The two-dimensional inverse scattering problem

It is demonstrated that the knowledge of the incident field and the scattered far fields at one frequency may be employed to determine the size, shape, and location of a perfectly conducting scatterer. The reconstruction of the scattering body is accomplished via an analytic continuation procedure that generates the fields in the neighborhood of the scatter from the specified far-field distribution. The geometry of the body is then determined by locating a closed surface for which the total tangential electric field, i.e., the sum of the tangential components of the incident and scattered field, is zero. Whereas exact knowledge of the entire far field is sufficient to determine the scatterer, a technique is also given for size and shape determination when only part of the far field is available. Numerical examples of several different geometries are given for ranges of ka (a the largest dimension of the body) from 0.2 to 10. Geometries considered were elliptic and circular cylinders, conducting strips, and two cylinders. Plots of the fields reconstructed from the far-field data are compared to the known solutions, and the accuracy of the procedure is demonstrated. The effects of noise in the far-field pattern is also considered, and it is shown that even with noise levels of -20 dB the scattering geometry can be recovered.