Dg. Fischer, The information content of weakly scattered fields: implications for near-field imaging of three-dimensional structures, J MOD OPT, 47(8), 2000, pp. 1359-1374
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.