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Proceedings Paper

Profile inversion via successive overrelaxation
Author(s): Ralph E. Kleinman; Peter M. van den Berg
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Paper 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.

Paper Details

Date Published: 1 November 1990
PDF: 11 pages
Proc. SPIE 1351, Digital Image Synthesis and Inverse Optics, (1 November 1990); doi: 10.1117/12.23626
Show Author Affiliations
Ralph E. Kleinman, Univ. of Delaware (United States)
Peter M. van den Berg, Delft Univ. of Technology (Netherlands)


Published in SPIE Proceedings Vol. 1351:
Digital Image Synthesis and Inverse Optics
Arthur F. Gmitro; Paul S. Idell; Ivan J. LaHaie, Editor(s)

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