1 / 15

Diffraction Tomography in Dispersive Backgrounds

Diffraction Tomography in Dispersive Backgrounds. Tony Devaney Dept. Elec. And Computer Engineering Northeastern University Boston, MA 02115 Email: tonydev2@aol.com. A.J. Devaney, “Linearized inverse scattering in attenuating media,” Inverse Problems 3 (1987) 389-397.

wschultz
Download Presentation

Diffraction Tomography in Dispersive Backgrounds

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Diffraction Tomography in Dispersive Backgrounds Tony Devaney Dept. Elec. And Computer Engineering Northeastern University Boston, MA 02115 Email: tonydev2@aol.com A.J. Devaney, “Linearized inverse scattering in attenuating media,” Inverse Problems3 (1987) 389-397 Other approaches discussed in: • A. Schatzberg and A.J.D., ``Super-resolution in diffraction tomography, Inverse Problems 8 (1992) 149-164 • K. Ladas and A.J.D., ``Iterative methods in geophysical diffraction tomography, Inverse Problems 8 (1992) 119-132 • R. Deming and A.J.D., ``Diffraction tomography for multi-monostatic gpr, Inverse Problems 13 (1997) 29-45

  2. Experimental Configuration n() O(r,) s0 s Generalized Projection-Slice Theorem E. Wolf, Principles and development of diffraction tomography, Trends in Optics, Anna Consortini, ed. [Academic Press, San Diego, 1996] 83-110

  3. Forward scatter data Back scatter data z Born Inverse Scattering k=real valued Ewald Spheres k 2k Ewald Sphere Limiting Ewald Sphere

  4. Born Inversion for Fixed Frequency Problem: How to generate inversion from Fourier data on spherical surfaces Inversion Algorithms: Fourier interpolation (classical X-ray crystallography) Filtered backpropagation (diffraction tomography) A.J.D. Opts Letts, 7, p.111 (1982) Filtering of data followed by backpropagation: FilteredBackpropagationAlgorithm Fourier based methods fail if k is complex: Need new theory

  5. Pulse Propagation in a Dispersive Background n() O(r,) s0 s

  6. Fourier Transformed Scattered Field Close in u.h.p. Choose a complex frequency 0 such that k(0 ) is real valued There is no reason a priori to dismiss this possibility, butwill it work? Roots of dispersion relationship with real k are in l.h.p.

  7. Simple Conducting Medium Complex in l.h.p. Real valued Im  Complex  plane Branch point X <0 X Desired frequency 0 Re  Will not be able to close in u.h.p.: can only drop contour to branch points

  8. Lorentz Model b2=20x1032 0=16x1016  =.28x1016 Real n Imag n K.E. Oughstun and G.C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics [Springer-Verlag, 1994, New York]

  9. Lorentz Medium Im  Complex  plane Re  <0 - Desired frequency 0 X - + x x Poles of n() Branch Cuts Roots of dispersion relationship must lie above branch points Im 0>-

  10. Contour Plot of Re ik() Im  Re  Real k Branch point

  11. Mesh Plot of Re ik()

  12. Exciting the Plane Wave n() s0 O(r,) Close in l.h.p. Non-attenuating mode of medium

  13. The Complete Pulse Im  Complex  plane Re  -0 0 X X Branch Cuts Precursors Can the non-attenuating plane wave be excited; i.e., is it dominated by the precursors?

  14. Asymptotic Analysis K.E. Oughstun and G.C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics [Springer-Verlag, 1994, New York] Im  Steepest Descent Contour Complex  plane Saddle point X Re  -0 0 X X X X X Saddle point X Saddle point Plane wave excited Plane wave not excited

  15. Summary and Questions • Have reviewed one possible approach to inversion in dispersive backgrounds • Method is based on computing the temporal Fourier transform of pulsed data • at complex frequencies for which the wavenumber of the background is real • Method will not work for simple conducting media but appears feasible for • Lorentz media • The idea behind the approach suggests that it may be possible to excite • non-decaying, plane wave pulses using complex frequencies • Asymptotic analysis is required to determine the feasibility of the theory

More Related