Nonlinear differential equation for the reflection coefficient of a pure conducting medium and its novel inverse scattering solution

A nonlinear differential equation for the reflection coefficient of a pure conducting medium is derived by using a microwave networking technique, which can be approximately solved by a nonlinear renormalization method. From the renormalization solution of the reflection coefficient, a novel inverse scattering formula to the conductivity profile is further investigated in the closed form. Reconstruction examples show that the novel formula is more accurate than the results in D.B. Ge et al. (1991) and T.J. Cui et al. (1992)