Marengo Edwin A, Galagarza Edson S, Solimene Raffaele
J Opt Soc Am A Opt Image Sci Vis. 2017 Sep 1;34(9):1561-1576. doi: 10.1364/JOSAA.34.001561.
Direct or forward wave scattering admits three classical regimes in which the map from scatterer properties or scattering potential to the data is linear, namely, the Born, Rytov, and physical optics approximations. In this paper we derive a new decomposition of the forward scattering map which reveals a previously unknown approximate bilinear forward scattering relation. The latter is data-driven, i.e., it involves exact scattering data, and has the useful property that the dependence on the data and the potential is bilinear. This fundamental result naturally leads to a new linear inverse scattering approach that generalizes and is more broadly applicable than the classical Born-approximation-based imaging. The developed scattering and inverse scattering theory are presented in both plane wave and multipole expansion representations, and the possibility of exploiting support information is also formally addressed in the multipole domain. The paper includes computer simulations illustrating the derived theory and algorithms.
直接或正向波散射存在三种经典情况，其中从散射体特性或散射势到数据的映射是线性的，即玻恩近似、里托夫近似和物理光学近似。在本文中，我们推导了正向散射映射的一种新分解，它揭示了一种此前未知的近似双线性正向散射关系。后者是数据驱动的，即它涉及精确的散射数据，并且具有对数据和势的依赖是双线性的有用特性。这一基本结果自然地引出了一种新的线性逆散射方法，该方法比基于经典玻恩近似的成像更具一般性且适用范围更广。所发展的散射和逆散射理论以平面波和多极展开表示形式呈现，并且在多极域中也正式探讨了利用支撑信息的可能性。本文包含了说明所推导理论和算法的计算机模拟。
