PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 103 > pp. 67-100

FIELD AND SOURCE EQUIVALENCE IN SOURCE RECONSTRUCTION ON 3D SURFACES

By J. L. A. Quijano and G. Vecchi

Full Article PDF (728 KB)

Abstract:
This paper describes in detail different formulations of the inverse-source problem, whereby equivalent sources and/or fields are to be computed on an arbitrary 3-D closed surface from the knowledge of complex vector electric field data at a specified (exterior) surface. The starting point is the analysis of the formulation in terms of the Equivalence Principle, of the possible choices for the internal fields, and of their practical impact. Love's (zero interior field) equivalence is the only equivalence form that yields currents directly related to the fields on the reconstruction surface; its enforcement results in a pair of coupled integral equations. Formulations resulting in a single integral equation are also analyzed. The first is the single-equation, two-current formulation which is most common in current literature, in which no interior field condition is enforced. The single-current (electric or magnetic) formulation deriving from continuity enforcement of one field is also introduced and analyzed. Single-equation formulations result in a simpler implementation and a lower computational load than the dual-equation formulation, but numerical tests with synthetic data support the benefits of the latter. The spectrum of the involved (discretized) operators clearly shows a relation with the theoretical Degrees of Freedom (DoF) of the measured field for the dual-equation formulation that guarantees extraction of these DoF; this is absent in the single-equation formulation. Examples confirm that single-equation formulations do not yield Love's currents, as observed both with comparison with reference data and via energetic considerations. The presentation is concluded with a test on measured data which shows the stability and usefulness of the dual-equation formulation in a situation of practical relevance.

Citation:
J. L. A. Quijano and G. Vecchi, "Field and source equivalence in source reconstruction on 3D surfaces," Progress In Electromagnetics Research, Vol. 103, 67-100, 2010.
doi:10.2528/PIER10030309
http://www.jpier.org/PIER/pier.php?paper=10030309

References:
1. Alvarez, Y., F. Las-Heras, and M. R. Pino, "Reconstruction of equivalent currents distribution over arbitrary three-dimensional surfaces based on integral equation algorithms," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 12, 3460-3468, Dec. 2007.
doi:10.1109/TAP.2007.910316

2. Alvarez, Y., F. Las-Heras, M. R. Pino, and J. A. Lopez, Acceleration of the sources reconstruction method via the fast multipole method, IEEE Antennas and Propagation Society International Symposium, 2008. AP-S 2008 , 1-4, Jul. 2008.

3. Alvarez, Y., T. Sarkar, and F. Las-Heras, Improvement of the sources reconstruction techniques: Analysis of the svd algorithm and the rwg basis functions, IEEE Antennas and Propagation Society International Symposium, 5644-5647, Jun. 2007.

4. Araque, J. and G. Vecchi, "Removal of unwanted structural interactions from antenna measurements," IEEE Antennas and Propagation Society International Symposium, 2009. APSURSI'09, 1-4, Jun. 2009.
doi:10.1109/APS.2009.5171590

5. Araque, J. L. A. and G. Vecchi, "Improved-accuracy source reconstruction on arbitrary 3-D surfaces," IEEE Antennas and Wireless Propagation Letters, Vol. 8, 1046-1049, 2009.
doi:10.1109/LAWP.2009.2031988

6. Balanis, C. A., Antenna Theory: Analysis and Design, 3 Ed., Wiley-Interscience, Apr. 2005.

7. Bertero, M. and P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics Publising, 1998.

8. Blanch, S., R. G. Yaccarino, J. Romeu, and Y. Rahmat-Samii, Near-field to far-field transformation of bi-polar measurements by equivalent magnetic current approach, IEEE Antennas and Propagation Society International Symposium, 561-564, Baltimore MD, Jun. 1996.

9. Bucci, O. M., L. Crocco, and T. Isernia, "Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups ," J. Opt. Soc. Am. A, Vol. 16, No. 7, 1788-1798, 1999.
doi:10.1364/JOSAA.16.001788

10. Bucci, O. M. and G. Franceschetti, "On the spatial bandwidth of scattered fields," IEEE Transactions on Antennas and Propagation, Vol. 35, No. 12, 1445-1455, Dec. 1987.
doi:10.1109/TAP.1987.1144024

11. Bucci, O. M. and G. Franceschetti, "On the degrees of freedom of scattered fields," IEEE Transactions on Antennas and Propagation, Vol. 37, No. 7, 918-926, Jul. 1989.
doi:10.1109/8.29386

12. Bucci, O. M., C. Gennarelli, and C. Savarese, "Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples," IEEE Transactions on Antennas and Propagation, Vol. 46, No. 3, 351-359, Mar. 1998.
doi:10.1109/8.662654

13. Chew, W. C., Y. M. Wang, G. Otto, D. Lesselier, and J. C. Bolomey, "On the inverse source method of solving inverse scattering problems ," Inverse Problems, Vol. 10, No. 3, 547-553, 1994.
doi:10.1088/0266-5611/10/3/004

14. 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 Transactions on Antennas and Propagation, Vol. 57, No. 4, 1178-1185, Apr. 2009.
doi:10.1109/TAP.2009.2015828

15. Ergul, O. and L. Gurel, "Stabilization of integral-equation formulations for the accurate solution of scattering problems involving low-contrast dielectric objects," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 3, 799-805, Mar. 2008.
doi:10.1109/TAP.2008.916971

16. Vipiana, F., A. Polemi, S. Maci, and G. Vecchi, "A mesh-adapted closed-form regular kernel for 3D singular integral equations," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 6, 1687-1698, Jun. 2008.
doi:10.1109/TAP.2008.923334

17. Glisson, A., "An integral equation for electromagnetic scattering from homogeneous dielectric bodies ," IEEE Transactions on Antennas and Propagation, Vol. 32, No. 2, 173-175, Feb. 1984.
doi:10.1109/TAP.1984.1143279

18. Golub, G. H. and C. F. van Loan, Matrix Computations (Johns Hopkins Studies in Mathematical Sciences), 3rd Ed., The Johns Hopkins University Press, Oct. 1996.

19. Hansen, J. E., Spherical Near-field Antenna Measurements, Vol. 26, IEE Electromagnetic Waves Series, Stevenage Herts England Peter Peregrinus Ltd., 1988 .

20. Harrington, R. F., "Time Harmonic Electromagnetic Fields," IEEE Press, 2001.

21. Hsiao, G. C. and R. E. Kleinman, "Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 45, No. 3, 316-328, Mar. 1997.
doi:10.1109/8.558648

22. Las-Heras, F., Y. Alvarez, M. R. Pino, and M. Alvarez, Sources reconstruction techniques for the diagnosis and characterization of antennas of complex geometry , Proceedings of ICONIC, 182-187, Jun. 2007.

23. Las-Heras, F., M. R. Pino, S. Loredo, Y. Alvarez, and T. K. Sarkar, "Evaluating near-field radiation patterns of commercial antennas," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 8, 2198-2207, Aug. 2006.
doi:10.1109/TAP.2006.879190

24. Laurin, J. J., J. F. Zurcher, and F. Gardiol, "Near-field diagnostics of small printed antennas using the equivalent magnetic current approach ," IEEE Transactions on Antennas and Propagation, Vol. 49, No. 5, 814-828, May 2001.
doi:10.1109/8.929636

25. Leibfritz, M. M., F. M. Landstorfer, and T. F. Eibert, An equivalent source method to determine complex excitation levels of antenna arrays from near-field measurements, The Second European Conference on Antennas and Propagation, 2007. EuCAP 2007, 1-7, Nov. 2007.

26. Alvarez Lopez, Y., C. Cappellin, F. Las-Heras, and O. Breinbjerg, "On the comparison of the spherical wave expansion-to-plane wave expansion and the sources reconstruction method for antenna diangostics ," Progress In Electromagnetics Research, Vol. 87, 245-262, 2008.
doi:10.2528/PIER08092202

27. Lopez, Y. A., F. Las-Heras Andres, M. R. Pino, and T. K. Sarkar, "An improved super-resolution source reconstruction method," IEEE Transactions on Instrumentation and Measurement, Vol. 58, No. 11, 3855-3866, Nov. 2009.
doi:10.1109/TIM.2009.2020847

28. Marengo, E. A. and R. W. Ziolkowski, "Nonradiating and minimum energy sources and their fields: Generalized source inversion theory and applications," IEEE Transactions on Antennas and Propagation, Vol. 48, No. 10, 1553-1562, Oct. 2000.
doi:10.1109/8.899672

29. Marengo, E. A. and A. J. Devaney, "The inverse source problem of electromagnetics: Linear inversion formulation and minimum energy solution," IEEE Transactions on Antennas and Propagation, Vol. 47, No. 2, 410-412, Feb. 1999.
doi:10.1109/8.761085

30. Marengo, E. A., A. J. Devaney, and F. K. Gruber, "Inverse source problem with reactive power constraint," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 6, 1586-1595, Jun. 2004.
doi:10.1109/TAP.2004.829408

31. Martini, E., G. Carli, and S. Maci, "An equivalence theorem based on the use of electric currents radiating in free space," IEEE Antennas and Wireless Propagation Letters, Vol. 7, 421-424, 2008.
doi:10.1109/LAWP.2008.2001764

32. Marx, E., "Integral equation for scattering by a dielectric," IEEE Transactions on Antennas and Propagation, Vol. 32, No. 2, 166-172, Feb. 1984.
doi:10.1109/TAP.1984.1143285

33. Mohajer, M., S. Safavi-Naeini, and S. K. Chaudhuri, "Surface current source reconstruction for given radiated electromagnetic fields ," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 2, 432-439, Feb. 2010.
doi:10.1109/TAP.2009.2037696

34. Nadeau, B. and J. J. Laurin, "Extrapolations using vectorial planar near-field measurements for EMC," IEEE Int. Symp. Electromag. Compat., Denver CO, 924-928, Aug. 1998.

35. Persson, K. and M. Gustaffson, "Reconstruction of equivalent currents using a near-field data transformation --- With radome applications," Progress In Electromagnetics Research, Vol. 54, 179-198, 2005.
doi:10.2528/PIER04111602

36. Petre, P. and T. K. Sarkar, "Planar near-field to far-field transformation using an equivalent magnetic current approach," IEEE Transactions on Antennas and Propagation, Vol. 40, No. 11, 1348-1356, Nov. 1992.
doi:10.1109/8.202712

37. Petre, P. and T. K. Sarkar, Theoretical comparison of modal expansion and integral equation methods for near-field to far-field transformation, Asia-Pacific Microwave Conference, 1992. APMC'92, Vol. 2, 713-716, Aug. 1992.

38. Sarkar, T. K. and A. Taaghol, "Near-field to near/far-field trans-formation for arbitrary near-field geometry, utilizing an equivalent magnetic current," IEEE Transactions on Electromagnetic Compatibility, Vol. 38, No. 3, 536-542, Aug. 1996.
doi:10.1109/15.536088

39. Sarkar, T. K. and A. Taaghol, "Near-field to near/far-field transformation for arbitrary near-field geometry utilizing an equivalent electric current and mom," IEEE Transactions on IEEE Transactions on, Vol. 47, No. 3, 566-573, Mar. 1999.

40. Stratton, J. A. and L. J. Chu, "Diffraction theory of electromagnetic waves," Phys. Rev., Vol. 56, No. 1, 99-107, Jul. 1939.
doi:10.1103/PhysRev.56.99

41. Van Den Berg, P. M., E. Korkmaz, and A. Abubakar, "A constrained conjugate gradient method for solving the magnetic ¯eld boundary integral equation," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 6, 1168-1176, Jun. 2003.
doi:10.1109/TAP.2003.812275

42. Woodworth, M. B. and A. D. Yaghjian, "Derivation, application, and conjugate gradient solution of dual-surface integral equations or three-dimensional, multi-wavelength perfect conductors ," Progress In Electromagnetics Research, Vol. 5, 103-129, 1991.

43. Yla-Oijala, P. and M. Taskinen, "Well-conditioned muller formulation for electromagnetic scattering by dielectric objects," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 10, 3316-3323, Oct. 2005.
doi:10.1109/TAP.2005.856313


© Copyright 2014 EMW Publishing. All Rights Reserved