The information content of weakly scattered fields: Implications for near-field imaging of three-dimensional structures

Abstract

The structural information carried by the homogeneous and evanescent components of the scattered field is investigated for the case of a single plane wave, either homogeneous or evanescent, incident on a weakly scattering three-dimensional medium. For homogeneous plane wave incidence, it is shown that, unlike the one-to-one mapping that exists in the case of scattering from thin (i.e. two-dimensional) structures, the evanescent components of the scattered field are related to the three-dimensional Fourier transform of the dielectric susceptibility through a generalized Radon transform. For evanescent plane wave incidence, a reciprocal relationship exists between the homogenous components of the scattered field and the three-dimensional Fourier transform of the susceptibility. Inversion techniques are outlined for these two cases, as well as other experimental modalities, which explicitly require, except for separable media, complete (i.e. multiple view) measurement data. These results have direct bearing on total internal reflection microscopy (TIRM), and they yield insight into the limitations of more general near-field imaging techniques.