A generalized iterative approach to curved-ray tomography

Abstract A generalized iterative approach to the tomographic reconstruction of strongly refracting fields is proposed. The mappings for existing iterative schemes are recognized to be special cases of a more general form, and this form is shown to possess an arbitrary operator which affects convergence but may be changed without altering the roots of the original mapping. This, therefore, provides the basis for defining new recursive sequences which may converge in cases where the standard iterative schemes are divergent. To illustrate the approach, two enhanced schemes are developed by making particular selections for the arbitrary operator, and a 1 -D boundary layer type field is reconstructed from numerically simulated interferometric data.