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This paper describes a simple algorithm for reconstructing the complex index of refraction of a bounded object immersed in a known background from a knowledge of how the object scatters known incident radiation. The method described here is versatile accommodating both spatially and frequency varying incident fields and allowing a priori information about the scatterer to be introduced in a simple fashion. Numerical results show that this new algorithm outperforms the modified gradient approach which until now has been one of the most effective reconstruction algorithms available.

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A method for reconstructing the location and the shape of a bounded impenetrable object from measured scattered field data is presented. The algorithm is, in principle, the same as that used for reconstructing the conductivity of a penetrable object and uses the fact that for high conductivity the skin depth of the scatterer is small, in which case the only meaningful information produced by the algorithm is the boundary of the scatterer. A striking increase in efficiency is achieved by incorporating into the algorithm the fact that for large conductivity the contrast is dominated by a large positive imaginary part. This fact, together with the knowledge that the scatterer is constrained in some test domain, constitute the only a priori information about the scatterer that is used. There are no other implicit assumptions about the location, connectivity, convexity, or boundary conditions. Some refinements of the algorithm which reduce the number of points at which the unknown function is updated are incorporated to further increase efficiency. Results of a number of numerical examples are presented which demonstrate the effectiveness of the location and shape reconstruction algorithm.

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A method for reconstructing the complex index of refraction of a bounded inhomogeneous object from measured scattered field data is presented. The index and the unknown fields within the object are simultaneously reconstructed in an iterative algorithm. The method is a refinement of earlier work which incorporates a more effective way to update the unknowns at each stage of the iteration. Considerable efficiency in the algorithm is achieved. Some numerical examples are given indicating the limits on the contrasts which can be reconstructed. These limits show that the range of contrasts that may be reconstructed is extended over that achievable with the earlier work.