Inverse source problem in an oblate spheroidal geometry

IEEE Transactions on Antennas and Propagation

Volumn 54, Issue 11, 2006, Pages 3418-3428

  Sten, Johan C E ^a   Marengo, Edwin A ^b  

^a VTT TECHNICAL RESEARCH CENTRE OF FINLAND   (Finland)

^b Northeastern University   (United States)

Author keywords

Inverse source problem; Minimum energy source; Nonradiating source; Spheroidal wave

Indexed keywords

COMPUTATIONAL GEOMETRY; DIRECTIONAL PATTERNS (ANTENNA); ELECTROMAGNETIC FIELD THEORY; INVERSE PROBLEMS;

HILBERT SPACE; MINIMUM ENERGY SOURCE; OBLATE SPHEROIDAL GEOMETRY;

ANTENNAS;

EID: 35349002652     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2006.884292     Document Type: Article

References (36)

1. E. A. Marengo and R. W. Ziolkowski, "Nonradiating and minimumenergy sources and their fields: Generalized source inversion theory and applications," IEEE Trans. Antennas Propag., vol. AP-48, pp. 1553-1562, 2000.
2. E. A. Marengo, A. J. Devaney, and R. W. Ziolkowski, "Inverse source problem and minimum-energy sources," J. Opt. Soc. Amer. A, vol. 17, pp. 34-45, 2000.
3. E. A. Marengo and A. J. Devaney, "The inverse source problem of electromagnetics: Linear inversion formulation and minimum energy solution," IEEE Trans. Antennas Propag., vol. 47, pp. 410-412, 1999.
4. N. Bleistein and J. K. Cohen, "Nonuniqueness in the inverse source problem in acoustics and electromagnetics," J. Math. Phys., vol. 18, pp. 194-201, 1977.
5. E. A. Marengo, A. J. Devaney, and R. W. Ziolkowski, "New aspects of the inverse source problem with far field data," J. Opt. Soc. Amer. A, vol. 16, pp. 1612-1622, 1999.
6. A. J. Devaney and E.Wolf, "Multipole expansions and plane-wave representations of the electromagnetic field," J. Math. Phys., vol. 15, pp. 234-244, 1974.
7. J. C.-E. Sten, "Reconstruction of electromagnetic minimum energy sources in a prolate spheroid," Radio Sci., vol. 39, 2004, RS2020.
8. A. J. Devaney, "Inverse source and scattering problems in ultrasonics," IEEE Trans. Sonics Ultrason., vol. 30, pp. 355-364, 1983.
9. R. P. Porter and A. J. Devaney, "Holography and the inverse source problem," J. Opt. Soc. Amer., vol. 72, pp. 327-330, 1982.
10. S. Nordebo and M. Gustafsson, "Statistical signal analysis for the inverse source problem of electromagnetics," IEEE Trans. Signal Processing, vol. 54, pp. 2357-2361, Jun. 2006.
11. D. A. B. Miller, "Communicating with waves between volumes: Evaluating orthogonal spatial channels and limits on coupling strengths," Appl. Optics, vol. 39, pp. 1681-1699, 2000.
12. A. S. Y. Poon, R. W. Brodersen, and D. N. C. Tse, "Degrees of freedom in multiple-antenna channels: A signal space approach," IEEE Trans. Info. Theory, vol. 51, pp. 523-536, 2005.
13. A. Brancaccio, G. Leone, and R. Pierri, "Information content of Born scattered fields: Results in the circular cylindrical case," J. Opt. Soc. Amer. A, vol. 15, pp. 1909-1917, 1998.
14. R. Pierri and F. Soldovieri, "On the information content of the radiated fields in the near zone over bounded domains," Inv. Probl., vol. 14, pp. 321-337, 1998.
15. L. W. Hanlen, A. J. Grant, and R. A. Kennedy, "On capacity for single-frequency spatial channels," in ITW 2004 Conf. Proc., San Antonio, TX, 2004, pp. 446-451.
16. J. C.-E. Sten, P. K. Koivisto, and A. Hujanen, "Limitations for the radiation Q for small antennas enclosed in a spheroidal volume: Axial polarisation," AEÜ Int. J. Electron. Comm., vol. 55, no. 3, pp. 198-204, 2001.
17. J. C.-E. Sten, "Radiation Q of a small antenna in an oblate spheroidal volume: Transverse-to-axis polarisation," AEÜ Int. J. for Electron. Comm., vol. 57, no. 3, pp. 201-205, 2003.
18. L. J. Chu, "Physical limitations of omni-directional antennas," J. Appl. Phys., vol. 19, pp. 1163-1175, 1948.
19. R. F. Harrington, "Effect of antenna size on gain, bandwidth and efficiency," J. Nat. Bur. Stand., vol. 64D, pp. 1-12, 1960.
20. R. E. Collin and S. Rothschild, "Evaluation of antenna Q," IEEE Trans. Antennas Propag., vol. AP-12, pp. 23-27, 1964.
21. R. L. Fante, "Quality factor of general ideal antennas," IEEE Trans. Antennas Propag., vol. AP-17, pp. 151-157, 1969.
22. J. D. Jackson, Classical Electrodynamics, 3rd ed. New York: Wiley, 1998.
23. F. G. Friedlander, "An inverse problem for radiation fields," Proc. Lond. Math. Soc., vol. 3, pp. 551-576, 1973.
24. A. J. Devaney and E. Wolf, "Radiating and nonradiating classical current distributions and the fields they generate," Phys. Rev. D., vol. 8, pp. 1044-1047, 1973.
25. E. A. Marengo, A. J. Devaney, and F. K. Gruber, "Inverse source problem with reactive power constraint," IEEE Trans. Antennas Propag., vol. AP-52, pp. 1586-1595, 2004.
26. M. Bertero, "Linear inverse and ill-posed problems," in Advances in Electronics and Electron Physics, P. W. Hawkes, Ed. New York: Academic Press, 1989, vol. 75, pp. 1-120.
27. E. A. Marengo and R. W. Ziolkowski, "Inverse source problem with regularity constraints: Normal solution and nonradiatin source components," Pure Appl. Optics: J. Optics A, vol, 2, pp. 179-187, 2000.
28. C. Flammer, Spheroidal Wave Functions. Stanford, CA: Stanford Univ. Press, 1957.
29. L.-W. Li, X.-K. Kang, and M.-S. Leong, Spheroidal Wave Functions in Electromagnetic Theory. New York: Wiley, 2002.
30. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover, 1972.
31. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. Burlington, MA: Elsevier Academic Press, 2005.
32. F. Soldovieri and R. Persico, "Reconstruction of an embedded slab from multifrequency scattered field data under the distorted Born approximation," IEEE Trans. Antennas Propag., vol. 52, pp. 2348-2356, 2004.
33. L.-W. Li, M.-S. Leong, T.-S. Yeo, P.-S. Kooi, and K.-Y. Tan, "Computation of spheroidal harmonics with complex arguments: A review with an algorithm," Phys. Rev. E, vol. 58, pp. 6792-6806, 1998.
34. E. A. Marengo, A. J. Devaney, and E. Heyman, "Analysis and characterization of scalar, ultrawideband volume sources and the fields they radiate - Part II: Square pulse excitation," IEEE Trans. Antennas Propag., vol. AP-46, pp. 243-250, 1998.
35. P. Wolfe, "Eigenfunctions of the integral equation for the potential of a charged disk," J. Math. Phys., vol. 12, no. 7, pp. 1215-1218, 1971.
36. J. Boersma and E. Danicki, "On the solution of an integral equation arising in potential problems for circular and elliptic disks," SIAM J. Appl. Math., vol. 53, pp. 931-941, 1993.