Journal of Nondestructive Evaluation

, Volume 5, Issue 2, pp 95–106 | Cite as

Two-dimensional inverse born approximation in ultrasonic flaw characterization

  • K. C. Tam


A method is developed to characterize flaws of arbitrary shape by using ultrasound pulse echoes at multiple coplanar incident directions. The three-dimensional image reconstruction problem is reduced to a series of two-dimensional image reconstructions, thereby avoiding the difficulties associated with three-dimensional image reconstructions, such as taking and processing a large amount of data, and the complications associated with three-dimensional image reconstructions, such as three-dimensional interpolation, long computing time, etc. The reconstructed two-dimensional images represent the two-dimensional projections or shadows of the three-dimensional flaw characteristic function. Each projection image is reconstructed independently using well-developed computerized tomography reconstruction techniques. If the shape of the flaw is not too irregular, or if the fine details of the shape are not of interest, only a few of these projection images suffice to characterize the flaw. The magnitude scaling problem and the alignment problem of the echoes at different incident directions can be handled easily in the algorithm. Simulation studies yielded encouraging results.

Key words

Ultrasound imaging flaw characterization computerized tomography inverse Born approximation 


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  1. 1.
    J. E. Gubernatis, E. Domany, and J. A. Krumhansl, Formal aspects of the theory of the scattering of ultrasound by flaws in elastic materials,J. Appl. Phys. 48:2804 (1977).Google Scholar
  2. 2.
    J. H. Rose and J. A. Krumhansl, Determination of flaw characteristics from ultrasonic scattering data,J. Appl. Phys. 50:2951 (1979).Google Scholar
  3. 3.
    D. O. Thompson and S. J. Wormley, Long and intermediate wavelength flaw reconstruction, inReview of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti eds. (Plenum Press, New York, 1985), Vol. 4A, p. 287.Google Scholar
  4. 4.
    J. H. Rose, R. K. Elsley, B. Tittman, V. V. Varadan, and V. K. Varadan, Inversion of ultrasonic scattering data, inAcoustic, Electromagnetic and Elastic Wave Scattering, V. V. Varadan and V. K. Varadan eds. (Pergamon, New York, 1980).Google Scholar
  5. 5.
    B. D. Cook, S. Wilson, and R. L. McKinney, Ramp wave processing of long wavelength ultrasonic scattering information,Proc. DARPA/AFWAL Review of Progress in Quantitative NDE, September 1981, AFWAL-TR-81-4080, p. 396.Google Scholar
  6. 6.
    J. H. Rose and J. M. Richardson, Time domain Born approximation,J. Nondestr. Eval. 3:45 (1982).Google Scholar
  7. 7.
    H. J. Scudder, Introduction to computer aided tomography,Proc. IEEE 66:628 (1978).Google Scholar
  8. 8.
    R. W. Gerchberg, Super-resolutions through error energy reduction,Opt. Acta 21:709 (1974).Google Scholar
  9. 9.
    A. Papoulis, A new algorithm in spectral analysis and bandlimited extrapolation,IEEE Trans. Circuits Syst. CAS-22:735 (1975).Google Scholar
  10. 10.
    A. Klug and R. A. Crowther, Three-dimensional image reconstruction from the viewpoint of information theory,Nature 238:435 (1972).Google Scholar
  11. 11.
    C. F. Ying and R. Truell, Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid,J. Appl. Phys. 27:1086 (1956).Google Scholar
  12. 12.
    K. C. Tam and V. Perez-Mendez, Principles of tomographical imaging with limited angle input,J. Opt. Soc. Am. 71:582 (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • K. C. Tam
    • 1
  1. 1.General Electric Company, Corporate Research and DevelopmentSchenectady

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