Beyond the Born approximation in one- and two-dimensional profile reconstruction.

Abstract

The problem of reconstructing dielectric profiles in both one and two dimensions from measurements of the scattered electric field is discussed in this dissertation. We formulate a governing equation for the electric field outside of the dielectric slab using the Green's function method. Embedded inside this equation for the electric field is both the unknown slab profile and the unknown total field inside the dielectric scatterer. To remove the unknown field quantity, we use different models for the total field inside the slab. These models reduce the governing equation to situations relating the scattered electric field to the Fourier transform of the slab and object profile (defined as the difference between the dielectric constant of the scatterer and the dielectric constant of the background medium). However, these models are only valid for low frequency. To recover the high frequency information and invert for the dielectric profile, we use a technique known as super-resolution. In the one-dimensional case, we find that model for the field inside the scatterer based upon the form of the field outside the scatterer (which we call the advanced approximation) gives the best reconstructions for a wide variety of profiles. Finally, we vary the parameters associated with super-resolution and examine the resulting reconstructions in the one-dimensional case. We find that using a minimum number of frequency samples, smaller frequency spacings between the samples, and longer reconstruction vectors lead to better reconstructions in the advanced scheme.