Huang Guoqiang, Wu Daixuan, Luo Jiawei, Huang Yin, Shen Yuecheng
Opt Express. 2020 Mar 30;28(7):9487-9500. doi: 10.1364/OE.389133.
Characterizing the transmission matrix (TM) of a multimode fiber (MMF) benefits many fiber-based applications and allows in-depth studies on the physical properties. For example, by modulating the incident field, the knowledge of the TM allows one to synthesize any optical field at the distill end of the MMF. However, the extraction of optical fields usually requires holographic measurements with interferometry, which complicates the system design and introduces additional noise. In this work, we developed an efficient method to retrieve the TM of the MMF in a referenceless optical system. With pure intensity measurements, this method uses the extended Kalman filter (EKF) to recursively search for the optimum solution. To facilitate the computational process, a modified speckle-correlation scatter matrix (MSSM) is constructed as a low-fidelity initial estimation. This method, termed EKF-MSSM, only requires 4N intensity measurements to precisely solve for N unknown complex variables in the TM. Experimentally, we successfully retrieved the TM of the MMF with high precision, which allows optical focusing with the enhancement (>70%) close to the theoretical value. We anticipate that this method will serve as a useful tool for studying physical properties of the MMFs and potentially open new possibilities in a variety of applications in fiber optics.
表征多模光纤（MMF）的传输矩阵（TM）有利于许多基于光纤的应用，并能对物理特性进行深入研究。例如，通过调制入射场，传输矩阵的知识使人们能够在多模光纤的输出端合成任何光场。然而，光场的提取通常需要使用干涉测量的全息测量方法，这使系统设计变得复杂并引入了额外的噪声。在这项工作中，我们开发了一种在无参考光学系统中检索多模光纤传输矩阵的有效方法。通过纯强度测量，该方法使用扩展卡尔曼滤波器（EKF）递归地搜索最优解。为了简化计算过程，构建了一个改进的散斑相关散射矩阵（MSSM）作为低保真度的初始估计。这种被称为EKF-MSSM的方法仅需要4N次强度测量就能精确求解传输矩阵中的N个未知复变量。在实验中，我们成功地高精度检索了多模光纤的传输矩阵，这使得光聚焦增强（>70%）接近理论值。我们预计这种方法将成为研究多模光纤物理特性的有用工具，并可能在光纤光学的各种应用中开辟新的可能性。
