复杂介质反射矩阵中单次散射和递归散射的权重
Weight of single and recurrent scattering in the reflection matrix of complex media
摘要：
在非均匀介质中，波场可以分解为称为玻恩展开的无穷级数。玻恩展开式的每一项对应于一个散射级，因此理论上可以区分单个和多个散射场分量。实验上，实际测量的是所有散射级干涉的总场。传统的成像方法通常依赖于可以忽略多次散射贡献的假设。在后向散射配置中，该假设对于小深度有效，并且对于大于散射平均自由程$\ell_s$的深度开始失效。因此，在实验数据中估计单次和多次散射的相对量是一个关键问题。为此，一个单一的散射估计器$\hatρ$计算的反射矩阵已被引入，以评估的重量，在后向散射波场中的单一散射。在这篇文章中，这个估计的意义进行了调查，并特别注意经常性散射。在衍射极限实验中，如果第一个和最后一个散射事件发生在相同的分辨率单元中，则多次散射序列被称为是递归的。经常性散射被证明是负责单次散射和更高的散射阶数的玻恩展开之间的相关性，引起的偏见估计$\hatρ$，而应该被称为共焦散射比。有趣的是，一个更强大的估计是建立在一个集中的基础上投影的反射矩阵。该论点是支持的数值模拟，以及超声数据获得约1.5 MHz的模型介质中的尼龙棒浸在水中。从更一般的角度来看，这项工作提出了有关经常性散射对波成像的影响的基本问题。
英文摘要：
In a heterogeneous medium, the wavefield can be decomposed as an infinite series known as the Born expansion. Each term of the Born expansion corresponds to a scattering order, it is thus theoretically possible to discriminate single and multiple scattering field components. Experimentally, what is actually measured is the total field in which all scattering orders interfere. Conventional imaging methods usually rely on the assumption that the multiple scattering contribution can be disregarded. In a back-scattering configuration, this assumption is valid for small depths, and begins to fail for depths larger than the scattering mean-free path $\ell_s$. It is therefore a key issue to estimate the relative amount of single and multiple scattering in experimental data. To this end, a single scattering estimator $\hatρ$ computed from the reflection matrix has been introduced in order to assess the weight of single scattering in the backscattered wavefield. In this article, the meaning of this estimator is investigated and a particular attention is given to recurrent scattering. In a diffraction-limited experiment, a multiple scattering sequence is said to be recurrent if the first and last scattering events occur in the same resolution cell. Recurrent scattering is shown to be responsible for correlations between single scattering and higher scattering orders of the Born expansion, inducing a bias to the estimator $\hatρ$ that should rather be termed confocal scattering ratio. Interestingly, a more robust estimator is built by projecting the reflection matrix in a focused basis. The argument is sustained by numerical simulations as well as ultrasonic data obtained around 1.5~MHz in a model medium made of nylon rods immersed in water. From a more general perspective, this work raises fundamental questions about the impact of recurrent scattering on wave imaging.
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