Recent development in wavefront shaping shows the promise to employ multimode fibers (MMFs) to deliver images in endoscopy. In these applications, retrieving the transmission matrix (TM) of the MMF is especially important. Among existing non-holographic approaches, feedback-based wavefront shaping requires a large number of measurements, while directly measuring the TM can be easily trapped into local optimums if the constraints are insufficient. To reduce the required number of measurements, we combine the concepts of these two approaches and develop a scheme termed feedback-assisted TM measurements. We show that under such a hybrid scheme, less than ${{3}}N$ intensity measurements are sufficient to accurately retrieve one row of the TM that contains $N$ unknown complex elements. As a proof of concept, we experimentally demonstrated retrieving multiple rows of the TM of an MMF using the proposed scheme with high fidelity. In particular, a single focus and dual foci through the MMF with enhancements larger than 75% of the theoretical values were reported.

中文翻译：

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无参考系统中多模光纤的反馈辅助传输矩阵测量

波前整形的最新发展表明，有望在内窥镜检查中采用多模光纤 (MMF) 传输图像。在这些应用中，检索 MMF 的传输矩阵 (TM) 尤为重要。在现有的非全息方法中，基于反馈的波前整形需要大量的测量，而如果约束不足，直接测量 TM 很容易陷入局部最优。为了减少所需的测量次数，我们结合了这两种方法的概念并开发了一种称为反馈辅助 TM 测量的方案。我们表明，在这种混合方案下，小于${{3}}N$ 的强度测量足以准确地检索包含$N$ 的一行 TM未知的复杂元素。作为概念证明，我们通过实验证明了使用所提出的高保真方案检索 MMF 的多行 TM。特别是，报告了通过 MMF 的单焦点和双焦点增强大于理论值的 75%。