Tomography for properties of materials that bend rays: a tutorial

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Abstract
When tomography is performed with electromagnetic or acoustical radiation, refraction may cause sufficient bending of the probing rays that ordinary reconstruction algorithms, which are based on the assumption of straight rays, do not yield accurate results. The resulting problem of reconstructing the refractive-index distribution of an object from time of flight or optical path length data is nonlinear. Various approaches to solving this problem approximately have been proposed and subjected to modest numerical studies. These include iterative algorithms and techniques based on linearized inverse scattering theory. One exception is the case of axisymmetric objects for which an exact solution is known.