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Acoustical Imaging pp 365–383Cite as

An Exact Theory for Coherent Acoustic Probing

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Part of the book series: Acoustical Imaging ((ACIM,volume 11))

Abstract

In an inverse scattering problem, the fields in the inhomogeneous wave equation are known, and it is desired to solve for the source term. N. N. Bojarski has derived an Exact Inverse Scattering Theory for such “inverse source” problems. The problem of determining the generalized refractive index (i.e., the complex permeability and dielectric constant for an electromagnetic problem, or the velocity and absorption for an acoustic problem) distribution of an inhomogeneous medium from measurements of the fields scattered by the medium can also be treated using this theory. This solution is applicable to all remote probing problems, including radar, sonar, “profiling” of inhomogeneous propagation media, nondestructive evaluation, and seismic exploration.

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References

  1. N. N. Bojarski, “Inverse Scattering,” Naval Air Systems Command, third quarterly report to Contract N00019–73-C-0312 (NASC-C2–Q3), October 1973.

    Google Scholar 

  2. N. N. Bojarski, “Inverse. Scattering,” Naval Air Systems Command, final report on Contract N00019–73-C-0312, February 1974.

    Google Scholar 

  3. N. N. Bojarski, “Exact Inverse Scattering,” presented at the Annual Meeting of USNC/URSI, October 20–23, 1975, Boulder, Colorado.

    Google Scholar 

  4. N. Bleistein and N. N. Bojarski, “Recently Developed Formulations of the Inverse Problem in Acoustics and Electromagnetics,” report MS-R-7501, (AD/A-003 588 ) Department of Mathematics, Denver Research Institute, University of Denver, Colorado, 1974.

    Google Scholar 

  5. W. R. Stone, “Holographic Reconstruction is Usually a Poor Solution to the Inverse Scattering Problem: A Comparison Between the Bojarski Exact Inverse Scattering Theory and Holography as Applied to the Holographic Radio Camera,” presented at the 1980 International Optical Computing Conference, April 8–11, 1980, Washington, DC; to appear in SPIE Proceedings, Vol. 231.

    Google Scholar 

  6. N. N. Bojarski, “Exact Inverse Scattering,” presented at the 1980 “DARPA/AF Review of Quantitative NDE, July 14–18, 1980, La Jolla, CA; to appear in conference proceedings.

    Google Scholar 

  7. N. Bleistein and J. Cohen, “Nonuniqueness in the Inverse Source Problem in Acoustics and Electromagnetics,” Journal of Mathematical Physics, 18: 194–201, 1977.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. W. R. Stone, “A Uniqueness Proof for the Bojarski Exact Inverse Scattering Theory, and Its Consequences for the Holographic Radio Camera,” presented at the URSI National Radio Science Meeting, Boulder, Colorado, January 9–13, 1978.

    Google Scholar 

  9. N. N. Bojarski, “A Wave Equation for Radiating Source Distributions,” presented at the URSI National Radio Science Meeting, Boulder, Colorado, November 6–9, 1979.

    Google Scholar 

  10. W. R. Stone, “The Nonexistence of Nonradiating Sources and the Uniqueness of the Solution to the Inverse Scattering Problem,” presented at the North America Radio Science meeting, June 2–6, 1980, Quebec, Canada.

    Google Scholar 

  11. R. D. Mager and N. Bleistein, “An Examination of the Limited Aperture Problem of Physical Optics Inverse Scattering,” IEEE Trans. Ant. Prop. AP-26: 695–699, 1978.

    Article  ADS  Google Scholar 

  12. W. R. Stone, “The Resolution of an Aperture for Coherent Imaging,” presented at the Optical Society of America Annual Meeting, San Francisco, California, October 23–27, 1978.

    Google Scholar 

  13. W. R. Stone, “Numerical Studies of the Effects of Noise and Spatial Bandlimiting on Source Reconstructions Obtained using the Bojarski Exact Inverse Scattering Theory,” presented at the URSI spring meeting, College Park, Maryland, May 15–19, 1978.

    Google Scholar 

  14. W. M. Lewis, “Physical Optics Inverse Scattering”, IEEE Trans. Ant. Prop., AP-17, 308–314, 1969.

    Google Scholar 

  15. N. N. Bojarski, “Exact Inverse Scattering Theory”, report on contract N00014–76-C-0082, March 1980.

    Google Scholar 

  16. N. N. Bojarski, “Passive Seismic Artillery Location by Exact Inverse Scattering”, report on contract N00014–79-C-0189, July 1980.

    Google Scholar 

  17. Y. T. Lo, “A Mathematical Theory of Antenna Arrays with Randomly Spaced Elements, “IRE Transactions on Antennas and Propagation, AP-12, May 1964.

    Google Scholar 

  18. Bernard D. Steinberg, “The Peak Sidelobe of the Phased Array Having Randomly Located Elements,” IEEE Transactions on Antennas and Propagation, AP-20, March 1972.

    Google Scholar 

  19. Bernard D. Steinberg, Principles of Aperture and Array System Design, John Wiley & Sons, New York, 1976, Chapters 8 and 9.

    Google Scholar 

  20. Earl N. Powers and Bernard D. Steinberg, “Valley Forge Research Center Adaptive Array,” USNC/URSI Annual Meeting, Boulder, CO, October 1975.

    Google Scholar 

  21. N. N. Bojarski, “Three-Dimensional Electromagnetic Short-Pulse Inverse Scattering,” Report SPL 67–3, Syracuse University Research Corporation, Syracuse, New York, February 1967.

    Google Scholar 

  22. N. N. Bojarski, “Electromagnetic Inverse Scattering Theory,” Syra- cuse University Research Corporation, Syracuse, New York, December 1968.

    Google Scholar 

  23. N. N. Bojarski, “Electromagnetic Inverse Scattering,” Naval Air Systems Command, June 1972.

    Google Scholar 

  24. N. N. Bojarski, “Inverse Scattering Inverse Source Theory,” Office of Naval Research, Contract N00014–76-C-0082, November 1980.

    Google Scholar 

  25. N. N. Bojarski, “Low Frequency Inverse Scattering,” Office of Naval Research, Contract N00014–76-C-0082, July 25, 1980.

    Google Scholar 

  26. N. Bleistein and J. K. Cohen, “A Survey of Recent Progress on Inverse Problems,” University of Denver Department of Mathematics Report MS-R- 7806, 1978.

    Google Scholar 

  27. R. J. Collier, C. B. Burkhart, and L. H. Lin, Optical Holography, New York: Academic Press, 1971, Section 13. 3.

    Google Scholar 

  28. B. P. Hildebrand and B. B. Brenden, An Introduction to Acoustical Holography, New York: Plenum Press, 1972, Chapter 4.

    Google Scholar 

  29. W. R. Stone, “Numerical Considerations in the Application of the Exact Inverse Scattering Theory,” presented at the 17th Annual Meeting of the Society of Engineering Science, Atlanta, GA, December 15–17, 1980.

    Google Scholar 

  30. W. R. Stone, “How to Get Off the Fourier Domain (“Ewald”) Sphere in the Inverse Scattering Problem,” presented at the National Radio Science Meeting of USNC/URSI, Boulder, CO, January 12–16, 1981.

    Google Scholar 

  31. R. F. Harrington, Time Harmonic Electromagnetic Fields, New York, McGraw-Hill Book Company, 1961, Equations 4 through 124.

    Google Scholar 

  32. G. C. Sherman, “Application of the Convolution Theorem to Ray- leigh’s Integral Formulas,” J. Opt. Soc. Am., 57, 546–547, 1967.

    Article  Google Scholar 

  33. W. R. Stone, “The Concept, Design, and Operation of a Demonstra- tion Holographic Radio Camera,” Ph.D. dissertation, Applied Physics and Information Sciences, University of California, San Diego, 1978.

    Google Scholar 

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Author information

Authors and Affiliations

  1. IRT Corporation, 1446 Vista Claridad, La Jolla, CA, 92037, USA

    W. Ross Stone

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  1. W. Ross Stone
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Editors and Affiliations

  1. Naval Postgraduate School, Monterey, California, USA

    John P. Powers

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© 1981 W. Ross Stone

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Stone, W.R. (1981). An Exact Theory for Coherent Acoustic Probing. In: Powers, J.P. (eds) Acoustical Imaging. Acoustical Imaging, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1137-9_24

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  • DOI: https://doi.org/10.1007/978-1-4684-1137-9_24

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-1139-3

  • Online ISBN: 978-1-4684-1137-9

  • eBook Packages: Springer Book Archive

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