Inverse scattering of a layered and dispersionless dielectric half-space, part I: Reflection data from plane waves at normal incidence

An inverse scattering theory and two inversion algorithms for the reconstruction of the dielectric profile of an inaccessible, layered, and dispersionless half-space are presented. The source and receiver are located at a distance above the inaccessible region. The source is an artificial electromagnetic source which is assumed to be capable of radiating plane waves at normal incidence for all the positive frequencies. In this case the receiver measures the reflection coefficient phase and amplitude for all the positive frequencies. Alternatively, the source is radiating an impulsive plane wave and the receiver measures the impulse response of the inaccessible region. From either of these data, the dielectric profile of the inaccessible region is constructed uniquely and exactly. Two numerical algorithms are developed and their performance is examined for the cases of precise and imprecise data. It is also shown that if the inaccessible half-space is made of an inhomogeneous layer of known thickness on top of a uniform half-space of known dielectric constant, then the average value of the refractive index profile of the inhomogeneous layer and the refractive index at the edges of the layer can be estimated from the minimum and maximum values of the reflection coefficient amplitude. Results are given for these estimates for five different inhomogeneous layers.