Abstract

Iterative schemes for tomographically reconstructing refractive-index fields are examined to establish sufficient conditions for convergence. The mappings which these algorithms represent are shown to be of a form n = f(n) amenable to analysis by the contraction mapping theorem, and a criterion is thereby provided for identifying convergent behavior and determining the number of iterations required to produce an approximate solution which is within a prescribed neighborhood of the limiting or fixed point n*. As an example, this approach is applied for the case where a 1-D refractive-index field is iteratively reconstructed from numerically simulated interferometric data.

© 1989 Optical Society of America

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