Wave Modeling for Inverse Problems with Acoustic, Electromagnetic, and Elastic Waves

  • Karl J. Langenberg


Applied inverse problems comprise radar remote sensing, geophysical exploration, medical diagnostics, nondestructive testing a.s.o., and as such, acoustic, electromagnetic, and elastic waves are under concern. Therefore, appropriate models have to be found to solve the inverse scattering problem for these types of waves algorithmically. Essentially, the linearization of the direct as well as the inverse scattering problem is most often required, and the underlying model is either the weak scattering (Born) approximation, or the physical optics (Kirchhoff) approximation. This allows a unified treatment of the scalar — acoustic — as well as the vector inverse scattering problem for electromagnetic and elastic waves, thus yielding full Polarimetric backpropagation inversion schemes. In order to check the validity of the linearization and the influence of insufficient experimental data due to aperture or frequency bandwidth limitations, simulations are required utilizing appropriate numerical codes. Here, we essentially present results for acoustic and elastic wave scattering obtained with our AFIT and EFIT Finite Difference codes.


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  1. [1]
    K.J. Langenberg: Introduction to the Special Issue on Inverse Problems, Wave Motion 11 (1989) 99–112CrossRefzbMATHGoogle Scholar
  2. [2]
    R. Marklein, P. Fellinger: Mathematisch-numerische Modellierung der Ausbreitung und Beugung akustischer Wellen, Seminar “Modelle und Theorien für die Ultraschallprüfung” der Deutschen Gesellschaft für zerstörungsfreie Prüfung, Berlin 1990Google Scholar
  3. [3]
    T. Kreutter, S. Klaholz, A. Brüll, J. Sahm, A.Hecht: Optimierung und Anwendung eines schnellen Abbildungsalgorithmus für die Schmiedewellenprüfung, ibid.Google Scholar
  4. [4]
    T. Weiland: On the Numerical Solution of Maxwell’s Equations and Applications in the Field of Accelerator Physics, Particle Accelerators 15 (1984)Google Scholar
  5. [5]
    U. Aulenbacher, K.J. Langenberg: Analytical Representation of Transient Ultrasonic Phsed-Array Near- and Far-Fields, J. Nondestr. Eval. 1 (1980) 53CrossRefGoogle Scholar
  6. [6]
    K.J. Langenberg, M. Fischer, M. Berger, G. Weinfurter: Imaging Performance of Generalized Holography, J. Opt. Soc. Am. 3 (1986) 329ADSCrossRefGoogle Scholar
  7. [7]
    R.P. Porter: Diffraction-Limited Scalar Image Formation with Holograms of Arbitrary Shape, J. Opt. Soc. Am. 60 (1970) 1051ADSCrossRefGoogle Scholar
  8. [8]
    N.N. Bojarski: Exact Inverse Scattering Theory, Radio Science 16 (1981) 1025ADSCrossRefGoogle Scholar
  9. [9]
    G.T. Herman, H.K. Tuy, K.J. Langenberg. P. Sabatier: Basic Methods of Tomography and Inverse Problems, Adam Hilger, Bristol 1987zbMATHGoogle Scholar
  10. [10]
    V. Schmitz, W. Müller, G. Schäfer: Practical Experiences with L-SAFT, in: Review of Progress in Quantitative Nondestructive Evaluation, Eds.: D.O. Thompson, D.E. Chimenti, Plenum Press, New York 1986Google Scholar
  11. [11]
    K. Mayer, R. Marklein, K.J. Langenberg, T. Kreutter: Threedimensional Imaging System based on Fourier Transform Synthetic Aperture Focussing Technique, Ultrasonics 28 (1990) 241–255CrossRefGoogle Scholar
  12. [12]
    A.J. Devaney, G. Beylkin: Diffraction Tomography Using Arbitrary Transmitter and Receiver Surfaces, Ultrasonic Imaging 6 (1984) 181Google Scholar
  13. [13]
    P. Fellinger, K.J. Langenberg: Numerical Techniques for Elastic Wave Propagagtion and Scattering, in: Elastic Waves and Ultrasonic Nondestructive Evaluation, Eds.: S.K. Datta, J.D. Achenbach, Y.S. Rajapakse, North-Holland, Amsterdam 1990Google Scholar
  14. [14]
    K.J. Langenberg, T. Kreutter, K. Mayer, P. Fellinger: Inverse Scattering and Imaging, ibid.Google Scholar
  15. [15]
    K.J. Langenberg, M. Brandfaß, P. Fellinger, T. Gurke, T. Kreutter: A Unified Theory of Multidimensional Electromagnetic Vector Inverse Scattering within the Kirchhoff or Born Approximation, in: Vector Inverse Methods in Radar Target Imaging, Ed.: H. Überall, Springer, Berlin 1991 (to appear)Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Karl J. Langenberg
    • 1
  1. 1.Dept. Electrical EngineeringUniversity of KasselKasselGermany

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