In Optical Diffraction Tomography (ODT) the refractive index is reconstructed from images with different illuminating
wavefronts. In most cases the Born approximation is assumed, although this limits the applicability of the technique to
weak-scattering problems. In this work we examine the scattering problem from first principles beginning from the
Helmholtz equation that governs scalar diffraction and wave propagation. We demonstrate the use of the Born
approximation and show typical errors when it is applied in practice. Solution of the Helmholtz equation using a Finite
Element Method (FEM) with an appropriate Absorbing Boundary Condition (ABC) is described, and a non-linear
optimization technique, the Conjugate Gradient Method (CGM), previously proposed for microwave imaging, is applied
to the inverse problem.