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IEEE Transactions on Antennas and Propagation
Volume 47 Number 7, July 1999

Table of Contents for this issue

Complete paper in PDF format

Local Spectral Analysis of Short-Pulse Excited Scattering from Weakly Inhomogeneous Media-- Part I: Forward Scattering

Timor Melamed, Ehud Heyman, Senior Member, IEEE, and Leopold B. Felsen, Life Fellow, IEEE

Page 1208.

Abstract:

In this two-part sequence, we extend a previously formulated pulsed plane wave (PPW)-based time-domain (TD) diffraction tomography [1] for forward and inverse scattering from weakly inhomogeneous lossless nondispersive media to a more highly localized pulsed beam (PB) wavepacket-based diffraction tomography. In the PPW version, the incident and scattered fields have been parameterized in the space-time wavenumber domain in terms of slant-stacked TD plane waves whose wavefronts move through the scattering medium at the ambient propagation speed, thereby accumulating information along time-resolved laterally extended planar cuts. The PB parameterized localization confines the laterally sampled regions to the spatial domains of influence transverse to the relevant beam axes. These localizations are performed in two stages. The present paper implements the PB parameterization by PB post processing of the forward scattered fields excited by an incident PPW; the companion paper [2] deals with the inverse problem by back propagation of the PB parameterized data. An "ultimate" localization of a space-time resolved scattering cell, achieved via scattered and incident PB's (PB post and preprocessing) will be addressed elsewhere, but is briefly summarized in [2].

References

  1. T. Melamed, Y. Ehrlich, and E. Heyman, "Short-pulse inversion of inhomogeneous media: A time-domain diffraction tomography," Inverse Problems, vol. 12, pp. 977-993, 1996.
  2. T. Melamed, E. Heyman, and L. B. Felsen, "Local spectral analysis of short-pulse excited scattering from weakly inhomogeneous media--Part II: Inverse scattering," IEEE Trans. Antennas Propagat., this issue, pp. 1218-1227.
  3. T. Melamed and E. Heyman, "Spectral analysis of time-domain diffraction tomography," Radio Sci., vol. 32, pp. 593-604, 1997.
  4. T. Melamed, "Phase-space beam summation: A local spectrum analysis for time-dependent radiation," J. Electromagn. Waves Appl., vol. 11, pp. 739-773, 1997.
  5. E. Heyman and L. B. Felsen, "Complex source pulsed beam fields," J. Opt. Soc. Amer. vol. 6, pt. A, 806-817, 1989.
  6. E. Heyman, "Pulsed beam propagation in an inhomogeneous medium," IEEE Trans. Antennas Propagat., vol. 42, pp. 311-319, 1994.
  7. E. Heyman and T. Melamed, "Certain considerations in aperture synthesis of ultrawideband/short-pulse radiation," IEEE Trans. Antennas Propagat., vol. 42, pp. 518-525, 1994.
  8. E. Heyman and L. B. Felsen, "Weakly dispersive spectral theory of transients (STT): Part I--Formulation and interpretation; Part II--Evaluation of the spectral integral; Part III--Applications," IEEE Trans. Antennas Propagat., vol. AP-35, pp. 80-86; pp. 574-580; pp. 1258-1266, 1987.
  9. B. Z. Steinberg, E. Heyman, and L. B. Felsen, "Phase space beam summation for time dependent radiation from large apertures: Continuous parametrization," J. Opt. Soc. Amer. A, vol. 8, no. 943-958, 1991.
  10. T. B. Hansen and A. D. Yaghjian, "Planar near-field scanning in the time-domain--Part I: Fomulation," IEEE Trans. Antennas Propagat., vol. 42, pp. 1280-1291, 1994.
  11. T. B. Hansen and A. D. Yaghjian, "Planar near-field scanning in the time-domain: Part II--Sampling theorem and computation schemes," IEEE Trans. Antennas Propagat., vol. 42, no. 1292-1300, 1994.
  12. M. J. Bastiaans, "Signal descriptions by means of a local frequency spectrum," in Proc. SPIE: Transformat. Opt. Signal Processing, vol. 373, pp. 49-62, 1981.
  13. B. Z. Steinberg, E. Heyman, and L. B. Felsen, "Phase space beam summation for time-harmonic radiation from large apertures," J. Opt. Soc. Amer., vol. 8, pt. A, no. 41-59, 1991.
  14. J. R. Taylor, Scattering Theory.New York: Wiley, 1972.
  15. J. B. Keller, "Accuracy and validity of the Born and Rytov approximations," J. Opt. Soc. Amer., vol. 59, pp. 1003-1004, 1969.
  16. A. J. Devaney, "Diffraction tomography," in Inverse Methods in Electromagnetic Imaging--Part II, W. M. Boerner, Ed.Dodrecht, Holland: Reidel, 1985.
  17. D. Miller, M. Orstaglio, and G. Beylkin, "A new slant on seismic imaging: Migration and integral geometry," Geophys., vol. 52, no. 943-964, 1987.