volume | PIER Journals

Abstract

A non-canonical inhomogeneous background medium is one whose Green's function cannot be obtained by an analytical method. Electromagnetic scattering from objects embedded in a non-canonical inhomogeneous background medium is very challenging because of the computational complexity with the calculation of its Green's function and the multiple scattering between objects and the background. This work applies the Diagonal Tensor Approximation (DTA) to calculate the scattering from arbitrary objects in a noncanonical inhomogeneous background. Previously, the DTA has only been applied to a canonical background such as a homogeneous or layered background media. This approach employs a numerical method to obtain all Green's functions required in the calculation; an accurate DTA is used to calculate the scattering properties. In order to reduce the large number of simulations, we employ the symmetry and reciprocity in the Green's function calculation. Furthermore, considering that most realistic imaging measurements are made through a voltage probe usually represented by a wave port, we develop a method to convert the scattered field on the probe (the antenna) to the measured wave port voltage. Numerical results show that this method can obtain accurate scattering characteristics from arbitrary objects in a non-canonical inhomogeneous background medium in a microwave imaging system.

1. Harrington, R. F., Field Computation by Moment Method, 1968.

2. Born, M. and E. Wolf, Principles of Optics, Pergamon, 1980.

3. Habashy, T. M., R. W. Groom, and B. R. Spies, "Beyond the born and Rytov approximations. A nonlinear approach to electromagnetic scattering," J. Geophys. Res., Vol. 98, 1759-1775, 1993.
doi:10.1029/92JB02324 Google Scholar

4. C., Torres-Verdin and T. M. Habashy, "Rapid 2.5-D forward modeling and inversion via a new nonlinear scattering approximation," Radio Sci., Vol. 29, 1051-1079, 1994.
doi:10.1029/94RS00974 Google Scholar

5. Zhang, M. S. and S. Fang, "Three-dimensinal quasi-linear electromagnetic inversion," Radio Sci., Vol. 31, 741-754, 1996.
doi:10.1029/96RS00719 Google Scholar

6. Zhang, M. S. and S. Fang, "Quasi-linear approximation in 3-D electromagnetic modeling," Geophysics, Vol. 61, 646-665, 1996.
doi:10.1190/1.1443994 Google Scholar

7. Zhang, M. S. and S. Fang, "Quasi-linear series in three-dimensinal electromagnetic modeling," Radio Sci., Vol. 32, 2167-2188, 1997.
doi:10.1029/97RS00050 Google Scholar

8. Song, L. P. and Q. H. Liu, "Fast three-dimensional electromagnetic nonlinear inversion in layered media with a novel scattering approximation," Inverse Problems, Vol. 20, 171-194, 2004.
doi:10.1088/0266-5611/20/6/S11 Google Scholar

9. Song, L.-P. and Q. H. Liu, "A new approximation to three-dimensional electromagnetic scattering," IEEE Geosci. Remote Sensing Lett., Vol. 2, No. 2, 238-242, April 2005.
doi:10.1109/LGRS.2005.846836 Google Scholar

10. Zhang, Z. Q. and Q. H. Liu, "Two nonlinear inverse methods for electromagnetic induction measurements," IEEE Trans. Geosci. Remote Sensing, Vol. 39, No. 6, 1331-1339, June 2001.
doi:10.1109/36.927456 Google Scholar

11. Cui, T. J., W. C. Chew, A. A. Alaeddin, and Y. H. Zhang, "Fast forward solvers for the low-frequency detection of buried dielectric objects," IEEE Trans. Geosci. Remote Sensing, Vol. 41, 2026-2036, 2003. Google Scholar

12. Miller, E. L. and A. S. Willsky, "Wavelet-based methods for the nonlinear inverse scattering problem using the extended born approximation," Radio Sci., Vol. 31, 51-65, 1996.
doi:10.1029/95RS03130 Google Scholar

13. Tseng, H. W., K. H. Lee, and A. Becker, "3D interpretation of electromagnetic data using a modified extended Born approximation," Geophysics, Vol. 68, 127-137, 2003.
doi:10.1190/1.1543200 Google Scholar

14. Liu, Q. H., Z. Q. Zhang, T. T. Wang, J. A. Bryan, G. A. Ybarra, L. W. Nolte, and W. T. Joines, "Active microwave imaging I: 2-D forwardand inverse scattering methods," IEEE Trans. Microwave Theory Tech., Vol. 50, 123-133, January 2002. Google Scholar

15. Yu, C., M. Q. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. H. Liu, "Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data," IEEE Trans. Microwave Theory Tech., Vol. 56, No. 4, 991-1000, 2008.
doi:10.1109/TMTT.2008.919661 Google Scholar

16. Li, F., Li, F., Q. H. Liu, and L.-P. Song, "Three-dimensional reconstruction of objects buried in layered media using Born and distorted Born iterative methods," IEEE Geosci. Remote Sensing Lett., Vol. 1, No. 2, 107-111, 2004.
doi:10.1109/LGRS.2004.826562 Google Scholar

17. Abubakar, A., P. M. van den Berg, and J. T. Fokkema, "Towards non-linear inversion for characterization of time-lapse phenomena through numerical modeling," Geophys. Prospect., Vol. 51, 285-293, 2003.
doi:10.1046/j.1365-2478.2003.00369.x Google Scholar

18. Yuan, M. Q., C. Yu., J. P. Stang, R. T. George, G. A. Ybarra, W. T. Joines, and Q. H. Liu, W. T. Joines, and Q. H. Liu, "Experiments and simulations of an antenna array for biomedical microwave imaging applications," URSI Meeting, San Diego, CA, July 2008. Google Scholar

19. Yu, C., M. Q. Yuan, J. P. Stang, J. E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. H. Liu, "Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data," IEEE Trans. Microwave Theory Tech., Vol. 56, No. 1, 991-1000, 2008. Google Scholar

20. Yu, C., M. Q. Yuan, and Q. H. Liu, "Reconstruction of 3D objects from multi-freqiency experimental data with a fast DBIM-BCG method," Inverse Problems , Vol. 25, Feb. 2009. Google Scholar

21. Gelius, L.-J., "Electromagnetic scattering approximations revisited," Progress In Electromagnetics Research, Vol. 76, 75-94, 2007.
doi:10.2528/PIER07062501 Google Scholar

22. Yu, C., M. Q. Yuan, Y. Zhang, J. Stang, R. T. George, G. A. Ybarra, W. T. Joines, and Q. H. Liu, "Microwave imaging in layered media: 3-D image reconstruction from experimental data," IEEE Trans. Antennas Propagat., Vol. 58, No. 2, February 2010. Google Scholar

23. Hernondez-Lopez, M. A. and M. Quintillan-Gonzalez, "Coupling and footprint numerical features for a bow-tie antenna array," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 6, 779-794, 2005.
doi:10.1163/1569393054069037 Google Scholar

24. Guo, B., Y. Wang, J. Li, P. Stoica, and R. Wu, "Microwave imaging via adaptive beamforming methods for breast cancer detection," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 1, 53-63, 2006.
doi:10.1163/156939306775777350 Google Scholar

25. Yu, J., M. Yuan, and Q. H. Liu, "A wideband half oval patch antenna for breast imaging," Progress In Electromagnetics Research, Vol. 98, 1-13, 2009.
doi:10.2528/PIER09090304 Google Scholar

26. Gwarek, W. and M. Celuch-Marcysiak, "Wide-band S-parameter extraction form FDTD simulations for propagating and evanescent modes in inhomogenous guides," IEEE Trans. Microwave Theory Tech., Vol. 51, No. 8, 1920-1928, August 2003.
doi:10.1109/TMTT.2003.815265 Google Scholar

27. Chew, W. C. and Q. H. Liu, "Inversion of induction tool measurements using the distorted Born iterative method and CGFFHT," IEEE Trans. Geosci. Remote Sensing, Vol. 32, 878-884, July 1994. Google Scholar

28. Newman, G. A., "Cross well electromagnetic inversion using integral and differential equations," Geophysics, Vol. 60, 899-910, 1995.
doi:10.1190/1.1443825 Google Scholar

29. Torres-Verdin, C. and T. M. Habashy, "A two-step linear inversion of two-dimensional electrical conductivity," IEEE Trans. Antennas Propagat., Vol. 43, 405-415, 1995.
doi:10.1109/8.376039 Google Scholar

30. Van den Berg, P. M., M. van der Horst, and , "Nonlinear inversion in induction logging using the modified gradient method," Radio Sci., Vol. 30, 1355-1369, 1995.
doi:10.1029/95RS01764 Google Scholar

31. Howard, Jr., A. Q., W. C. Chew, and M. C. Moldoveanu, "A new correction to the born approximation," IEEE Trans. Geosci. Remote Sensing, Vol. 28, 394-399, May 1990.
doi:10.1109/36.54365 Google Scholar

Dr. Mengqing Yuan

Prof. Qing Huo Liu