Imaging with Higher Order Diffraction Tomography

This paper describes several higher order models for the fields scattered by an object and the computational techniques involved. The Born and the Rytov approximations are easily extended to include higher order terms but like most series their range of convergence is limited. Another technique to be described is based on algebraic techniques and can be shown to always converge. Unfortunately, numerical instabilities limit this approach to objects with a refractive index change of less than 20-30%. This paper will describe numerical approaches for each of these higher order models It reports the region of convergence for the Born and Rytov series and objects that lead to stable solutions for the algebraic approach.