基于加速Wirtinger流的纳米级三维相恢复
3D Phase Retrieval at Nano-Scale via Accelerated Wirtinger Flow
摘要：
以非常高的分辨率对3D纳米结构进行成像在各种科学领域中至关重要。然而，由于光传播的基本限制，我们只能通过高度非线性的投影映射，其中各种信息（包括相位）丢失，通过3D样本的2D强度测量间接测量对象。因此，重建涉及反转高度非线性和看似不可逆的映射。在本文中，我们介绍了一种新的技术，直接从一个准确的非线性传播模型重建的3D对象。此外，我们描述了该模型的模糊性，并利用先验知识来减轻其影响，并显着减少所需的测量次数，从而减少采集时间。我们证明了我们的算法的性能，通过数值实验，旨在纳米级的三维集成电路重建。此外，我们提供了严格的理论保证收敛平稳。
英文摘要：
Imaging 3D nano-structures at very high resolution is crucial in a variety of scientific fields. However, due to fundamental limitations of light propagation we can only measure the object indirectly via 2D intensity measurements of the 3D specimen through highly nonlinear projection mappings where a variety of information (including phase) is lost. Reconstruction therefore involves inverting highly non-linear and seemingly non-invertible mappings. In this paper, we introduce a novel technique where the 3D object is directly reconstructed from an accurate non-linear propagation model. Furthermore, we characterize the ambiguities of this model and leverage a priori knowledge to mitigate their effect and also significantly reduce the required number of measurements and hence the acquisition time. We demonstrate the performance of our algorithm via numerical experiments aimed at nano-scale reconstruction of 3D integrated circuits. Moreover, we provide rigorous theoretical guarantees for convergence to stationarity.
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