Multifrequency version of the modified gradient algorithm for reconstruction of complex refractive indices

Ralph E. Kleinman; Peter M. van den Berg; Bert Jan Kooij; Bernard Duchene; Dominique Lesselier; Marc Lambert; Vikass Monebhurrun

doi:10.1117/12.284718

9 December 1997 Multifrequency version of the modified gradient algorithm for reconstruction of complex refractive indices

Ralph E. Kleinman, Peter M. van den Berg, Bert Jan Kooij, Bernard Duchene, Dominique Lesselier, Marc Lambert, Vikass Monebhurrun

Author Affiliations +

Proceedings Volume 3171, Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications; (1997) https://doi.org/10.1117/12.284718
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

The modified gradient algorithm has been shown to provide a stable method for reconstructing complex refractive indices (acoustic and electromagnetic) of bounded isotropic inhomogeneities in a variety of 2D problems where the size of the inhomogeneity is of the order of one to three wavelengths. The essential features of the method will be summarized including the use of regularization techniques for resolving discontinuities in the refractive index. The method involves the iterative construction of a global optimizer of a functional consisting of the error in satisfying an integral form of the field equation (the Lippmann-Schwinger equation) and the discrepancy between measured and predicted data. The optimizer is a function pair consisting of the refractive index and the field within the inhomogeneity. The extension of this method to 3D problems and multifrequency data is described. While the extension to three dimensions presents no basic theoretical difficulties, the computational problem is much more complicated. A way to ameliorate this complication by adjusting the integral form of the field equation is described. When data is available at more than one frequency the algorithm must be further modified and these modifications are given. In this case it is necessary to have a priori information on the dispersion relation in the inhomogeneity, for example, in electromagnetics an assumption that the medium is Maxwellian. Results of numerical experiments will be presented to illustrate both the strengths and weaknesses of the method.

Citation Download Citation

Ralph E. Kleinman, Peter M. van den Berg, Bert Jan Kooij, Bernard Duchene, Dominique Lesselier, Marc Lambert, and Vikass Monebhurrun "Multifrequency version of the modified gradient algorithm for reconstruction of complex refractive indices", Proc. SPIE 3171, Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications, (9 December 1997); https://doi.org/10.1117/12.284718

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