高分辨率、大视场无标记成像：基于像差校正的闭式复场重建
High-resolution, large field-of-view label-free imaging via aberration-corrected, closed-form complex field reconstruction
AI总结：
提出闭式复场重建方法APIC，融合FPM和Kramers-Kronig优势，实现高分辨率大视场无标记成像，无需迭代即可校正像差，速度提升2.8倍，鲁棒性优于FPM。
摘要：
计算成像方法赋予现代显微镜高分辨率、大视场、无像差成像的能力。其中一种主流的计算无标记成像方法，傅里叶叠层显微术（FPM），通过使用多个倾斜照明来有效提高传统显微镜的空间带宽积，实现高通量成像。然而，其迭代重建方法容易受参数选择影响，计算成本高，且在过度像差下往往失败。近年来，空间Kramers-Kronig方法表明可以解析重建复场，但缺乏校正像差或提供扩展分辨率增强的能力。在此，我们提出一种闭式方法，称为APIC，它融合了这两种方法的优势。APIC建立了一个新的解析相位检索框架，首次证明了与暗场测量相关的复场解析重建的可行性。此外，APIC无需额外硬件即可解析检索成像系统的复像差。通过避免迭代算法，APIC无需人为设计的收敛度量，且总能获得闭式复场解。由于其解析性质，APIC重建的保真度和正确性得到保证。我们通过实验证明，在相同测量次数下，当FPM失败时，APIC能给出正确的重建结果。同时，使用256（长度方向）的图像块尺寸，APIC的计算速度提高了2.8倍。我们还证明，与FPM相比，APIC对像差具有前所未有的鲁棒性——在实验中使用NA 0.25物镜时，APIC能够处理最大相位差超过3.8π的像差。
英文摘要：
Computational imaging methods empower modern microscopy with the ability of producing high-resolution, large field-of-view, aberration-free images. One of the dominant computational label-free imaging methods, Fourier ptychographic microscopy (FPM), effectively increases the spatial-bandwidth product of conventional microscopy by using multiple tilted illuminations to achieve high-throughput imaging. However, its iterative reconstruction method is prone to parameter selection, can be computationally expensive and tends to fail under excessive aberrations. Recently, spatial Kramers-Kronig methods show it is possible to analytically reconstruct complex field but lacks the ability of correcting aberrations or providing extended resolution enhancement. Here, we present a closed-form method, termed APIC, which weds the strengths of both methods. A new analytical phase retrieval framework is established in APIC, which demonstrates, for the first time, the feasibility of analytically reconstructing the complex field associated with darkfield measurements. In addition, APIC can analytically retrieve complex aberrations of an imaging system with no additional hardware. By avoiding iterative algorithms, APIC requires no human designed convergence metric and always obtains a closed-form complex field solution. The faithfulness and correctness of APIC's reconstruction are guaranteed due to its analytical nature. We experimentally demonstrate that APIC gives correct reconstruction result while FPM fails to do so when constrained to the same number of measurements. Meanwhile, APIC achieves 2.8 times faster computation using image tile size of 256 (length-wise). We also demonstrate APIC is unprecedentedly robust against aberrations compared to FPM - APIC is capable of addressing aberration whose maximal phase difference exceeds 3.8$π$ when using a NA 0.25 objective in experiment.
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