Enhanced Resolution in Structured Media

The aim of this paper is to prove that we can achieve a resolution enhancement in detecting a target inclusion if it is surrounded by an appropriate structured medium. The physical notions of resolution and focal spot are revisited. Indeed, the resolution enhancement is estimated in terms of the material parameters of the structured medium.

[1]  Yves Capdeboscq,et al.  A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction , 2003 .

[2]  Marco Avellaneda,et al.  Optimal bounds and microgeometries for elastic two-phase composites , 1987 .

[3]  H. Ammari,et al.  Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell equations , 2001 .

[4]  A. Devaney A filtered backpropagation algorithm for diffraction tomography. , 1982, Ultrasonic imaging.

[5]  Liliana Borcea,et al.  Edge Illumination and Imaging of Extended Reflectors , 2008, SIAM J. Imaging Sci..

[6]  M. Avellaneda,et al.  Compactness methods in the theory of homogenization , 1987 .

[7]  Eric Sonnendrücker,et al.  Lectures on parameter identification , 2003 .

[8]  M. Vogelius,et al.  Gradient Estimates for Solutions to Divergence Form Elliptic Equations with Discontinuous Coefficients , 2000 .

[9]  L. Nikolova,et al.  On ψ- interpolation spaces , 2009 .

[10]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[11]  G. Milton The Theory of Composites , 2002 .

[12]  M. Vogelius,et al.  Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogen , 2000 .

[13]  Graeme W. Milton,et al.  Theory of Composites. Cambridge Monographs on Applied and Computational Mathematics , 2003 .

[14]  F. Murat,et al.  Compacité par compensation , 1978 .

[15]  Eric Bonnetier,et al.  An asymptotic formula for the voltage potential in a perturbed ε-periodic composite medium containing misplaced inclusions of size ε , 2006, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[16]  Metin Öztürk,et al.  Univalent harmonic mappings , 1996 .

[17]  A K Louis,et al.  Locating radiating sources for Maxwell's equations using the approximate inverse , 2008 .

[18]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[19]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[20]  H. Ammari,et al.  Reconstruction of Small Inhomogeneities from Boundary Measurements , 2005 .

[21]  N. Meyers An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations , 1963 .

[22]  Josselin Garnier,et al.  Wave Propagation and Time Reversal in Randomly Layered Media , 2007 .

[23]  T. D. Mast,et al.  Focusing and imaging using eigenfunctions of the scattering operator. , 1997, The Journal of the Acoustical Society of America.

[24]  ANYAN,et al.  Estimates for Elliptic Systems from Composite Material , 2003 .

[25]  A.J. Devaney Time reversal imaging of obscured targets from multistatic data , 2005, IEEE Transactions on Antennas and Propagation.

[26]  D. Owen Handbook of Mathematical Functions with Formulas , 1965 .

[27]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[28]  Mathias Fink,et al.  Eigenmodes of the time reversal operator: a solution to selective focusing in multiple-target media , 1994 .

[29]  P. Bassanini,et al.  Elliptic Partial Differential Equations of Second Order , 1997 .

[30]  Habib Ammari,et al.  An Introduction to Mathematics of Emerging Biomedical Imaging , 2008 .

[31]  Michael Vogelius,et al.  Identification of conductivity imperfections of small diameter by boundary measurements. Continuous , 1998 .

[32]  Steven Kusiak,et al.  The scattering support , 2003 .

[33]  G. Alessandrini,et al.  Univalent σ-Harmonic Mappings , 2001 .

[34]  G. Lerosey,et al.  Focusing Beyond the Diffraction Limit with Far-Field Time Reversal , 2007, Science.

[35]  G. Lerosey,et al.  Time reversal of electromagnetic waves. , 2004, Physical review letters.

[36]  P. Anselone,et al.  Collectively Compact Operator Approximation Theory and Applications to Integral Equations , 1971 .