非凸优化用于多模光纤传输矩阵的最优恢复
Nonconvex optimization for optimum retrieval of the transmission matrix of a multimode fiber
AI总结：
本文提出一种改进的非凸优化方法，用于从强度测量中高效恢复多模光纤的传输矩阵，数值和实验验证表明其在聚焦效率、鲁棒性和速度上优于现有相位恢复算法，并支持高保真图像传输。
摘要：
传输矩阵（TM）使得光能够通过多模光纤（MMFs）等复杂介质进行控制，在过去十年中于生物光子学等领域引起了极大关注。复数传输矩阵的测量备受期待，因为它支持光场的完全调制，然而由于通常需要全息装置，其测量要求很高。已有研究尝试直接通过强度测量恢复传输矩阵，使用了若干具有代表性的相位恢复算法，但这些算法仍存在恢复速度慢或次优的问题，尤其是在噪声环境下。本文提出了一种改进的非凸优化方法。通过数值评估表明，非凸方法在更少的运行时间或采样率下提供了最优的聚焦效率。在不同信噪比下的对比测试进一步表明，该方法在传输矩阵恢复方面具有更好的鲁棒性。实验上，多组单点和多点聚焦演示共同验证了多模光纤传输矩阵的最优恢复。还在多模光纤的工作平面上进行了聚焦扫描，在采样率为8时，我们的方法达到了金标准全息方法的93.6%的效率。基于恢复的传输矩阵，通过另一次相位恢复可以实现高保真度的多模光纤图像传输。得益于并行操作和GPU加速，非凸方法可以在普通计算机上以42.3秒恢复一个8685×1024的传输矩阵（采样率=8）。总之，所提出的方法为传输矩阵恢复提供了最优效率和快速实现，这将促进其在深组织光学成像、操控和治疗中的广泛应用。
英文摘要：
Transmission matrix (TM) allows light control through complex media such as multimode fibers (MMFs), gaining great attention in areas like biophotonics over the past decade. The measurement of a complex-valued TM is highly desired as it supports full modulation of the light field, yet demanding as the holographic setup is usually entailed. Efforts have been taken to retrieve a TM directly from intensity measurements with several representative phase retrieval algorithms, which still see limitations like slow or suboptimum recovery, especially under noisy environment. Here, a modified non-convex optimization approach is proposed. Through numerical evaluations, it shows that the nonconvex method offers an optimum efficiency of focusing with less running time or sampling rate. The comparative test under different signal-to-noise levels further indicates its improved robustness for TM retrieval. Experimentally, the optimum retrieval of the TM of a MMF is collectively validated by multiple groups of single-spot and multi-spot focusing demonstrations. Focus scanning on the working plane of the MMF is also conducted where our method achieves 93.6% efficiency of the gold standard holography method when the sampling rate is 8. Based on the recovered TM, image transmission through the MMF with high fidelity can be realized via another phase retrieval. Thanks to parallel operation and GPU acceleration, the nonconvex approach can retrieve an 8685$\times$1024 TM (sampling rate=8) with 42.3 s on a regular computer. In brief, the proposed method provides optimum efficiency and fast implementation for TM retrieval, which will facilitate wide applications in deep-tissue optical imaging, manipulation and treatment.
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