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Inverse scattering from an orthotropic medium. (English) Zbl 0885.35143
The authors consider the scattering of time harmonic electromagnetic waves by a two-dimensional orthotropic medium with constant dielectric. In the first part, they study the direct problem by boundary integral equation methods. The fundamental solution and the single- and double-layer potentials are constructed via transformation to the classical Helmholtz equation. The second part is devoted to the inverse scattering problem. This is the problem to determine the refractive index from measurements of the far field pattern. A uniqueness result is proven and a numerical method for the reconstruction of the index of refraction is proposed. Some numerical results demonstrate advantages and disadvantages of the method.

35R30Inverse problems for PDE
35Q60PDEs in connection with optics and electromagnetic theory
35P25Scattering theory (PDE)
Full Text: DOI
[1] Colton, D.; Erbe, C.: Spectral theory for the magnetic far field operator in an orthotropic medium. Nonlinear problems in applied mathematics, 96-103 (1996) · Zbl 0886.35167
[2] Colton, D.; Kirsch, A.: A simple method for solving inverse scattering problems in the resonance region. Inverse problems 12, 383-393 (1996) · Zbl 0859.35133
[3] Colton, D.; Kress, R.: Integral equation methods in scattering theory. (1983) · Zbl 0522.35001
[4] Colton, D.; Kress, R.: Inverse acoustic and electromagnetic scattering theory. (1992) · Zbl 0760.35053
[5] D. Colton, P. Monk, A linear sampling method for the detection of leukemia using microwaves. SIAM J. Applied Math., to appear. · Zbl 0907.92014
[6] Dautry, R.; Lions, J. L.: 4th ed. Mathematical analysis and numerical methods for science and technology. Mathematical analysis and numerical methods for science and technology 1 (1990)
[7] Isakov, V.: On uniqueness in the inverse transmission scattering problem. Comm. partial differential equations 15, 1565-1587 (1990) · Zbl 0728.35148
[8] Kirsch, A.; Kress, R.: Uniqueness in inverse obstacle scattering. Inverse problems 9, 285-299 (1993) · Zbl 0787.35119
[9] Kress, R.: Linear integral equations. (1989) · Zbl 0671.45001
[10] Kress, R.; Roach, G. F.: Transmission problems for the Helmholtz equation. J. math. Phys. 19, 1433-1437 (1978) · Zbl 0433.35017
[11] Maue, A. W.: Über die formulierung eines allgemeinen beugungsproblems durch eine integralgleichung. Z. physik 126, 601-618 (1949) · Zbl 0033.14101
[12] Miranda, C.: Partial differential equations of elliptic type. (1970) · Zbl 0198.14101
[13] R. Potthast, Electromagnetic scattering from an orthotropic medium, submitted for publication. · Zbl 0980.78004
[14] R. Potthast, Integral equation methods in electromagnetic scattering from an anisotropic medium, submitted for publication. · Zbl 1054.78014
[15] Vekua, I. N.: New methods for solving elliptic equations. (1967) · Zbl 0146.34301