Nonlinear Inverse Scattering Methods for Large Objects

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WPC 2 R B J Z X Courier #| x x 6 X @ K X @ QMS JetScript QMSJETSC.PRS x @ h h h h }X @T ? x x x x 6 X @ K X @ T R & H H H H 6 X @ K h @ 2 u 6~ ; ) ! t - S :t @ ,` ; & % t : u 2 4 " u$ u t 3 y u O t 2 9302145 Chew The previous support period under the 5 year PYI grant enabled the investigator to make significant progress in both inverse and forward scattering theory. New non linear inverse scattering methods were developed to account for multiple scattering effects within the scattering object. The Born iterative method (BIM) and distorted Born iterative method (DBIM) were developed that demonstrated the inversion of objects with contrasts as great as 10:1 and exhibited super resolution on the order of 0.1 wavelengths. Another new technique known as the local shape function (LSF) method was developed to perform inverse scattering on metallic scatters where previous methods failed to produce a convergent solution due to extremely strong nonlinearities. Recently it was found that the LSF method could also be used for the inversion of dielectric scatters and bypass the 10:1 contrast limitation. The need to invert very large scattering objects stimulated research in fast forward scattering solvers. These fast algorithms solve the scattering problem exactly and achieve computational savings by exploiting inherent redundancies in the scattering calculations. The first of these algorithms (RTMA) solved the ? 0 scattering problem valid for all incidence sources in )(N 2.5 ) operations by exploiting translational properties of wave phenomenon. T he next algorithm (RATMA) exploited an aggregation ? property resulting in an O(N 2 ) algorithm. The new algorithm (NEPAL) instead uses the surface equivalence principle resulting in ? an O(N 1.5 ) algorithm that is amenable to parallel processing. The current proposal is to continue progress in developing new nonlinear inverse scattering theories. We plan to move away for the Born type methods and exploit new ways of parameterizing the scattering object in order to achieve the best possible reconstruction. We will use our progress in fast forward scattering solvers as building blocks to speed up the inversion and solve much larger objects. Other means of solving large objects, particularly objects buried in a slowly varying inhomogeneous background would be investigated as well. Finally, we wish to develop new experimental apparatus that can achieve high fidelity measurements so that the full potential of these new inverse methods could be achieved in a practical system.