Linearized electromagnetic inversion of inhomogeneous media with dispersion

A frequency-domain inverse scattering problem for inhomogeneous media with spatially varying dispersion characteristics is considered. The standard classical dispersion law for an isotropic semi-conducting dielectric is presented in a generalized form with frequency and spatial dependencies separated. Subsequent discretization in the dispersion parameters space allows for an efficient multi-source, multi-frequency formulation of the problem. Numerical examples of two-dimensional linearized inversion in the neighbourhood of absorption lines and for media with relaxation are presented.

[1]  A. Oberafo.  Electrical conductivity and thermoelectric power of alloys in the As-Te and As40-xTe60-yInx+y molten systems , 1975 .

[2]  Anders Karlsson,et al.  Direct and inverse scattering from dispersive media , 1994 .

[3]  Gerhard Kristensson,et al.  Direct and inverse scattering in the time domain for a dissipative wave equation. II. Simultaneous reconstruction of dissipation and phase velocity profiles , 1986 .

[4]  Gerhard Kristensson,et al.  Direct and inverse scattering in the time domain for a dissipative wave equation. III. Scattering operators in the presence of a phase velocity mismatch , 1987 .

[5]  Frank Natterer,et al.  Inversion of the attenuated Radon transform , 2001 .

[6]  Peter M. van den Berg,et al.  Convergent Born series for large refractive indices , 1990 .

[7]  Tsili Wang,et al.  GPR imaging using the generalized Radon transform , 2000 .

[8]  Vadim A. Markel,et al.  Near-field tomography without phase retrieval. , 2001, Physical review letters.

[9]  Gerhard Kristensson,et al.  Direct and inverse scattering in the time domain for a dissipative wave equation. Part 1: Scattering operators , 1986 .

[10]  M. Nieto-Vesperinas,et al.  Direct solution to the inverse scattering problem for surfaces from near-field intensities without phase retrieval. , 1995, Optics letters.

[11]  K. Nugent,et al.  Quantitative phase‐amplitude microscopy I: optical microscopy , 2002, Journal of microscopy.

[12]  Tarek M. Habashy,et al.  Linear inverse problems in wave motion: nonsymmetric first-kind integral equations , 2000 .

[13]  Robert J Krueger,et al.  An electromagnetic inverse problem for dispersive media , 1985 .