Theory and Computation of Mask-Aided Phase Retrieval

x射线晶体学是测定分子结构（如dna和蛋白质）的金标准。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）的技术具有确定单个大分子非晶体结构的潜力。为了恢复被光子探测过程破坏的相位信息，CDI的一个重要组成部分是解决非晶体结构的相位恢复数学问题。研究者研究随机掩码法作为一种方法来恢复这些信息。由于光信号传播一段距离后的检测和重建是光通信和信息处理的基本程序，因此对非晶体结构进行有效和高效的相位恢复不仅会影响CDI的发展，还会影响美国国家研究委员会2012年报告“光学和光子学：我们国家的基本技术”中提出的一些重大挑战问题的进展。研究生在这个项目的过程中得到训练。本课题的重点是发展随机掩码法（RMM）的数学基础和数值方案，以提高当前CDI的性能。RMM是一种定量编码孔径成像技术，在光子检测中采用随机掩模，在重建中利用掩模效应。研究者和他的同事们研究了RMM在以下方面显著提高性能的潜力：准确的重建、高效的计算、改进的数据质量、减少对数据和先验知识的需求，所有这些都对CDI的最终影响至关重要。

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.