Brütt Cécile, Aubry Alexandre, Gérardin Benoît, Derode Arnaud, Prada Claire
Institut Langevin, ESPCI Paris, PSL University, Université Paris Cité, CNRS, 75005 Paris, France.
Safran Tech, Digital Sciences and Technologies Department, Rue des Jeunes Bois, Châteaufort, 78114 Magny-Les-Hameaux, France.
Phys Rev E. 2022 Aug;106(2-2):025001. doi: 10.1103/PhysRevE.106.025001.
In a heterogeneous medium, the wave field 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 contribution to the field. 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 ℓ_{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 ρ[over ̂] computed from the reflection matrix has been introduced in order to assess the weight of single scattering in the backscattered wave field. In this paper, 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 ρ[over ̂] 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.
在非均匀介质中，波场可以分解为一个无穷级数，即所谓的玻恩展开。玻恩展开的每一项都对应一个散射阶数，因此从理论上讲，可以区分单次散射和多次散射对场的贡献。在实验中，实际测量的是所有散射阶数相互干涉的总场。传统成像方法通常依赖于可以忽略多次散射贡献的假设。在背散射配置中，对于小深度，这个假设是有效的，但对于大于散射平均自由程ℓs的深度，这个假设开始失效。因此，估计实验数据中单次散射和多次散射的相对量是一个关键问题。为此，引入了一种从反射矩阵计算得到的单次散射估计量ρ̂，以评估背散射波场中单次散射的权重。在本文中，研究了这个估计量的意义，并特别关注了循环散射。在衍射极限实验中，如果第一次和最后一次散射事件发生在同一个分辨率单元中，则称多次散射序列是循环的。结果表明，循环散射是单次散射与玻恩展开中高阶散射阶数之间相关性的原因，这会给估计量ρ̂带来偏差，该估计量更确切地应称为共焦散射比。有趣的是，通过在聚焦基上投影反射矩阵构建了一个更稳健的估计量。数值模拟以及在浸入水中的尼龙棒制成的模型介质中1.5MHz左右获得的超声数据支持了这一观点。从更一般的角度来看，这项工作提出了关于循环散射对波成像影响的基本问题。
