Field reconstructions and range tests for acoustics and electromagnetics in homogeneous and layered media

In acoustic and electromagnetic scattering various methods for the reconstruction of the shape of an unknown object are examined. In particular, the multiwave range test is developed based upon the range test in the acoustic case. This method reconstructs the shape of the object from the data of many incident plane waves without the need of knowing the boundary condition of the unknown object. Strong connections between this method and other methods from shape reconstruction are presented. With this method an alternative approach to the singular sources method is developed. Further, the range test, based upon one incident plane wave, is carried over to the 3D electromagnetic case. For all methods under consideration numerical examples for the acoustic case (2D) and the electromagnetic case (3D) are presented.We participated in the BMBF-funded project for the improvement of existing handheld mine detectors. Here, a full reconstructions of the metal parts of mines, under small modifications of the metal detector, is tried. This has the aim of significantly reduce the false alarm rate. During this research a program were developed and implemented, which simulates the setting in two-layered media using integral equations in a fast and efficient way. Also it provides two different methods of reconstructing the shape of the object. The Greens tensor for two-layered media were constructed via an new approach and adapted to the situation at hand.