Inverse scattering using the heiyler equation

The reconstruction of the refractive index of a dielectric body from scattered field data is known as the inverse scattering problem. In the present work this problem is addressed within the Heitler equation method. This equation was originally used by Heitler in his treatment of radiation damping and relates the on shell components of the T matrix directly to the scattering potential. The motivation for using, this equation to inverse scattering problems stems from the1act that the data collected in a scattering experiment contain only the components that lie on the energy shell. We shall limit our attention only to the cases where the wave propagation is governed by the scalar Helmholtz equation. The theoretical formulation developed applies to the general two dimensional problem. Furthermore, an iterative reconstruction algorithm that recovers the unknown index of refraction is introduced. The proposed method is tested with simulated scattered field data. The scattering objects used are, assumed to be two dimensional and purely dielectric. In addition, for simplification purposes, they possess cylindrical symmetry. The results indicate that this method can improve Upon the Born approximation. Specifically it is shown that the method converges to a solution after a few a iterations with a great improvement on a Mean Square Error criterion compared to the Born method. The method works equally well for lossy and non-lossy objects and the greatest improvement is observed. for the imaginary part of the- refractive index.