On the Two-dimensional Inverse Scattering Problems in Electromagnetics

In recent years, inverse scattering problems have received much attention because of their important applications. Given the incident and scattered waves, an inverse scattering problem in general is to determine the properties of the scatterer. In radar or sonar a known incident wave and observed scattered wave are used to detect the properties and the presence of aircraft or submarine objects; in MRI scanning, tomography X-rays and ultrasound, scattered waves are used to determine the presence or properties of tumors by detecting density variations, to name a few. In this article, we are concerned with the two-dimensional electromagnetic inverse scattering problem. An iterative algorithm for the transversal electric waves will be given based on a singular domain integral equation formulation. Basic features of a scattering object such as shape, location and index of refraction will be recovered from measurements of the field scattered by the object (when illuminated by electromagnetic waves with the magnetic vector polarized along the cylinder axis). Some numerical experiments are included to illustrate the efficiency of the algorithm.

Keywords:

• Maxwell Equations
• Te- And Tm-polarizations
• Inverse Scattering Problems
• Singular Integral Equations
• 1991 Mathematics Subject Classifications: Primary 81u40
• Secondary 45f15
• 35j05