volume | PIER Journals

Abstract

The scattering problem of time-harmonic electromagnetic plane waves by an impedance and a dielectric ellipsoid is considered. A low-frequency formulation of the direct scattering problem using the Rayleigh approximation is described. Considering far-field data, an inverse electromagnetic scattering problem is formulated and studied. A finite number of measurements of the leading-order term of the electric far-field pattern in the low-frequency approximation leads to specifying the semi-axes of the ellipsoid. The orientation of the ellipsoid is obtained by using the Euler angles. Corresponding results for the sphere, spheroid, needle and disc can be obtained considering them as geometrically degenerate forms of the ellipsoid for suitable values of its geometrical parameters.

1. Athanasiadis, C., P. Martin, and I. G. Stratis, "On spherical-wave scattering by a spherical scatterer and related near-field inverse problems," IMA J. Appl. Math., Vol. 66, 539-549, 2001.
doi:10.1093/imamat/66.6.539

2. Athanasiadis, C., Wave Propagation Elements and Applications, HOU, 2015.

3. Athanasiadis, C. and N. Tsitsas, "Point-source excitation of a layered sphere: Direct and far-field inverse scattering problems," Quarterly Journal of Mechanics and Applied Mathematics, Vol. 61, 549-580, 2008.
doi:10.1093/qjmam/hbn017

4. Apostolopoulos, T., K. Kiriaki, and D. Polyzos, "The inverse scattering problem for a rigid ellipsoid in linear elasticity," Inverse Problems, Vol. 6, 1-9, 1990.
doi:10.1088/0266-5611/6/1/003

5. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd Ed., Springer, 1998.
doi:10.1007/978-3-662-03537-5

6. Dassios, G., "The inverse scattering problem for the soft ellipsoid," Journal of Mathematical Physics, Vol. 28, 2858-2862, 1987.
doi:10.1063/1.527684

7. Dassios, G. and K. Kiriaki, "Size, orientation, and thickness identification of an ellipsoidal shell," Workshop on Inverse Problems and Imaging, Glasgow 1989, Proceedings, 38-48, Glasgow, 1991.

8. Dassios, G. and R. Lucas, "Inverse scattering for the penetrable ellipsoid and ellipsoidal boss," Journal of the Acoustical Society of America, Vol. 99, 1877-1882, 1996.
doi:10.1121/1.415370

9. Dassios, G. and R. Lucas, "Electromagnetic imaging of ellipsoids and ellipsoidal bosses," Quarterly Journal of Mechanics and Applied Mathematics, Vol. 51, 413-426, 1998.
doi:10.1093/qjmam/51.3.413

10. Dassios, G. and R. Kleinman, Low Frequency Scattering, Oxford University Press, 2000.

11. Dassios, G., Ellipsoidal Harmonics: Theory and Applications, Cambridge University Press, 2012.
doi:10.1017/CBO9781139017749

12. Lucas, R. J., "An inverse problem in low-frequency scattering by a rigid ellipsoid," Journal of the Acoustical Society of America, Vol. 95, 2330-2333, 1994.
doi:10.1121/1.409868

13. Shifrin, E. I. and P. S. Shushpannikov, "Reconstruction of an ellipsoidal defect in anisotropic elastic solid, using results of one static test," Inverse Problems in Science and Engineering, Vol. 21, 781-800, 2013.
doi:10.1080/17415977.2012.738677

14. Vafeas, P., "Revisiting the low-frequency dipolar perturbation by an impenetrable ellipsoid in a conductive surrounding," Mathematical Problems in Engineering, Vol. 2017, 1-16, 2017.
doi:10.1155/2017/9420658

Dr. Evangelia S. Athanasiadou

Dr. Stefania Zoi

Dr. Ioannis Arkoudis