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

The structural information carried by the homogeneous and evanescent compon ents of the scattered field is investigated for the case of a single plane wave, either homogeneous or evanescent, incident on a weakly scattering thr ee-dimensional medium. For homogeneous plane wave incidence, it is shown th at, unlike the one-to-one mapping that exists in the case of scattering fro m thin (i.e. two-dimensional) structures, the evanescent components of the scattered field are related to the three-dimensional Fourier transform of t he dielectric susceptibility through a generalized Radon transform. For eva nescent plane wave incidence, a reciprocal relationship exists between the homogenous components of the scattered field and the three-dimensional Four ier 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) measure ment data. These results have direct bearing on total internal reflection m icroscopy (TIRM), and they yield insight into the limitations of more gener al near-field imaging techniques.