宽场照明随机介质中动态后向散射相干波的随机矩阵描述
Random matrix description of dynamically backscattered coherent waves propagating in a wide-field-illuminated random medium
摘要：
波在随机介质中的传播在光学和量子物理中起着重要的作用。相干波在随机介质中的多次散射决定了其输运过程。散射体的布朗运动扰动每个传播轨迹并在后向散射方向上形成动态散斑图案。在这项研究中，我们应用随机矩阵理论（RMT）的后向散射强度矩阵的本征值密度的调查。我们发现，动态散斑图可以用来解耦单次和多次后向散射分量。多次散射分量的Wishart随机矩阵符合Marcenko-Pastur定律，而单次散射分量具有低秩特性。因此，我们提出了一种策略，用于估计一阶和二阶矩的单次和多次散射组件，分别基于Marcenko-Pastur定律和跟踪分析。电场蒙特卡罗模拟和在体实验表明，该方法在隐藏吸收目标检测和在体血流成像中具有潜在的应用价值。该方法也适用于微波、超声等宽场传播的相干域弹性散射现象。
英文摘要：
The wave propagation in random medium plays a critical role in optics and quantum physics. Multiple scattering of coherent wave in a random medium determines the transport procedure. Brownian motions of the scatterers perturb each propagation trajectory and form dynamic speckle patterns in the backscattered direction. In this study, we applied the random matrix theory (RMT) to investigate the eigenvalue density of the backscattered intensity matrix. We find that the dynamic speckle patterns can be utilized to decouple the singly and multiply backscattered components. The Wishart random matrix of multiple scattering component is well described by the Marcenko-Pastur law, while the single scattering part has low-rank characteristic. We therefore propose a strategy for estimating the first and the second order moments of single and multiple scattering components, respectively, based on the Marcenko-Pastur law and trace analysis. Electric field Monte Carlo simulation and in-vivo experiments demonstrate its potential applications in hidden absorbing object detection and in-vivo blood flow imaging. Our method can be applied to other coherent domain elastic scattering phenomenon for wide-filed propagation of microwave, ultrasound and etc.
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