Analytical techniques are used to solve two inverse radiative-transfer problems, for a 5nite plane-parallel medium, that are (i) based on the binomial scattering law and (ii) based on the Henyey–Greenstein scattering law. In addition, previously reported analytical results (valid for isotropic scattering) that yield an analytical inverse solution for the unknown optical thickness of the medium ...

We present a numerical comparison of the so-called ‘linear sampling’ inverse scattering methods developed by Colton and Kirsch, published in this journal, and linearized tomographic inverse scattering algorithms based on either holographic filtered backpropagation principles or a plain matrix inversion scheme. Although we restrict ourselves to two-dimensional obstacle scattering, we investigate...

A rigorous theory of the inverse scattering transform for the defocusing nonlinear Schrödinger equation with nonvanishing boundary values q± ≡ q0e± as x → ±∞ is presented. The direct problem is shown to be well posed for potentials q such that q − q± ∈ L1,2(R±), for which analyticity properties of eigenfunctions and scattering data are established. The inverse scattering problem is formulated a...

A recently developed inverse scattering algorithm [A. J. Devaney and M. Dennison, Inverse Probl., 19, 855 (2003) and M. Dennison and A. J. Devaney, Inverse Probl., 20, 1307 (2004)] is described and applied in a computer simulation study of optical diffraction tomography (ODT). The new algorithm is superior to standard ODT reconstruction algorithms, such as the filtered backpropagation algorithm...

We consider an inverse problem for the scattering of an obliquely incident electromagnetic wave by an impedance cylinder. In previous work, we have shown that the direct scattering problem is governed by a pair of Helmholtz equations subject to coupled oblique boundary conditions, where the wave number depends on the frequency and the incident angle with respect to the axis of the cylinder. In ...