A non-iterative and non-interferometric computational imaging method to reconstruct a complex wave field called synthetic aperture imaging based on Kramers–Kronig relations (KKSAI) is reported. By collecting images through a modified microscope system with pupil modulation capability, we show that the phase and amplitude profile of the sample at pupil limited resolution can be extracted from as few as two intensity images by using Kramers–Kronig (KK) relations. It is established that as long as each subaperture’s edge crosses the pupil center, the collected raw images are mathematically analogous to off-axis holograms. This in turn allows us to adapt a recently reported KK-relations-based phase recovery framework in off-axis holography for use in KKSAI. KKSAI is non-iterative, free of parameter tuning, and applicable to a wider range of samples. Simulation and experiment results have proved that it has much lower computational burden and achieves the best reconstruction quality when compared with two existing phase imaging methods.

中文翻译：

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基于Kramers-Kronig关系的非迭代复波场重构

报道了一种基于 Kramers-Kronig 关系 (KKSAI) 重建复杂波场的非迭代和非干涉计算成像方法，称为合成孔径成像。通过具有瞳孔调制功能的改进显微镜系统收集图像，我们表明可以使用 Kramers-Kronig (KK) 关系从少至两个强度图像中提取瞳孔受限分辨率下样本的相位和幅度轮廓。确定只要每个子孔径的边缘穿过瞳孔中心，收集的原始图像在数学上类似于离轴全息图。这反过来又使我们能够在离轴全息术中采用最近报道的基于 KK 关系的相位恢复框架，以用于 KKSAI。KKSAI 是非迭代的，无需参数调整，适用于更广泛的样本。