Electromagnetic field transformations are important for electromagnetic simulations and for measurements. Especially for field measurements, the influence of the measurement probe must be considered, and this can be achieved by working with weighted field transformations. This paper is a review paper on weighted field transformations, where new information on algorithmic properties and new results are also included. Starting from the spatial domain weighted radiation integral involving free space Green's functions, properties such as uniqueness and the meaning of the weighting function are discussed. Several spectral domain formulations of the weighted field transformation integrals are reviewed. The focus of the paper is on hierarchical multilevel representations of irregular field transformations with propagating plane waves on the Ewald sphere. The resulting Fast Irregular Antenna Field Transformation Algorithm (FIAFTA) is a versatile and efficient transformation technique for arbitrary antenna and scattering fields. The fields can be sampled at arbitrary irregular locations and with arbitrary measurement probes without compromising the accuracy and the efficiency of the algorithm. FIAFTA supports different equivalent sources representations of the radiation or scattering object: 1) equivalent surface current densities discretized on triangular meshes, 2) plane wave representations, 3) spherical harmonics representations. The current densities provide for excellent spatial localization and deliver most diagnostics information about the test object. A priori information about the test object can easily be incorporated, too. Using plane wave and spherical harmonics representations, the spatial localization is not as good as with spatial current densities, but still much better than in the case of conventional modal expansions. Both far-field based expansions lead to faster transformations than the equivalent currents and in particular the orthogonal spherical harmonics expansion is a very attractive and robust choice. All three expansions are well-suited for efficient echo suppression by spatial filtering. Various new field transformation and new computational performance results are shown in order to illustrate some capabilities of the algorithm.
Thomas F. Eibert,
Raimund A. M. Mauermayer,
"Electromagnetic Field Transformations for Measurements and Simulations (Invited Paper)," Progress In Electromagnetics Research,
Vol. 151, 127-150, 2015. doi:10.2528/PIER14121105
6. Rumsey, V. H., "Reaction concept in electromagnetic theory," Physical Review, Vol. 94, No. 6, 1484-1494, 1954. doi:10.1103/PhysRev.94.1483
7. Richmond, J. H., "A reaction theorem and its application to antenna impedance calculation," IRE Trans. on Antennas and Propag., 515-520, Nov. 1961.
8. Harrington, R.-F., Field Computation by Moment Methods, IEEE Press, Piscataway, 1992.
9. Chew, W. C., J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House Publishers, 2001.
10. Yla-Oijala, P., "Calculation of CFIE impedance matrix elements with RWG and n × RWG functions," IEEE Trans. on Antennas and Propag., Vol. 51, No. 8, 1837-1846, 2003. doi:10.1109/TAP.2003.814745
11. Li, L. and T. F. Eibert, "A projection height independent adaptive radial-angular-R2 transformation for singular integrals," IEEE Trans. on Antennas and Propag., Vol. 62, No. 10, 5381-5386, 2014. doi:10.1109/TAP.2014.2344103
12. Araque Quijano, J. L. 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
13. Jorgensen, E., P. Meincke, and C. Cappellin, "Advanced processing of measured fields using field reconstruction techniques," European Conference on Antennas and Propagation, 3880-3884, Rome, Apr. 2011.
14. Kılıc, E. and T. F. Eibert, "A three-dimensional microwave imaging technique combining inverse equivalent current and finite element methods," XXXI URSI General Assembly and Scientific Symposium, Beijing, China, Aug. 2014.
15. Kılıc, 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. doi:10.1016/j.jcp.2015.02.004
16. Bucci, O. V., G. d’Elia, G. Leone, and R. Pierri, "Far-field pattern determination from the near-field amplitude on two surfaces," IEEE Trans. on Antennas and Propag., Vol. 38, No. 11, 1772-1779, 1990. doi:10.1109/8.102738
17. Isernia, T., G. Leone, and R. Pierri, "Radiation pattern evaluation from near-field intensities on planes," IEEE Trans. on Antennas and Propag., Vol. 44, No. 5, 701-710, 1996. doi:10.1109/8.496257
18. Schnattinger, G., C. Lopez, E. Kılı¸c, and T. F. Eibert, "Fast near-field far-field transformation for phaseless and irregular antenna measurement data," Advances in Radio Science, Vol. 12, 171-177, 2014. doi:10.5194/ars-12-171-2014
19. Lopez, C., R. A. M. Mauermayer, and T. F. Eibert, "Extending the plane wave based fast irregular antenna field transformation algorithm for amplitude-only data," European Conference on Antennas and Propagation, Lisbon, Portugal, Apr. 2015.
20. Yaghjian, A. D., "An overview of near-field antenna measurements," IEEE Trans. on Antennas and Propag., Vol. 34, No. 1, 30-45, 1986. doi:10.1109/TAP.1986.1143727
21. 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 Trans. on Antennas and Propag., Vol. 55, No. 12, 3460-3468, 2007. doi:10.1109/TAP.2007.910316
22. 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. on Antennas and Propag., Vol. 57, No. 4, 1178-1185, 2009. doi:10.1109/TAP.2009.2015828
23. 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," Progress In Electromagnetics Research, Vol. 106, 377-394, 2010. doi:10.2528/PIER10061604
24. Petre, P. and T. K. Sarkar, "Planar near-field to far-field transformation using an equivalent magnetic current approach," IEEE Trans. on Antennas and Propag., Vol. 40, No. 11, 1348-1356, 1992. doi:10.1109/8.202712
25. Eibert, T. F., "A diagonalized multilevel fast multipole method with spherical harmonics expansion of the k-space integrals," IEEE Trans. on Antennas and Propag., Vol. 53, No. 2, 814-817, 2005. doi:10.1109/TAP.2004.841310
26. 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 Propag. Intern. Symp., San Diego, CA, 2008.
27. Schmidt, C. H., M. M. Leibfritz, and T. F. Eibert, "Fully probe-corrected near-field far-field transformation employing plane wave expansion and diagonal translation operators," IEEE Trans. on Antennas and Propag., Vol. 56, No. 3, 737-746, 2008. doi:10.1109/TAP.2008.916975
28. Schmidt, C. H. and T. F. Eibert, "Multilevel plane wave based near-field far-field transformation for electrically large antennas in free-space or above material halfspace," IEEE Trans. on Antennas and Propag., Vol. 57, No. 5, 1382-1390, 2009. doi:10.1109/TAP.2009.2016699
29. Qureshi, M. A., C. H. Schmidt, and T. F. Eibert, "Adaptive sampling in multilevel plane wave based near-field far-field transformed planar near-field measurements," Progress In Electromagnetic Research, Vol. 126, 481-497, 2012. doi:10.2528/PIER12020804
30. Qureshi, M. A., C. H. Schmidt, and T. F. Eibert, "Efficient near-field far-field transformation for nonredundant sampling representation on arbitrary surfaces in near-field antenna measurements," IEEE Trans. on Antennas and Propag., Vol. 61, No. 4, 2025-2033, 2013. doi:10.1109/TAP.2012.2231932
31. Yinusa, K. and T. F. Eibert, "A multi-probe antenna measurement technique with echo suppression capability," IEEE Trans. on Antennas and Propag., Vol. 61, No. 10, 5008-5016, 2013. doi:10.1109/TAP.2013.2271495
32. Schnattinger, G. and T. F. Eibert, "Solution to the full vectorial 3D inverse source problem by multi-level fast multipole method inspired hierarchical disaggregation," IEEE Trans. on Antennas and Propag., Vol. 60, No. 7, 3325-3335, 2012. doi:10.1109/TAP.2012.2196946
33. Kılıc, E. and T. F. Eibert, "An inverse scattering technique based on finite element — Boundary integral method," Progress In Electromagnetics Research Symposium Abstracts, 777, Stockholm, Sweden, Aug. 12–15, 2013.
34. Qureshi, M. A., C. H. Schmidt, and T. F. Eibert, "Near-field error analysis for arbitrary scanning grids using fast irregular antenna field transformation algorithm," Progress In Electromagnetics Research B, Vol. 48, 197-220, 2013. doi:10.2528/PIERB12121502
35. Schnattinger, G., R. A. M. Mauermayer, and T. F. Eibert, "Monostatic radar cross section near-field far-field transformations by multilevel plane wave decomposition," IEEE Trans. on Antennas and Propag., Vol. 62, No. 8, 4259-4268, 2014. doi:10.1109/TAP.2014.2323429
36. Fritzel, T., A. Geise, C. H. Schmidt, H.-J. Steiner, T. F. Eibert, O. Wiedenmann, and M. Paquay, "Concept of a portable antenna measurement system for large-scale and multi-contour near-field measurements," 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements, ESA/ESTEC, Noordwijk, The Netherlands, 2013.
37. Bucci, O. M. and G. Franceschetti, "On the spatial bandwidth of scattered fields," IEEE Trans. on Antennas and Propag., Vol. 35, No. 12, 1445-1455, 1987. doi:10.1109/TAP.1987.1144024
38. Bucci, O. M., C. Gennarelli, and C. Savarese, "Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples," IEEE Trans. on Antennas and Propag., Vol. 46, No. 3, 351-359, 1998. doi:10.1109/8.662654
39. Bucci, , O. M. and C. Gennarelli, "Application of nonredundant sampling representation of electromagnetic fileds to NF-FF transformation techniques," International Journal of Antennas and Propagation, Vol. 2012, 1-14, 2011.
40. Gregson, S., J. McCormick, and C. Parini, Principles of Planar Near-field Antenna Measurements, IET Electromagnetic Waves, UK, 2007. doi:10.1049/PBEW053E_ch1
42. Laitinen, T., S. Pivnenko, J. M. Nielsen, and O. Breinbjerg, "Theory and practice of the FFT/matrix inversion technique for probe-corrected spherical near-field antenna measurements with higher-order probes," IEEE Trans. on Antennas and Propag., Vol. 58, No. 8, 2623-2631, 2010. doi:10.1109/TAP.2010.2050437
43. Hansen, T. B., "Spherical near-field scanning with higher-order probes," IEEE Trans. on Antennas and Propag., Vol. 59, No. 11, 4049-4059, 2011. doi:10.1109/TAP.2011.2164217
44. Hansen, T. B., "Exact Gaussian-beam theory for outgoing and standing spherical waves: Application to transmitting and receiving antennas," IEEE Trans. on Antennas and Propag., Vol. 60, No. 3, 1291-1302, 2012. doi:10.1109/TAP.2011.2180342
45. Chew, W. C., T. J. Cui, and J. M. Song, "A FAFFA-MLFMA algorithm for electromagnetic scattering," IEEE Trans. on Antennas and Propag., Vol. 50, No. 11, 1641-1649, 2002. doi:10.1109/TAP.2002.802162
46. Cui, T. J., W. C.Chew, G. Chen, and J. M. Song, "Efficient MLFMA, RPFMA, and FAFFA algorithms for EM scattering by very large structures," IEEE Trans. on Antennas and Propag., Vol. 52, No. 3, 759-770, 2004. doi:10.1109/TAP.2004.825491
47. Hansen, T. B., "Translation operator based on Gaussian beams for the fast multipole method in three dimensions," Wave Motion, Vol. 50, 940-954, 2013. doi:10.1016/j.wavemoti.2013.03.006
48. Tzoulis, A. and T. F. Eibert, "Efficient electromagnetic near-field computation by the multilevel fast multipole method employing mixed near-field/far-field translations," IEEE Antennas and Wireless Propagation Letters, Vol. 4, 449-452, 2005. doi:10.1109/LAWP.2005.860195
49. Eibert, T. F., "A multilevel fast spectral domain algorithm for electromagnetic analysis of infinite periodic arrays with large unit cells," Advances in Radio Science, Vol. 4, 111-115, 2006.
51. Saad, Y., Iterative Methods for Sparse Linear Systems, PWS, Boston, 1996.
52. Sarvas, J., "Performing interpolation and anterpolation entirely by fast Fourier transform in the 3-D multilevel fast multipole algorithm," SIAM J. Numer. Anal., Vol. 41, No. 6, 2180-2196, 2003. doi:10.1137/S0036142902405655
53. Jarvenpaa, S. and P. Yl¨a-Oijala, "A global interpolator with low sample rate for multilevel fast multipole algorithm," IEEE Trans. on Antennas and Propag., Vol. 61, No. 3, 1291-1300, 2013. doi:10.1109/TAP.2012.2231927
54. Jarvenpaa, S. and P. Yla-Oijala, "Multilevel fast multipole algorithm with global and local interpolators," IEEE Trans. on Antennas and Propag., Vol. 62, No. 9, 4716-4725, 2014. doi:10.1109/TAP.2014.2333056
55. Eibert, T. F., "Some scattering results computed by the hybrid finite element — Boundary integral — Multilevel fast multipole method," IEEE Antennas and Propag. Magazine, Vol. 49, No. 2, 61-69, Apr. 2007. doi:10.1109/MAP.2007.376638
57. Nearfield Systems Inc., "Antenna measurement solutions,", www.nearfield.com.
58. Schmidt, C. H., D. T. Schobert, and T. F. Eibert, "Electric dipole based synthetic data generation for probe-corrected near-field antenna measurements," European Conference on Antennas and Propagation, 3269-3273, 2011.