Ptychography is an imaging technique which involves a sample being illuminated by a coherent, localized probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the sample (or probe) is shifted laterally in space to illuminate a new area of the sample whilst ensuring sufficient overlap. Near-field Ptychography (NFP) occurs when the sample is placed at a short defocus distance having a large Fresnel number. In this paper, we prove that certain NFP measurements are robustly invertible (up to an unavoidable global phase ambiguity) by constructing a point spread function and physical mask which leads to a well-conditioned lifted linear system. We then apply a block phase retrieval algorithm using weighted angular synchronization and prove that the proposed approach accurately recovers the measured sample. Finally, we also propose using a Wirtinger Flow for NFP problems and numerically evaluate that alternate approach both against our main proposed approach, as well as with NFP measurements for which our main approach does not apply.

翻译：叠层成像是一种成像技术，它涉及使用相干的、局部化的照明探针照射样品。当探针与样品相互作用时，光发生衍射，并检测到一个衍射图样。然后，样品（或探针）在空间中进行横向移动，以照射样品的新区域，同时确保足够的重叠。近场叠层成像（NFP）发生在样品放置于短离焦距离且具有大菲涅耳数的情况下。在本文中，我们通过构建一个点扩展函数和物理掩模，从而导出一个条件良好的提升线性系统，证明某些NFP测量结果（在不可避免的全局相位模糊度范围内）是稳健可逆的。然后，我们应用一种使用加权角度同步的块相位恢复算法，并证明所提出的方法能准确恢复被测样品。最后，我们还提出针对NFP问题使用Wirtinger流，并通过数值方法将该替代方法既与我们的主要方法进行比较，也与我们的主要方法不适用的NFP测量结果进行比较。