Direct and Inverse Electromagnetic Scattering

  • Wolfgang Rieger
  • André Buchau
  • Günther Lehner
  • Wolfgang M. Rucker
Conference paper

Abstract

The direct and inverse time-harmonic electromagnetic scattering from inhomogeneous media is considered. The physical problem of electromagnetic scattering from known objects is mathematically described by volume integral equations. Being able to master the direct problem is an absolute prerequisite to solving the corresponding inverse problem, which is naturally closely connected. When solving inverse scattering problems one tries to retrieve information about the unknown scatterer from the knowledge of incident probing waves and measured scattering data. We especially investigate methods to reconstruct the geometry and the material properties of inhomogeneous media from scattering data. The objects considered in this context axe either isotropic or anisotropic lossy dielectrics. The objects are assumed to be nonmagnetic. The inverse scattering problem can be formulated as a nonlinear optimization problem which is solved by means of iterative optimization schemes. Numerical examples demonstrate the efficiency of the proposed methods.

Keywords

Microwave Leukemia Haas Verse 

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References

  1. 1.
    Born M. and Wolf E. Principles of Optics. Pergamon Press, Oxford, 1964.Google Scholar
  2. 2.
    Chew, W. C. Waves and Fields in Inhomogeneous Media. Van Nostrand Reinhold, New York, 1990.Google Scholar
  3. 3.
    Colton, D. and Kress, R. Inverse Acoustic and Electromagnetic Scattering Theory. Applied Mathematical Sciences 93. Springer, Berlin Heidelberg New York, 1992.Google Scholar
  4. 4.
    Colton, D. and Monk, P. The detection and monitoring of leukemia using electromagnetic waves: mathematical theory. Inverse Problems, Vol. 10: 1235–1251, 1994.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Colton, D. and Monk, P. The detection and monitoring of leukemia using electromagnetic waves: numerical analysis. Inverse Problems, Vol. 11: 329–342, 1995.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Fadoulourahmane, S. An Inverse Problem for Time Harmonic Electromagnetic Waves In An Inhomogeneous Orthotropic Medium. Dissertation, University of Oulu, Oulu University Press, 1997.Google Scholar
  7. 7.
    Huber, C. J., Rieger, W., Haas, M. and Rucker, W. M. The numerical treatment of singular integrals in boundary element calculations. ACES Journal, Vol. 12, No. 2: 121–126, 1997.Google Scholar
  8. 8.
    Jacoby, S. L. S., Kowalik, J. S. and Pizzo, J. T. Iterative Methods for Nonlinear Optimization Problems. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1972.MATHGoogle Scholar
  9. 9.
    Kleinman, R. E. and van den Berg, P. M. Two-dimensional location and shape reconstruction. Radio Science, Vol. 29: 1157–1169, 1994.CrossRefGoogle Scholar
  10. 10.
    Lobel, P., Kleinman, R. E., Pichot, Ch., Blanc-Feraud, L. and Barlaud M. Conjugate-gradient method for solving inverse scattering with experimental data. IEEE Antennas and Propagation Magazine, Vol. 38: 48 - 51, 1996.CrossRefGoogle Scholar
  11. 11.
    Louis, A. K. Inverse und schlecht gestellte Probleme. Teubner, Stuttgart, 1989.MATHGoogle Scholar
  12. 12.
    Rieger, W., Buchau, A., Haas, M., Huber, C., Lehner G. and Rucker W. M. 2D-TE Inverse Medium Scattering: An Improved Variable Metric Method. IEEE AP-S International Symposium Digest, Vol. 3: 2140–2143, 1999.Google Scholar
  13. 13.
    Rieger, W., Buchau, A., Haas, M., Huber, C., Lehner G. and Rucker W. M. Image Reconstruction from Real Scattering Data. COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 18, No. 3: 382–394, 1999.Google Scholar
  14. 14.
    Rieger, W., Haas, M., Huber, C., Lehner G. and Rucker W. M. Inverse Electromagnetic Medium Scattering Using a Variable Metric Method. IEEE AP-S International Symposium Digest, Vol. 4: 2621–2624, 1997.CrossRefGoogle Scholar
  15. 15.
    Rieger, W., Haas, M., Huber, C., Lehner G. and Rucker W. M. Reconstruction of Inhomogeneous Lossy Dielectric Objects in One Dimension. ACES Journal, Vol. 12, No. 2: 54–59, 1997.Google Scholar
  16. 16.
    Rieger, W., Haas, M., Huber, C., Lehner G. and Rucker W. M. A New Approach to the 2D-TE Inverse Electromagnetic Medium Scattering. IEEE AP-S International Symposium Digest, Vol. 2: 706–709, 1998.Google Scholar
  17. 17.
    Rieger, W., Haas, M., Huber, C., Lehner G. and Rucker W. M. An Improved Iterative Scheme with Incorporated a priori Information applied to Real Scattering data. USNC/URSI National Radio Science Meeting Digest, p. 17, 1998.Google Scholar
  18. 18.
    Rieger, W., Haas, M., Huber, C., Lehner G. and Rucker W. M. A Novel Approach to the 2D-TM Inverse Electromagnetic Medium Scattering. IEEE Transactions on Magnetics, Vol. 35, No. 3: 1566–1569, 1999.CrossRefGoogle Scholar
  19. 19.
    Wang, Y. M. and Chew, W. C. An iterative solution of the two-dimensional electromagnetic inverse scattering problem. International Journal of Imaging Systems and Technology, Vol. 1: 100–108, 1989.CrossRefGoogle Scholar
  20. 20.
    Wolfersdorf von, L. Inverse und schlecht gestellte Probleme; Eine Einführung. Akademie Verlag, Berlin, 1994.MATHGoogle Scholar
  21. 21.
    Yaghjian, A. D. Electric dyadic green’s functions in the source region. Proceedings of the IEEE, Vol. 68: 248–263, 1980.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Wolfgang Rieger
    • 1
  • André Buchau
    • 1
  • Günther Lehner
    • 1
  • Wolfgang M. Rucker
    • 1
  1. 1.Institut für Theorie der ElektrotechnikUniversität StuttgartStuttgartGermany

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