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On the convergence of the Born series in optical tomography with diffuse light. (English) Zbl 1127.78010

Summary: We provide a simple sufficient condition for the convergence of the Born series in the forward problem of optical diffusion tomography. The Born series considered in this paper is an expansion of Green’s function or the T-matrix for the diffusion equation in an inhomogeneous medium in a functional power series in \(\delta \alpha (r)\) or \(\delta D(r)\) which are the deviations of the absorption and diffusion coefficients of the medium from their respective background values \(\alpha _{0}\) and \(D_{0}\). The condition we obtain depends only on upper bounds for the inhomogeneity functions but not on their detailed form or spatial extent.

MSC:

78A70 Biological applications of optics and electromagnetic theory
65R32 Numerical methods for inverse problems for integral equations