Far-field to Near-field Data Relations for the Inverse Electromagnetic Scattering Problem
Asian Journal of Research and Reviews in Physics,
Page 22-28
DOI:
10.9734/ajr2p/2021/v4i330144
Abstract
This paper considers (in general form) the problem of recovering information (size and material parameters) about the scattering object from far-field measurements. The order of solution and functions of each equation for the fields inside and outside the scattering object are discussed. Using well-known mathematical theorems, a simple equation has been derived that connects the far-field data on one side to the near-field data on the other side. Consequently, this equation has been used in an optimization procedure to find the parameters of the dielectric cylinder.
Keywords:
- Electromagnetic wave
- scattering
- inverse
- cylinder
- field
How to Cite
Abramov, A., & Yue, Y. (2021). Far-field to Near-field Data Relations for the Inverse Electromagnetic Scattering Problem. Asian Journal of Research and Reviews in Physics, 4(3), 22-28. https://doi.org/10.9734/ajr2p/2021/v4i330144
References
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Chen Z, Taflove A, Backman V. Photonic nanojet enhancement of backscattering of light by nanoparticles: A potential novel visible-light ultramicroscopy technique. Opt. Express. 2004;12:1214-1220.
Abramov A, Kostikov A, Yue Y. Scattering of electromagnetic wave by system of core / shell microsphere and nanoparticle. J. Adv. Electromagn. 2020;1(9):32-34.
Richmond J. Scattering by a dielectric cylinder of arbitrary cross section shape. IEEE trans. Ant. Prop. 1965;13(3):334-341.
Abramovits J, Stigan I. Handbook on special functions. Moscow: Nauka; 1979.
Borden B. Mathematical problems in radar inverse scattering. Inverse Problems. 2001;18(1):1-28.
Greene C, Wiebe P, Burczynski J, et al. Acoustical detection of high-density krill demersal layers in the submarine canyons off georges bank. Science. 1988; 241(4863):359-361.
Verschuur D, Berkhout A. Estimation of multiple scattering by iterative inversion, part ii: Practical aspects and examples. Geophysics. 1997;62(5):1596-1611.
Henriksson T, Joachimowicz N, Conessa C, et al. Quantitative microwave imaging for breast cancer detection using a planar 2.45 GHz system. IEEE Trans. Instrum. Meas. 2010;59(10):2691-2699.
Kagiwada H, Kalaba R, Timko S, et al. Associate memories for system identification: Inverse problems in remote sensing. Mathem. Comp. Modelling. 1990; 14:200–202.
Quarteroni A, Formaggia L, Veneziani A. Complex systems in biomedicine. New York: Springer; 2006.
Wang Y, Chew W. An iterative solution of the two-dimensional electromagnetic inverse scattering problem. Int. J. Imag. Syst. Techn. 1989;1:100-108.
Vogeler M. Reconstruction of the three-dimensional refractive index in electromagnetic scattering by using a propagation–backpropagation method. Inverse Problems. 2003;19:739-753.
Geffrin JM, Chaumet P, Eyraud C, et al. Electromagnetic three-dimensional reconstruction of targets from free space experimental data. Appl. Phys. Lett. 2008; 92:194103(1-4).
Kirsch A, Ritter S. A linear sampling method for inverse scattering from an open arc. Inverse Probl. 2000;16(1):89–105.
Agarwal K, Chen X, Zhong Y. A multipole-expansion based linear sampling method for solving inverse scattering problems. Opt. Expr. 2010;18(6):6366-6381.
Hagemann F, Arens T, Betcke T, et al. Solving inverse electromagnetic scattering problems via domain derivatives. Inverse Probl. 2019;35:084005.
Haddar H. The interior transmission problem for anisotropic Maxwell’s equations and its applications to the inverse problem. Math. Meth. Appl. Sci. 2004;27:2111–2129.
Thanh N, Beilina L, Klibanov M, et al. Reconstruction of the refractive index from experimental backscattering data using a globally convergent inverse method. SIAM J. Sci. Comput. 2014;36(3):B273–B293.
Taflove A, Hagness S. Computational electrodynamics: The finite-difference time-domain method. Boston: Artech House; 2005.
Chen Z, Taflove A, Backman V. Photonic nanojet enhancement of backscattering of light by nanoparticles: A potential novel visible-light ultramicroscopy technique. Opt. Express. 2004;12:1214-1220.
Abramov A, Kostikov A, Yue Y. Scattering of electromagnetic wave by system of core / shell microsphere and nanoparticle. J. Adv. Electromagn. 2020;1(9):32-34.
Richmond J. Scattering by a dielectric cylinder of arbitrary cross section shape. IEEE trans. Ant. Prop. 1965;13(3):334-341.
Abramovits J, Stigan I. Handbook on special functions. Moscow: Nauka; 1979.
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