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Far field model for time reversal and application to selective focusing on small dielectric inhomogeneities
1. | Inria (CORIDA Team), Villers-lès-Nancy, F-54600, France |
2. | Mathematics Department, US Naval Academy, 572C Holloway Road, Annapolis, MD 21402-5002, United States |
3. | Université de Lorraine, IECL, UMR 7502, Vandoeuvre-les-Nancy, F-54506, France |
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,", 55 of National Bureau of Standards Applied Mathematics Series, 55 (1964).
|
[2] |
H. Ammari, E. Iakovleva, D. Lesselier and G. Perrusson, Music-type electromagnetic imaging of a collection of small three-dimensional inclusions,, SIAM J. Sci. Comput., 29 (2007), 674.
doi: 10.1137/050640655. |
[3] |
H. Ammari, E. Iakovleva and S. Moskow, Recovery of small inhomogeneities from the scattering amplitude at a fixed frequency,, SIAM J. Math. Anal., 34 (2003), 882.
doi: 10.1137/S0036141001392785. |
[4] |
X. Antoine, B. Pinçon, K. Ramdani and B. Thierry, Far field modeling of electromagnetic time reversal and application to selective focusing on small scatterers,, SIAM J. Appl. Math., 69 (2008), 830.
doi: 10.1137/080715779. |
[5] |
T. Arens, A. Lechleiter and D. R. Luke, Music for extended scatterers as an instance of the factorization method,, SIAM J. Appl. Math., 70 (2009), 1283.
doi: 10.1137/080737836. |
[6] |
C. Ben Amar, N. Gmati, C. Hazard and K. Ramdani, Numerical simulation of acoustic time reversal mirrors,, SIAM J. Appl. Math., 67 (2007), 777.
doi: 10.1137/060654542. |
[7] |
L. Borcea, G. Papanicolaou and F. G. Vasquez, Edge illumination and imaging of extended reflectors,, SIAM J. Imaging Sciences, 1 (2008), 75.
doi: 10.1137/07069290X. |
[8] |
L. Borcea, G. Papanicolaou and F. G. Vasquez, Edge illumination and imaging of extended reflectors,, SIAM J. Imaging Sciences, 1 (2008), 75.
doi: 10.1137/07069290X. |
[9] |
D. H. Chambers and J. G. Berryman, Target characterization using decomposition of the time-reversal operator: Electromagnetic scattering from small ellipsoids,, Inverse Problems, 22 (2006), 2145.
doi: 10.1088/0266-5611/22/6/014. |
[10] |
Q. Chen, H. Haddar, A. Lechleiter and P. Monk, A sampling method for inverse scattering in the time domain,, Inverse Problems, 26 (2010).
doi: 10.1088/0266-5611/26/8/085001. |
[11] |
M. Cheney, The linear sampling method and the {MUSIC algorithm},, Inverse Problems, 17 (2001), 591.
doi: 10.1088/0266-5611/17/4/301. |
[12] |
D. Colton, H. Haddar and M. Piana, The linear sampling method in inverse electromagnetic scattering theory,, Inverse Problems, 19 (2003).
doi: 10.1088/0266-5611/19/6/057. |
[13] |
D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region,, Inverse Problems, 12 (1996), 383.
doi: 10.1088/0266-5611/12/4/003. |
[14] |
D. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory,", Springer-Verlag, (1998).
|
[15] |
A. Devaney, E. Marengo and F. Gruber, Time-reversal-based imaging and inverse scattering of multiply scattering point targets,, J. Acoust. Soc. Amer., 118 (2005), 3129.
doi: 10.1121/1.2042987. |
[16] |
A. Fannjiang, On time reversal mirrors,, Inverse Problems, 25 (2009).
doi: 10.1088/0266-5611/25/9/095010. |
[17] |
M. Fink, Acoustic time-reversal mirrors,, in, (2002), 17. Google Scholar |
[18] |
M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter and J.-L. Thomas, Time-reversed acoustics,, Rep. Prog. Phys., 63 (2000), 1933. Google Scholar |
[19] |
M. Fink and C. Prada, Acoustic time-reversal mirrors,, Inverse Problems, 17 (2001), 1761. Google Scholar |
[20] |
N. A. Gumerov and R. Duraiswami, Computation scattering from n spheres using multipole reexpansion,, J. Acoust. Soc. Amer., 112 (2002), 2688.
doi: 10.1121/1.1517253. |
[21] |
C. Hazard and K. Ramdani, Selective acoustic focusing using time-harmonic reversal mirrors,, SIAM J. Appl. Math., 64 (2004), 1057.
doi: 10.1137/S0036139903428732. |
[22] |
S. Hou, K. Solna and H. Zhao, Imaging of location and geometry for extended targets using the response matrix,, J. Comput. Phys., 199 (2004), 317.
doi: 10.1016/j.jcp.2004.02.010. |
[23] |
E. Iakovleva and D. Lesselier, Multistatic response matrix of spherical scatterers and the back-propagation of singular fields,, IEEE Trans. Antenna. Prop., 56 (2008), 825.
doi: 10.1109/TAP.2008.916913. |
[24] |
A. Kirsch, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator,, Inverse Problems, 14 (1998), 1489.
doi: 10.1088/0266-5611/14/6/009. |
[25] |
A. Kirsch, Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory,, Inverse Problems, 15 (1999), 413.
doi: 10.1088/0266-5611/15/2/005. |
[26] |
A. Kirsch, New characterizations of solutions in inverse scattering theory,, Appl. Anal., 76 (2000), 319.
doi: 10.1080/00036810008840888. |
[27] |
A. Kirsch, The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media,, Inverse Problems, 18 (2002), 1025.
doi: 10.1088/0266-5611/18/4/306. |
[28] |
R. Kress, Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering,, Quart. J. Mech. Appl. Math., 38 (1985), 323.
doi: 10.1093/qjmam/38.2.323. |
[29] |
G. Micolau, "Etude Théorique et Numérique de la Méthode de la Décomposition de L'opérateur de Retournement Temporel (D.O.R.T.) en Diffraction ÉlectromagnÉtique,", Ph.D thesis, (2001). Google Scholar |
[30] |
B. Pinçon and K. Ramdani, Selective focusing on small scatterers in acoustic waveguides using time reversal mirrors,, Inverse Problems, 23 (2007), 1.
doi: 10.1088/0266-5611/23/1/001. |
[31] |
C. Prada, S. Manneville, D. Spoliansky and M. Fink, Decomposition of the time reversal operator: Detection and selective focusing on two scatterers,, J. Acoust. Soc. Am., 99 (1996), 2067.
doi: 10.1121/1.415393. |
[32] |
E. Stein, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals,", Princeton University Press, (1993).
|
[33] |
B. Thierry, "Analyse et Simulations Numériques du Retournement Temporel et de la Diffraction Multiple,", Ph.D thesis, (2011). Google Scholar |
[34] |
H. Tortel, G. Micolau and M. Saillard, Decomposition of the time reversal operator for electromagnetic scattering,, J. Electromagn. Waves Appl., 13 (1999), 687.
doi: 10.1163/156939399X01113. |
[35] |
R. Wong, "Asymptotic Approximations of Integrals,", 34 of Classics in Applied Mathematics, 34 (2001).
doi: 10.1137/1.9780898719260. |
[36] |
A. Zaanen, "Linear Analysis. Measure and Integral, Banach and Hilbert Space, Linear Integral Equations,", Interscience Publishers Inc., (1953).
|
show all references
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,", 55 of National Bureau of Standards Applied Mathematics Series, 55 (1964).
|
[2] |
H. Ammari, E. Iakovleva, D. Lesselier and G. Perrusson, Music-type electromagnetic imaging of a collection of small three-dimensional inclusions,, SIAM J. Sci. Comput., 29 (2007), 674.
doi: 10.1137/050640655. |
[3] |
H. Ammari, E. Iakovleva and S. Moskow, Recovery of small inhomogeneities from the scattering amplitude at a fixed frequency,, SIAM J. Math. Anal., 34 (2003), 882.
doi: 10.1137/S0036141001392785. |
[4] |
X. Antoine, B. Pinçon, K. Ramdani and B. Thierry, Far field modeling of electromagnetic time reversal and application to selective focusing on small scatterers,, SIAM J. Appl. Math., 69 (2008), 830.
doi: 10.1137/080715779. |
[5] |
T. Arens, A. Lechleiter and D. R. Luke, Music for extended scatterers as an instance of the factorization method,, SIAM J. Appl. Math., 70 (2009), 1283.
doi: 10.1137/080737836. |
[6] |
C. Ben Amar, N. Gmati, C. Hazard and K. Ramdani, Numerical simulation of acoustic time reversal mirrors,, SIAM J. Appl. Math., 67 (2007), 777.
doi: 10.1137/060654542. |
[7] |
L. Borcea, G. Papanicolaou and F. G. Vasquez, Edge illumination and imaging of extended reflectors,, SIAM J. Imaging Sciences, 1 (2008), 75.
doi: 10.1137/07069290X. |
[8] |
L. Borcea, G. Papanicolaou and F. G. Vasquez, Edge illumination and imaging of extended reflectors,, SIAM J. Imaging Sciences, 1 (2008), 75.
doi: 10.1137/07069290X. |
[9] |
D. H. Chambers and J. G. Berryman, Target characterization using decomposition of the time-reversal operator: Electromagnetic scattering from small ellipsoids,, Inverse Problems, 22 (2006), 2145.
doi: 10.1088/0266-5611/22/6/014. |
[10] |
Q. Chen, H. Haddar, A. Lechleiter and P. Monk, A sampling method for inverse scattering in the time domain,, Inverse Problems, 26 (2010).
doi: 10.1088/0266-5611/26/8/085001. |
[11] |
M. Cheney, The linear sampling method and the {MUSIC algorithm},, Inverse Problems, 17 (2001), 591.
doi: 10.1088/0266-5611/17/4/301. |
[12] |
D. Colton, H. Haddar and M. Piana, The linear sampling method in inverse electromagnetic scattering theory,, Inverse Problems, 19 (2003).
doi: 10.1088/0266-5611/19/6/057. |
[13] |
D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region,, Inverse Problems, 12 (1996), 383.
doi: 10.1088/0266-5611/12/4/003. |
[14] |
D. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory,", Springer-Verlag, (1998).
|
[15] |
A. Devaney, E. Marengo and F. Gruber, Time-reversal-based imaging and inverse scattering of multiply scattering point targets,, J. Acoust. Soc. Amer., 118 (2005), 3129.
doi: 10.1121/1.2042987. |
[16] |
A. Fannjiang, On time reversal mirrors,, Inverse Problems, 25 (2009).
doi: 10.1088/0266-5611/25/9/095010. |
[17] |
M. Fink, Acoustic time-reversal mirrors,, in, (2002), 17. Google Scholar |
[18] |
M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter and J.-L. Thomas, Time-reversed acoustics,, Rep. Prog. Phys., 63 (2000), 1933. Google Scholar |
[19] |
M. Fink and C. Prada, Acoustic time-reversal mirrors,, Inverse Problems, 17 (2001), 1761. Google Scholar |
[20] |
N. A. Gumerov and R. Duraiswami, Computation scattering from n spheres using multipole reexpansion,, J. Acoust. Soc. Amer., 112 (2002), 2688.
doi: 10.1121/1.1517253. |
[21] |
C. Hazard and K. Ramdani, Selective acoustic focusing using time-harmonic reversal mirrors,, SIAM J. Appl. Math., 64 (2004), 1057.
doi: 10.1137/S0036139903428732. |
[22] |
S. Hou, K. Solna and H. Zhao, Imaging of location and geometry for extended targets using the response matrix,, J. Comput. Phys., 199 (2004), 317.
doi: 10.1016/j.jcp.2004.02.010. |
[23] |
E. Iakovleva and D. Lesselier, Multistatic response matrix of spherical scatterers and the back-propagation of singular fields,, IEEE Trans. Antenna. Prop., 56 (2008), 825.
doi: 10.1109/TAP.2008.916913. |
[24] |
A. Kirsch, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator,, Inverse Problems, 14 (1998), 1489.
doi: 10.1088/0266-5611/14/6/009. |
[25] |
A. Kirsch, Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory,, Inverse Problems, 15 (1999), 413.
doi: 10.1088/0266-5611/15/2/005. |
[26] |
A. Kirsch, New characterizations of solutions in inverse scattering theory,, Appl. Anal., 76 (2000), 319.
doi: 10.1080/00036810008840888. |
[27] |
A. Kirsch, The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media,, Inverse Problems, 18 (2002), 1025.
doi: 10.1088/0266-5611/18/4/306. |
[28] |
R. Kress, Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering,, Quart. J. Mech. Appl. Math., 38 (1985), 323.
doi: 10.1093/qjmam/38.2.323. |
[29] |
G. Micolau, "Etude Théorique et Numérique de la Méthode de la Décomposition de L'opérateur de Retournement Temporel (D.O.R.T.) en Diffraction ÉlectromagnÉtique,", Ph.D thesis, (2001). Google Scholar |
[30] |
B. Pinçon and K. Ramdani, Selective focusing on small scatterers in acoustic waveguides using time reversal mirrors,, Inverse Problems, 23 (2007), 1.
doi: 10.1088/0266-5611/23/1/001. |
[31] |
C. Prada, S. Manneville, D. Spoliansky and M. Fink, Decomposition of the time reversal operator: Detection and selective focusing on two scatterers,, J. Acoust. Soc. Am., 99 (1996), 2067.
doi: 10.1121/1.415393. |
[32] |
E. Stein, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals,", Princeton University Press, (1993).
|
[33] |
B. Thierry, "Analyse et Simulations Numériques du Retournement Temporel et de la Diffraction Multiple,", Ph.D thesis, (2011). Google Scholar |
[34] |
H. Tortel, G. Micolau and M. Saillard, Decomposition of the time reversal operator for electromagnetic scattering,, J. Electromagn. Waves Appl., 13 (1999), 687.
doi: 10.1163/156939399X01113. |
[35] |
R. Wong, "Asymptotic Approximations of Integrals,", 34 of Classics in Applied Mathematics, 34 (2001).
doi: 10.1137/1.9780898719260. |
[36] |
A. Zaanen, "Linear Analysis. Measure and Integral, Banach and Hilbert Space, Linear Integral Equations,", Interscience Publishers Inc., (1953).
|
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