When a narrowband coherent wavefront passes through or reflects off of a scattering medium, the input and output relationship of the incident field is linear and so can be described by a transmission matrix (TM). If the TM for a given scattering medium is known, one can computationally “invert” the scattering process and image through the medium. In this paper, we investigate the effect of broadband illumination, i.e., what happens when the wavefront is only partially coherent? Can one still measure a TM and “invert” the scattering? To accomplish this task, we measure TMs using the double-phase retrieval technique, a method that uses phase retrieval algorithms to avoid difficult-to-capture interferometric measurements. Generally, using the double-phase retrieval method requires performing massive amounts of computation. We alleviate this burden by developing a fast, GPU-accelerated algorithm, prVAMP, which lets us reconstruct $256^2\times 64^2$ TMs in under five hours. After reconstructing several TMs using this method, we find that, as expected, reducing the coherence of the illumination significantly restricts our ability to invert the scattering process. Moreover, we find that past a certain bandwidth, an incoherent, intensity-based scattering model better describes the scattering process and is easier to invert.

中文翻译：

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通过传输矩阵进行逆散射：宽带照明和快速相位检索算法

当窄带相干波前穿过散射介质或被散射介质反射时，入射场的输入和输出关系是线性的，因此可以用传输矩阵 (TM) 来描述。如果给定散射介质的 TM 已知，则可以通过计算“反转”散射过程并通过介质成像。在本文中，我们研究了宽带照明的影响，即当波前仅部分相干时会发生什么？仍然可以测量 TM 并“反转”散射吗？为了完成这项任务，我们使用双相位检索技术测量 TM，该方法使用相位检索算法来避免难以捕捉的干涉测量。通常，使用双阶段检索方法需要执行大量计算。我们通过开发一种快速的、GPU 加速的算法 prVAMP 来减轻这种负担，它使我们能够在五小时内重建 $256^2\times 64^2$ TM。使用这种方法重建几个 TM 后，我们发现，正如预期的那样，降低照明的相干性显着限制了我们反转散射过程的能力。此外，我们发现超过一定带宽后，非相干的、基于强度的散射模型更好地描述了散射过程并且更容易反演。