Reconstruction of permittivity profiles through a transformation of the differential equation for the reflection coefficient

In this paper a one-dimensional inverse scattering problem is considered. A n approximate inversion formula in a closed-form is derived. Using this for mula, an approximate permittivity profile is generated from the partial kno wledge of the frequency domain reflection coefficient. This formula is dedu ced through the application of a linear transformation to a nonlinear diffe rential equation for the frequency domain reflection coefficient. Examples are given to demonstrate the accuracy of this approximate inversion formula .