Advertisement

Digital Reconstruction of Acoustic Holograms in the Space Domain with a Vector Space Approximation

  • Hua Lee
  • Carl Schueler
  • Glen Wade
  • Jorge Fontana
Part of the Acoustical Imaging book series (ACIM, volume 9)

Abstract

We have developed a computer-assisted ultrasonic underwater imaging system. Until recently, we used back-propagation to reconstruct images. This method, accurate both in the near and far fields of the object, is an inverse filtering technique that operates in the spatial frequency domain and requires the taking of two Discrete Fourier transforms (DFT’s).

Here, we present a method based on back-projection, an alternative reconstruction technique which operates in the space domain and reconstructs images without any DFT’s. Back-projection is computationally as fast as a single DFT, and it is accurate in both the near and far fields. This new algorithm works because the spatial propagation of a point-source is known, and any object is a linear combination of point-sources. We, therefore, can construct a spatial propagation matrix which maps the object-wave field into a field at the receiver plane. To use the received data to obtain the object wave field requires the inverse matrix. The back-projection algorithm applies an approximation technique from vector-space algebra to estimate the inverse matrix and reconstruct an acceptable image of an unknown object.

We not only present computer simulations which demonstrate the feasibility of back-projection, but we also use a modified version of the above algorithm to correct simulated data that has been degraded by motion of the object during data acquisition. Results from simulated data are compared with those from experimental data.

Keywords

Discrete Fourier Transform Motion Correction Space Domain Inverse Filter Array Position 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C. F. Schueler, J. Fontana, and G. Wade, “Ultra-sonic Underwater Imaging System with Computer Image Processing and Reconstruction”, Proceedings of Ultrasonics International ′79, Graz, Austria, 15-17 May, 1979.Google Scholar
  2. [2]
    J. L. Sutton, “Underwater Acoustic Imaging”, Proc. of the IEEE, Vol. 67, No. 4 (1979), pp. 554–566.ADSCrossRefGoogle Scholar
  3. [3]
    D. G. Luenberger, Optimization by Vector Space Methods, John Wiley & Sons (1969), p. 163.Google Scholar
  4. [4]
    Ibid., pp. 161.Google Scholar
  5. [5]
    Ibid., pp. 165.Google Scholar
  6. [6]
    Ibid., pp. 150.Google Scholar
  7. [7]
    J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, (1968), pp. 44.Google Scholar
  8. [8]
    H. D. Collins and B. P. Hildebrand, “The Effects of Scanning Position and Motion Errors on Hologram Recording”, Acoustical Holography, Vol. 4, Plenum Press, 1972, pp. 467–501.CrossRefGoogle Scholar
  9. [9]
    L. Schlussler, A. E. Coello-Vera, G. Wade, and J. Fontana, “Motion Limitations of an Acoustic Holographic System Utilizing a Scanned Linear Array”, Optical Engineering, Vol. 16, No. 5, Sept.-Oct. 1977, pp. 426–431.ADSGoogle Scholar
  10. [10]
    N. B. Tse, L. Schlussler, J. Fontana, and G. Wade, “Computer-Corrected Reconstruction of Acoustic Holograms of Non-unifor-mly Moving Objects”, 1977 Ultrasonics Symposium Proceedings.Google Scholar
  11. [11]
    D. G. Luenberger, Introduction to Linear and Non-linear Pro-gramming, Addison-Wesley, 1973, pp. 148.Google Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Hua Lee
    • 1
  • Carl Schueler
    • 1
  • Glen Wade
    • 1
  • Jorge Fontana
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of CaliforniaSanta BarbaraUSA

Personalised recommendations