的一些国家研究理事会重大挑战问题的进展。“研究生在这个项目的过程中接受培训。 本计画的重点是发展随机遮罩法的数学基础与数值模式，以提升目前CDI的效能。 RMM是一种定量编码孔径成像技术，它在光子探测中采用随机掩模，并在重建中利用掩模效应。 研究人员和他的同事们研究了RMM在以下方面的显著性能提升潜力：准确重建，高效计算，提高数据质量，减少对数据和先验知识的需求，所有这些对CDI的最终影响都至关重要。

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.