  A broad class of imaging modalities involve the resolution of an
inverse-scattering problem. Among them, three-dimensional optical diffraction
tomography (ODT) comes with its own challenges. These include a limited range
of views, a large size of the sample with respect to the illumination
wavelength, and optical aberrations that are inherent to the system itself. In
this work, we present an accurate and efficient implementation of the forward
model. It relies on the exact (nonlinear) Lippmann-Schwinger equation. We
address several crucial issues such as the discretization of the Green
function, the computation of the far field, and the estimation of the incident
field. We then deploy this model in a regularized variational-reconstruction
framework and show on both simulated and real data that it leads to
substantially better reconstructions than the approximate models that are
traditionally used in ODT.
