相位恢复算法:原理、发展与应用（特邀）

研究表明，由于相位比振幅包含更多关于场的信息，因此相位测量在现代科学和工程的诸多分支中始终是研究的热点问题。在可见的电磁波范围内，相位信息很难通过现有的光电探测器直接采集获取。相位恢复技术提供了一种从捕获的强度信息中将相位信息“计算”出来的有效手段，并已成功应用于天文观测、生物医学成像和数字信号复原等多个科学领域。算法是相位恢复技术的核心，也是该技术发展和应用的关键。文中结合物理学原理和信号处理方法对相位恢复算法的基本原理进行阐述，综述了各类相位恢复算法的发展历程及其优缺点，并简单概述了相位恢复算法在光学领域的典型应用，最终指明其面临的挑战和未来的发展趋势:更优异的收敛性能和噪声鲁棒性、恢复更复杂物体相位信息的能力、多目标多任务集成的兼容性。

Phase retrieval algorithms: principles,developments and applications (invited)

Because the phase contains more information about the field in contrast to the amplitude, phase measurement has always been a hot topic in many branches of modern science and engineering. Within the visible range of electromagnetic wave, it is quite difficult to directly obtain phase information by the existing photodetectors. Phase retrieval provides an effective method to “figure out” the phase information from the captured intensity information, and has achieved successful applications in several scientific fields including astronomical observation, biomedical imaging and digital signal restoration. Algorithm is not only the core of phase retrieval, but is also the key to its development and applications. This paper demonstrates the basic principles of phase retrieval algorithms in combination with physical principles and signal processing methods, summarizes the development of various kinds of algorithms as well as their advantages and disadvantages, and briefly lists some typical applications in the field of optics. Finally, the challenges are pointed out, and the future development directions are described as: better convergence performance and noise robustness, phase-retrieval ability for more complex objects, compatibility for integration of multiple objectives and tasks.