Second-order iterative approach to inverse scattering: numerical results

We introduce an iterative algorithm for the reconstruction of dielectric pr ofile functions from scattered field data, in which each step corresponds t o the solution of a quadratic inversion problem. This means that, at each i teration, we perform a second-order approximation of the scattering operato r connecting the unknown profile to the data about a reference profile func tion. This procedure is then compared with a linear iterative inversion alg orithm, and it is pointed out that, within a prescribed class of profile fu nctions, the linear iterative inversion does not converge to the actual sol ution, whereas the proposed approach does. This feature can be explained by reference not only to the improved approximation provided by the addition of a further term for profile functions of a larger norm but also to the di fferent classes of functions that can be reconstructed by either the linear or the quadratic model. Numerical examples of profile reconstruction in th e scaler two-dimensional geometry, with far-zone scattered field data at a fixed frequency, confirm the theoretical analysis. (C) 2000 Optical Society of America [S0740-3232(00)00505-6].