Two-dimensional imaging of three-dimensional scatterer by using Linear Sampling Method

We consider the electromagnetic inverse scattering problem of determining the shape of scatterer, from a knowledge of incident plane waves and the far-field patterns of scattered fields. The method used is Linear Sampling Method. This method avoids non-linearity and handles severe ill-posedness with regularization incorporated. Discussed in this paper is to demonstrate the validity of reconstructing projections of three-dimensional scatterer by two-dimensional Linear Sampling Method, rather than by three-dimensional one. Numerical experiments indicate that the former obtains the same results as the latter does. Improvements are fewer points sampled, fewer far-field patterns required, and less computational time consumed. These characteristics partly depend on frequency to some extent. Frequency dependence is shown by numerical examples.