中文摘要：

与阻抗边界由障碍 D C 72 考虑一个反的散布问题。我们用点来源方法从它的远地模式 u【sup】∞【/sup】 调查散布的地 u【sup】s【/sup】 的重建。由使用边界积分方程方法，首先，我们由古典潜在的理论提供一条新途径给 Potthast 的点来源方法。这从任意的波浪散布的飞机波浪扩大点来源方法的范围。由分析 Hankel 功能的行为，第二，我们为从哪个改进了集中率的调整 paraaneter 的选择获得改进策略(与结果相比[15 ]) 为散布波浪的重建被完成。第三，数字实现被给为阻抗障碍测试倒置方法的有效性和稳定性。数学题目分类：35L， 35R。

英文摘要：

Consider an inverse scattering problem by an obstacle D belong to R^2 with impedance boundary. We investigate the reconstruction of the scattered field u^s from its far field pattern u^∞ using the point source method. First, by applying the boundary integral equation method, we provide a new approach to the point-source method of Potthast by classical potential theory. This extends the range of the point source method from plane waves to scattering of arbitrary waves. Second, by analyzing the behavior of the Hankel function, we obtain an improved strategy for the choice of the regularizing parameter from which an improved convergence rate （compared to the result of [15]） is achieved for the reconstruc- tion of the scattered wave. Third, numerical implementations are given to test the validity and stability of the inversion method for the impedance obstacle.