Profile inversion via successive overrelaxation

Ralph E. Kleinman; Peter M. van den Berg

doi:10.1117/12.23626

1 November 1990 Profile inversion via successive overrelaxation

Ralph E. Kleinman, Peter M. van den Berg

Proceedings Volume 1351, Digital Image Synthesis and Inverse Optics; (1990) https://doi.org/10.1117/12.23626
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

Abstract

A method for reconstructing the index of refraction of a bounded inhomogeneous object of known geometric configuration from measured far field scattering data is presented. This work is an extension of recent results on the direct scattering problem wherein the governing domain integral equation was solved iteratively by a successive relaxation technique. The relaxation parameter was chosen to minimize the residual error at each step. Convergence of this process was established for indices of refraction much larger than required for convergence of the Born approximation. For the inverse problem the same technique is applied except in this case both the index of refraction and the field are unknown. Iterative solutions for both unknowns are postulated with two relaxation parameters at each step. They are determined by simultaneously minimizing the residual errors in satisfying the domain integral equation and matching the measured data. Numerical results are presented for the dielectric slab. The algorithm is shown to be effective in cases where the iterative solution of the direct problem is rapidly convergent.

Citation Download Citation

Ralph E. Kleinman and Peter M. van den Berg "Profile inversion via successive overrelaxation", Proc. SPIE 1351, Digital Image Synthesis and Inverse Optics, (1 November 1990); https://doi.org/10.1117/12.23626

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