volume | PIER Journals

Abstract

Various formulations of the inverse equivalent surface-source problem and corresponding solution approaches are discussed and investigated. Starting from the radiation integrals of electric and magnetic surface current densities, the probe-corrected inverse equivalent source formulation is set up together with different forms of side constraints such as the zero-field or Love condition. The linear systems of equations resulting from the discretized forms of these equations are solved by the normal residual (NR) and normal error (NE) systems of equations. As expected and as demonstrated by the solution of a variety of inverse equivalent surface-source problems, related to synthetic as well as realistic antenna near-field measurement data, it is found that the iterative solution of the NE equations allows for a better control of the solution error and leads in general to a slightly faster convergence. Moreover, the results show that the incorporation of the zero-field condition into the solution process is in general not beneficial, which is also supported by the structure of the NE systems of equations. If desired, Love surface current densities, or just fields in general, can more easily be computed in a post-processing step. The accuracy of the obtained near-fields and far-fields depends more on the stopping criterion of the inverse source solver than on the particular choice of the equivalent surface-source representation, where the zero-field condition may influence the stopping criterion in a rather unpredictable way.

1. Parini, C., S. F. Gregson, J. McCormick, and D. J. V. Rensburg, Theory and Practice of Modern Antenna Range Measurements, The Institution of Engineering and Technology, 2014.

2. Petre, P. and T. 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. Google Scholar

3. Petre, P. and T. K. Sarkar, "Planar near-field to far-field transformation using an array of dipole probes," IEEE Transactions on Antennas and Propagation, Vol. 42, No. 04, 534-537, Apr. 1994. Google Scholar

4. 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, 2007. Google Scholar

5. Quijano, J. L. A. and G. Vecchi, "Field and source equivalence in source reconstruction on 3D surfaces," Progress In Electromagnetics Research, Vol. 103, 67-100, 2010. Google Scholar

6. Quijano, J. L. A. and G. Vecchi, "Near- and very near-field accuracy in 3-D source reconstruction," IEEE Antennas and Wireless Propagation Letters, Vol. 9, 634-637, 2010. Google Scholar

7. Jorgensen, E., P. Meincke, and C. Cappellin, "Advanced processing of measured fields using field reconstruction techniques," European Conference on Antennas and Propagation, Rome, Italy, 2011. Google Scholar

8. Jorgensen, E., D. W. Hess, P. Meincke, O. Borries, and C. Cappellin, "Antenna diagnostics on planar arrays using a 3D source reconstruction technique and spherical near-field measurements," European Conference on Antennas and Propagation, Prague, Tzech Republic, 2012. Google Scholar

9. Kilic, E. and T. F. Eibert, "Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods," Journal of Computational Physics, Vol. 288, 131-149, 2015. Google Scholar

10. 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. Google Scholar

11. Eibert, T. F., D. Vojvodic, and T. B. Hansen, "Fast inverse equivalent source solutions with directive sources," IEEE Transactions on Antennas and Propagation, Vol. 64, 4713-4724, Nov. 2016. Google Scholar

12. Eibert, T. F. and T. B. Hansen, "Inverse-source algorithm for antenna-field transformations using the weak form of the combined-source condition," European Conference on Antennas and Propagation, Paris, France, 2017. Google Scholar

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

14. Persson, K., M. Gustafsson, and G. Kristensson, "Reconstruction and visualization of equivalent currents on a radome using an integral representation formulation," Progress In Electromagnetics Research B, Vol. 20, 65-90, 2010. Google Scholar

15. Persson, K., M. Gustafsson, G. Kristensson, and B. Widenberg, "Radome diagnostics --- source reconstruction of phase objects with an equivalent currents approach," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 4, 2041-2051, Apr. 2014. Google Scholar

16. Farouq, M., M. Serhir, and D. Picard, "Matrix method for far-field calculation using irregular near-field samples for cylindrical and spherical scanning surfaces," Progress In Electromagnetics Research B, Vol. 63, 35-48, 2015. Google Scholar

17. Farouq, M., M. Serhir, and D. Picard, "Antenna far-field assessment from near-field measured over arbitrary surfaces," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 12, 5122-5130, 2016. Google Scholar

18. Saad, Y., Iterative Methods for Sparse Linear Systems, 2nd Ed., Society for Industrial and Applied Mathematics, 2003.

19. Sarkar, T. 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 Antennas and Propagation, Vol. 47, No. 3, 1178-1185, 1999. Google Scholar

20. 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, 2009. Google Scholar

21. Eibert, T. F., Ismatullah, E. Kaliyaperumal, and C. H. Schmidt, "Inverse equivalent surface current method with hierarchical higher order basis functions, full probe correction and multilevel fast multipole acceleration (invited paper)," Progress In Electromagnetics Research, Vol. 106, 377-394, 2010. Google Scholar

22. Eibert, T. F., E. Kilic, C. Lopez, R. A. Mauermayer, O. Neitz, and G. Schnattinger, "Electromagnetic field transformations for measurements and simulations (invited paper)," Progress In Electromagnetics Research, Vol. 151, 127-150, 2015. Google Scholar

23. Alvarez, Y., F. Las-Heras, and M. R. Pino, "Acceleration of the sources reconstruction method via the fast multipole method," IEEE Antennas and Propagation International Symposium, San Diego, CA, USA, 2008. Google Scholar

24. Foged, L. J., L. Scialacqua, F. Saccardi, J. L. A. Quijano, and G. Vecchi, "Application of the dualequation equivalent-current reconstruction to electrically large structures by fast multipole method enhancement," IEEE Antennas and Propagation Magazine, Vol. 56, No. 5, 264-273, 2014. Google Scholar

25. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas and Propagation Magazine, Vol. 35, No. 3, 7-12, 1993. Google Scholar

26. Chew, W. C., J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, 2001.

27. Eibert, T. F., "A diagonalized multilevel fast multipole method with spherical harmonics expansion of the k-space integrals," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 2, 814-817, 2005. Google Scholar

28. Lopez, Y. A., M. R. Pino, and F. Las-Heras, "Application of the adaptive cross approximation algorithm to the sources reconstruction method," European Conference on Antennas and Propagation, Berlin, Germany, 2009. Google Scholar

29. Wang, Y., T. F. Eibert, and Z. Nie, "Adaptive cross approximation algorithm accelerated inverse equivalent current method for near-field antenna measurement," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 3, 1874-1883, Mar. 2019. Google Scholar

30. Zhao, K., M. N. Vouvakis, and J.-F. Lee, "The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems," IEEE Transactions on Electromagnetic Compatibility, Vol. 47, No. 4, 763-773, 2005. Google Scholar

31. Hansen, T. B., A. Paulus, and T. F. Eibert, "On the condition number of a normal matrix in near-field to far-field transformations," IEEE Transactions on Antennas and Propagation, Vol. 67, 2028-2033, Mar. 2019. Google Scholar

32. 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. Google Scholar

33. Kornprobst, J., R. A. M. Mauermayer, E. Kilic, and T. F. Eibert, "An inverse equivalent surface current solver with zero-field enforcement by left-hand side Calderon projection," European Conference on Antennas and Propagation, 1-4, Krakau, Polen, 2019. Google Scholar

34. Kong, J. A., Electromagnetic Wave Theory, 2nd Ed., John Wiley & Sons, 1990.

35. Mauermayer, R. A. M. and T. F. Eibert, "Fast irregular antenna field transformation above perfectly conducting ground planes," European Conference on Antennas and Propagation (EUCAP), Davos, Switzerland, 2016. Google Scholar

36. Eibert, T. F. and R. A. M. Mauermayer, "Near-field far-field transformations for automobile antenna measurements," Applied Computational Electromagnetics Society Conference, Denver, CO, USA, 2018. Google Scholar

37. Eibert, T. F. and R. A. M. Mauermayer, "Equivalent sources based near-field far-field transformation above dielectric half space," Annual Symposium of the Antenna Measurement Techniques Association (AMTA), Williamsburg, VA, USA, 2018. Google Scholar

38. Neitz, O., R. A. M. Mauermayer, Y. Weitsch, and T. F. Eibert, "A propagating plane-wave based near-field transmission equation for antenna gain determination from irregular measurement samples," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 8, 4230-4238, Aug. 2017. Google Scholar

39. Love, A. E. H., "The integration of the equations of propagation of electric waves," Philosophical Transactions of the Royal Society A, Vol. 197, No. 287–289, 1-43, 1901. Google Scholar

40. Schelkunoff, S., "Some equivalence theorems of electromagnetics and their application to radiation problems," Bell System Technical Journal, Vol. 15, No. 1, 92-112, 1936. Google Scholar

41. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, Wiley- IEEE Press, 1997.

42. Mautz, J. R. and R. F. Harrington, "A combined-source solution for radiation and scattering from a perfectly conducting body," IEEE Transactions on Antennas and Propagation, Vol. 27, No. 4, 445-454, Jul. 1979. Google Scholar

43. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 1, 409-418, 1982. Google Scholar

44. Kornprobst, J. and T. F. Eibert, "An accurate low-order discretization scheme for the identity operator in the magnetic field and combined field integral equations," IEEE Transactions on Antennas and Propagation, Vol. 66, 6146-6157, Nov. 2018. Google Scholar

45. Eibert, T. F. and D. Vojvodic, "Fast inverse equivalent current solutions with surface currents in complex space," URSI Electromagnetic Theory Symposium, Espoo, Finland, 2016. Google Scholar

46. Hansen, T. B., "Translation operator based on Gaussian beams for the fast multipole method in three dimensions," Wave Motion, Vol. 50, No. 5, 940-954, 2013. Google Scholar

47. Altair, FEKO, , 2019, [Online], Available: https://altairhyperworks.com/product/FEKO.

48. NSI-MI, Microwave test systems, , 2019, [Online], Available: https://www.nsi-mi.com/.

49. Rohde & Schwarz, HF907, , 2019, double-ridged waveguide antenna.

50. Jin, J.-M., Theory and Computation of Electromagnetic Fields, John Wiley & Sons, Inc., 2015.

51. Rengarajan, S. R. and Y. Rahmat-Samii, "The field equivalence principle: Illustration of the establishment of the non-intuitive null fields," IEEE Antennas and Propagation Magazine, Vol. 42, No. 4, 122-128, 2000. Google Scholar

52. Yaghjian, A. D., "Three-dimensional planar surface-current equivalence theorem with application to receiving antennas as linear differential operators," Radio Science, Vol. 37, No. 2, VIC 4–1-VIC 4–10, 2002. Google Scholar

Mr. Jonas Kornprobst

Dr. Raimund A. M. Mauermayer

Dr. Ole Neitz

Mr. Josef Knapp

Dr. Thomas F. Eibert