volume | PIER Journals

Abstract

In this paper an inverse source problem is investigated. The measurement set-up is a reflector antenna covered by a radome. Equivalent currents are reconstructed on a surface shaped as the radome in order to diagnose the radome's interaction with the radiated field. To tackle this inverse source problem an analysis of a full-wave integral representation, with the equivalent currents as unknowns, is used. The extinction theorem and its associated integral equation ensure that the reconstructed currents represent sources within the radome. The axially symmetric experimental set-up reduces the computational complexity of the problem. The resulting linear system is inverted by using a singular value decomposition. We visualize how the presence of the radome alters the components of the equivalent currents. The method enables us to determine the phase shift of the field due to the transmission of the radome, i.e., the IPD (insertion phase delay). Also, disturbances due to defects, not observable in the measured near field, are localized in the equivalent currents.

1. Hansen, J. E., Spherical Near-Field Antenna Measurements, IEE Electromagnetic Waves Series, No. 26, Peter Peregrinus Ltd., Stevenage, UK, 1988.

2. Yaghjian, A. D., "An overview of near-field antenna measurements," IEEE Trans. Antennas Propagat., Vol. 34, No. 1, 30-45, January 1986. Google Scholar

3. Rahmat-Samii, Y., L. I. Williams, and R. G. Yaccarino, "The UCLA bi-polar planar-near-field antenna-measurement and diagnostics range," IEEE Antennas and Propagation Magazine, Vol. 37, No. 6, 16-35, December 1995. Google Scholar

4. Shifflett, J. A., "CADDRAD: A physical optics radar/radome analysis code for arbitrary 3D geometries," IEEE Antennas and Propagation Magazine, Vol. 6, No. 39, 73-79, 1997. Google Scholar

5. Andersson, M., "Software for analysis of radome performance," Proc. International Conference on Electromagnetics in Advanced Applications (ICEAA'05), 537-539, Torino, Italy, 2005. Google Scholar

6. Lee, J., E. M. Ferren, D. P. Woollen, and K. M. Lee, "Near-field probe used as a diagnostic tool to locate defective elements in an array antenna," IEEE Trans. Antennas Propagat., Vol. 36, No. 6, 884-889, 1988. Google Scholar

7. Rochblatt, D. J. and B. L. Seidel, "Microwave antenna holography," IEEE Trans. Microwave Theory Tech., Vol. 40, No. 6, 1294-1300, 1992. Google Scholar

8. Corey, L. E. and E. B. Joy, "On computation of electromagnetic ¯elds on planar surfaces from fields specified on nearby surfaces," IEEE Trans. Antennas Propagat., Vol. 29, No. 2, 402-404, 1981. Google Scholar

9. Friden, J., J., H. Isaksson, B. Hansson, and B. Thors, "Robust phase-retrieval for quick whole-body SAR assessment using dual plane amplitude-only data ," Electronics Letters, Vol. 45, No. 23, 1155-1157, 2009. Google Scholar

10. Marengo, E. A. and A. J. Devaney, "The inverse source problem of electromagnetics: Linear inversion formulation and minimum energy solution," IEEE Trans. Antennas Propagat., Vol. 47, No. 2, 410-412, Feb. 1999. Google Scholar

11. Nordebo, S., M. Gustafsson, and K. Persson, "Sensitivity analysis for antenna near-field imaging," IEEE Trans. Signal Process., Vol. 55, No. 1, 94-101, Jan. 2007. Google Scholar

12. Guler, M. G. and E. B. Joy, "High resolution spherical microwave holography," IEEE Trans. Antennas Propagat., Vol. 43, No. 5, 464-472, 1995. Google Scholar

13. Sten, J. C.-E. and E. A. Marengo, "Inverse source problem in the spheroidal geometry: Vector formulation," IEEE Trans. Antennas Propagat., Vol. 56, No. 4, 961-969, 2008. Google Scholar

14. Cappellin, C., O. Breinbjerg, and A. Frandsen, "Properties of the transformation from the spherical wave expansion to the plane wave expansion," Radio Sci., Vol. 43, No. 1, RS1012, 2008. Google Scholar

15. Cappellin, C., A. Frandsen, and O. Breinbjerg, "Application of the SWE-to-PWE antenna diagnostics technique to an offset reflector antenna," IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, 204-213, 2008. Google Scholar

16. Ziyyat, A., L. Casavola, D. Picard, and J. C. Bolomey, "Prediction of BTS antennas safety perimeter from NF to NF transformation: An experimental validation ," Proc. Antenna Measurement Techniques Association (AMTA), 22-26, Denver, US, 2001. Google Scholar

17. Soldovieri, F., C. Mola, R. Solimene, and R. Pierri, "Inverse source problem from the knowledge of radiated field over multiple rectilinear domains," Progress In Electromagnetics Research M, Vol. 8, 131-141, 2009. Google Scholar

18. Therond, F., J. C. Bolomey, N. Joachmowicz, and F. Lucas, "Electromagnetic diagnosis technique using spherical near-field probing ," Proc. EUROEM'94, 1218-1226, Bordeaux, France, 1994. Google Scholar

19. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, IEEE Press, New York, 1998.

20. Shore, R. A. and A. D. Yaghjian, Dual surface electric field integral equation, Air Force Research Laboratory Report, 2001.

21. Sarkar, T. K., A. Taaghol, and , "Near-field to near/far-field transformation for arbitrary near-field geometry utilizing an equivalent electric current and MoM ," IEEE Trans. Antennas Propagat., Vol. 47, No. 3, 566-573, Mar. 1999. Google Scholar

22. Laurin, J.-J., J.-F. Zurcher, and F. E. Gardiol, "Near-field diagnostics of small printed antennas using the equivalent magnetic current approach," IEEE Trans. Antennas Propagat., Vol. 49, No. 5, 814-828, 2001. Google Scholar

23. Las-Heras, F., M. R. Pino, S. Loredo, Y. Alvarez, and T. K. Sarkar, "Evaluating near-field radiation patterns of commercial antennas," IEEE Trans. Antennas Propagat., Vol. 54, No. 8, 2198-2207, 2006. Google Scholar

24. Las-Heras, F., B. Galocha, and Y. Alvarez, "On the sources reconstruction method application for array and aperture antennas diagnostics ," Microwave Opt. Techn. Lett., Vol. 51, No. 7, 1664-1668, 2009. Google Scholar

25. Eibert, T. F. and C. H. Schmidt, "Multilevel fast multipole accelerated inverse equivalent current method employing Rao-Wilton-Glisson discretization of electric and magnetic surface currents," IEEE Trans. Antennas Propagat., Vol. 57, No. 4, 1178-1185, 2009. Google Scholar

26. Quijano, J. L. A. and G. Vecchi, "Improved-accuracy source reconstruction on arbitrary 3-D surfaces," IEEE Antennas & Wireless Propagat. Lett., Vol. 8, 1046-1049, 2009. Google Scholar

27. Colton, D. and R. Kress, Integral Equation Methods in Scattering Theory, John Wiley & Sons, New York, 1983.

28. Strom, S., "Introduction to integral representations and integral equations for time-harmonic acoustic, electromagnetic and elastodynamic wave fields," Field Representations and Introduction to Scattering, Handbook on Acoustic, Electromagnetic and Elastic Wave Scattering, V. V. Varadan, A. Lakhtakia, and V. K. Varadan (eds.), Vol. 1, Ch. 2, 37-141, Elsevier Science Publishers,Amsterdam, 1991. Google Scholar

29. Persson, K., M. Gustafsson, and G. Kristensson, Reconstruction and visualization of equivalent currents on a radome using an integral representation formulation, Technical ReportLUTEDX/(TEAT-7184)/1-45/(2010), Lund University, Department of Electrical and Information Technology, P. O. Box 118, S-221 00 Lund, Sweden, 2010, http://www.eit.lth.se.

30. Silver, S., Microwave Antenna Theory and Design, Radiation Laboratory Series, Vol. 12, McGraw-Hill, New York, 1949.

31. Kleinman, R. E. and G. F. Roach, "Boundary integral equations for the three-dimensional Helmholtz equation," SIAM Review, Vol. 16, No. 2, 214-236, 1974. Google Scholar

32. Muller, C., "Foundations of the Mathematical Theory of Electromagnetic Waves," Springer-Verlag, Berlin, 1969. Google Scholar

33. Jones, D. S., Acoustic and Electromagnetic Waves, Oxford University Press, New York, 1986.

34. Nieto-Vesperinas, M., "Scattering and Diffraction in Physical Optics,", 2nd, World Scientific Publisher, Singapore, 2006. Google Scholar

35. Balanis, C. A., "Advanced Engineering Electromagnetics," John Wiley & Sons, New York, 1989. Google Scholar

36. Morita, N., N. Kumagai, and J. R. Mautz, "Integral Equation Methods for Electromagnetics," Artech House, Boston, London, 1990. Google Scholar

37. Poggio, A. J. and E. K. Miller, "Integral equation solutions of three-dimensional scattering problems," Computer Techniques for Electromagnetics, R. Mittra (ed.), Pergamon, New York, 1973. Google Scholar

38. Bondeson, A., T. Rylander, and P. Ingelstrom, Computational Electromagnetics, Springer-Verlag, Berlin, 2005. Google Scholar

39. Kress, R. and Linear Integral Equations, Springer-Verlag, Berlin Heidelberg, 1999, 2nd. Google Scholar

40. Mautz, J. R. and R. F. Harrington, "Radiation and scattering from bodies of revolution," Appl. Scientific Research, Vol. 20, No. 1, 405-435, 1969. Google Scholar

41. Andreasen, M., "Scattering from bodies of revolution," IEEE Trans. Antennas Propagat., Vol. 13, No. 2, 303-310, 1965. Google Scholar

42. Strang, G., Introduction to Applied Mathematics, Wellesley-Cambridge Press, Box 157, Wellesley, MA 02181, 1986.

43. Aster, R., B. Borchers, and C. Thurber, Parameter Estimation and Inverse Problems, Academic Press, New York, 2005.

44. Shore, R. A. and A. D. Yaghjian, "Dual-surface integral equations in electromagnetic scattering," IEEE Trans. Antennas Propagat., Vol. 53, No. 5, 1706-1709, 2005. Google Scholar

45. Persson, K. and M. Gustafsson, "Reconstruction of equivalent currents using a near-field data transformation --- with radome applications," Progress In Electromagnetics Research, Vol. 54, 179-198, 2005. Google Scholar

46. Balanis, C. A., Antenna Theory, 2nd Ed., John Wiley & Sons, New York, 1997.

47. Kozakoff, D. J., "Analysis of Radome-enclosed Antennas," Artech House, Boston, London, 1997. Google Scholar

48. Kong, J. A., "Electromagnetic Wave Theory," John Wiley & Sons. Google Scholar

49. Song, J. and W. Chew, "FMM and MLFMA in 3-D and fast Illinois solver code," Fast and Efficient Algorithms in Computational Electromagnetics, W. Chew, J.-M. Jin, E. Michielssen, and J. Song (eds.), 77-118, Artech House, 2001. Google Scholar

50. Persson, K. and M. Gustafsson, "Reconstruction of equivalent currents using the scalar surface integral representation,", Technical Report LUTEDX/(TEAT-7131)/1-25/(2005), Lund University Department of Electrical and Information Technology, P. O. Box 118, S-221 00 Lund, Sweden, 2005, http://www.eit.lth.se. Google Scholar

Dr. Kristin Persson

Dr. Mats Gustafsson

Professor Gerhard Kristensson