基于分解法的Neumann 边界条件反散射问题

The factorization method for the inverse scattering problem with Neumann boundary conditions

利用分解法研究Neumann边界条件下障碍物反散射问题和腔体反散射问题.该方法利用近场测量数据可以同时处理障碍物反散射问题和腔体反散射问题,而不需要对测量面和散射体之间的距离做任何渐近假设.首先给出两个反散射问题的数学模型,以及利用双层势能算子的跳跃关系和格林公式给出双层势能算子的相关估计结果.其次通过定义算子分别研究障碍物和腔体近场算子的分解情况.最后构造障碍物和腔体在Neumann边界条件下的成像函数.

The inverse scattering problem for obstacles and cavities with Neumann boundary conditions is studied by using the factorization method.The data from near-field measurements is used to deal with both inverse scattering for obstacles and cavities without making any asymptotic assumption about the distance between the measured surface and the scatterers.Firstly,mathematical model for the inverse scattering problem is given,and the results of the estimation of the double-layer operator are given by using the jump relation of the double-layer potential and Green's formula.Secondly,the decomposition of the near-field operators of obstacles and cavities is studied separately.Finally,the imaging function of obstacles and cavities under Neumann boundary conditions is constructed.