In the coherent diffraction imaging (CDI) techniques, a key point is to reconstruct the complex-valued object from the far-field intensity measurements, i.e., solving the phase retrieval problem. However, due to this ill-posed problem, traditional phase retrieval algorithms often encounter some problems associated with the iteration convergence. In this work, complementary phase modulations (CPM) are introduced to generate different far-field intensity measurements. The namely CPM-based method aims to find out the global optimal solution by imposing multi-dimensional constraints, including the diverse intensity images at the Fourier plane and the CPM at the object plane. It is proved by the numerical simulations and the optical experiments that the convergence speed and the recovery accuracy could be greatly improved. Furthermore, the shifting complementary phase modulations (SCPM)-based method is proposed by introducing more CPMs. The reconstruction performance is further improved even when the phase range is larger, and the support constraints are not required. In addition, the SCPM-based method is more robust to the Poisson noise. With the outstanding reconstruction performance, the CPM-based methods may be helpful to phase imaging in the application of visible-light microscopy and X-ray imaging.

在相干衍射成像（CDI）技术中，一个关键点是从远场强度测量中重建复值对象，即解决相位反演问题。然而，由于这种不适定问题，传统的相位检索算法经常会遇到一些与迭代收敛相关的问题。在这项工作中，引入了互补相位调制 (CPM) 以生成不同的远场强度测量值。即基于CPM的方法旨在通过施加多维约束来找出全局最优解，包括傅立叶平面上的不同强度图像和物平面上的CPM。数值模拟和光学实验证明，收敛速度和恢复精度可以大大提高。此外，通过引入更多的 CPM，提出了基于移位互补相位调制 (SCPM) 的方法。即使相位范围更大，重建性能也得到进一步提高，并且不需要支撑约束。此外，基于 SCPM 的方法对泊松噪声的鲁棒性更强。凭借出色的重建性能，基于 CPM 的方法可能有助于可见光显微镜和 X 射线成像应用中的相位成像。