7 December 1982 Reconstruction Of The Index Of Refraction Of A Sphere From Scattering Phase-Shifts At One Frequency
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Abstract
The scattering phase-shifts δlf(k) (f = 0, 1, 2, ...) are generally assumed to be retrievable from scattering data on cross sections. The problem of reconstructing the object generating these data at fixed frequency (energy) was solved in the quantum mechanical framework by Newton and Sabatier, for cases with spherical symmetry. Their work applies equally well to scalar waves satisfying the wave equation with a radially distributed index of refraction. The main purpose of the paper is to show how these phase-shifts can be used to reconstruct the index of refraction numerically using a procedure that avoids the possible emergence of "transparent" distributions, yielding a unique solution.
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C. Eftimiu, C. Eftimiu, P. L. Huddleston, P. L. Huddleston, } "Reconstruction Of The Index Of Refraction Of A Sphere From Scattering Phase-Shifts At One Frequency", Proc. SPIE 0358, Applications of Mathematics in Modern Optics, (7 December 1982); doi: 10.1117/12.934067; https://doi.org/10.1117/12.934067
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