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给出了双空间指示函数方法在三维柱面对称波导中电磁波的反散射问题的推广.基于这个观察:当Green函数的点源在障碍物内部时,那么远域数据的赋权积分可以很好地近似估计Green函数,但是当Green函数的点源在障碍物外部时,那么远域数据的赋权积分就不能很好地近似估计Green函数.建立一个积分方程:它的右边是点源在所重构区域的Green函数,那么我们可以知道这个积分方程的解的范数在未知障碍物的内部有极大值,而这些取得极大值的点所围成的区域恰好就是所重构的障碍物区域.方法最显著的优势在于它不依赖于未知障碍物的边界条件.
The generalization of the anti-scattering of electromagnetic waves in a three-dimensional cylindrical symmetric waveguide by the double spatial indication function method is given. Based on this observation, when the point source of the Green function is inside an obstacle, then the weighted integral of far-field data can be very strong However, when the point source of Green's function is outside the obstacle, then the weighted integral of the far-field data can not approximate Green's function well. To establish an integral equation: Then we can know that the norm of the solution of this integral equation has a maximum value inside the unknown obstacle and the area surrounded by the points with the maximum value is just the reconstructed area Obstacle area The most significant advantage of the method is that it does not depend on the boundary conditions of unknown obstacles.