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Inverse Source Problem

Inverse Source Problem . A.J. Devaney Department of Electrical and Computer Engineering Northeastern University Boston, MA 02115 tonydev2@aol.com , devaney@ece.neu.edu. Research supported by Delaware MURI. A.J. Devaney and Mei-Li, “ The inverse source problem in non-homogeneous

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Inverse Source Problem

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  1. Inverse Source Problem A.J. Devaney Department of Electrical and Computer Engineering Northeastern University Boston, MA 02115 tonydev2@aol.com , devaney@ece.neu.edu Research supported by Delaware MURI A.J. Devaney and Mei-Li, “The inverse source problem in non-homogeneous background media”, accepted to JOSAA AFOSR San Antonio Meeting

  2. E(r,), H(r,) j(r,), (r,) Inverse Source Problem E(r,), H(r,) Determine charge current distribution that radiates a prescribed field j(r,), (r,) Non-unique due to N.R. charge-current distributions Radome Determine charge current distribution that radiates a prescribed field in presence of known background structure and subject to “energy” constraints AFOSR San Antonio Meeting

  3. AFOSR San Antonio Meeting

  4. Radiation Problem Background potential Radiation Condition AFOSR San Antonio Meeting

  5. Inverse Source Problem Determine the source that generates a prescribed field everywhere outside the source region Determine the source that generates a prescribed radiation pattern Radiation pattern multipole expansion Determine the source that generates a prescribed set of multipole moments AFOSR San Antonio Meeting

  6. Non-uniqueness-N.R. Sources Pseudo-inverse: Minimize “source energy” Minimum energy source AFOSR San Antonio Meeting

  7. Free-space Case AFOSR San Antonio Meeting

  8. Multipole Expansion AFOSR San Antonio Meeting

  9. Free-space I.S.P. AFOSR San Antonio Meeting

  10. Eigenvalues tend to zero exponentially fast when l>k0a Stable source possible only if L k0a Source Energy AFOSR San Antonio Meeting

  11. AFOSR San Antonio Meeting

  12. AFOSR San Antonio Meeting

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  15. I.S.P. In a Non-Homogeneous Background • Motivation: • Most antennas include passive structures that • can be modeled this way • The radiation patterns generated by such “composite” • sources may have interesting properties Field dependent “effective” source AFOSR San Antonio Meeting

  16. Scattering Wave States AFOSR San Antonio Meeting

  17. Spherically Symmetrical Backgrounds Same as free space case with spherical Bessel functions replaced with the radial wave functions AFOSR San Antonio Meeting

  18. Inverse Problem Same as free space case with spherical Bessel functions replaced with the radial wave functions AFOSR San Antonio Meeting

  19. Minimum Energy Source Same as free space case with spherical Bessel functions replaced with the radial wave functions AFOSR San Antonio Meeting

  20. Piece-wise Constant Backgrounds AFOSR San Antonio Meeting

  21. Eigenvalues AFOSR San Antonio Meeting

  22. Eigenvalues tend to zero exponentially fast when l>k0a Stable source possible only if L k0a Source Energy AFOSR San Antonio Meeting

  23. AFOSR San Antonio Meeting

  24. Source Energy AFOSR San Antonio Meeting

  25. Future Work • Include source-field interaction constraints • Full EM case • Other examples • Planar backgrounds AFOSR San Antonio Meeting

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