Gaussian beams and Legendre polynomials as invariants of the time reversal operator for a large rigid cylinder

Journal of the Acoustical Society of America

Volumn 120, Issue 5, 2006, Pages 2746-2754

  Aubry, Alexandre ^a   De Rosny, Julien ^a   Minonzio, Jean Gabriel ^a   Prada, Claire ^a   Fink, Mathias ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC FIELDS; ANTENNA ARRAYS; POLYNOMIALS; REMOTE SENSING; VECTORS;

DORT METHOD; GAUSSIAN MODES; RIGID CYLINDER; SINGULAR VALUE DECOMPOSITION;

GAUSSIAN NOISE (ELECTRONIC);

ACOUSTICS; ARTICLE; DECOMPOSITION; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MODEL; NORMAL DISTRIBUTION; PRIORITY JOURNAL; REMOTE SENSING; TECHNIQUE; TRANSDUCER;

EID: 33750293356     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.2357700     Document Type: Article

References (22)

1. C. Prada and M. Fink, " Eigenstates of the time reversal operator: A solution to selective focusing in multiple-target media., " Wave Motion 20, 151-163 (1994).
2. E. Kerbrat, C. Prada, D. Cassereau, and M. Fink, " Imaging in the presence of grain noise using the decomposition of the time reversal operator., " J. Acoust. Soc. Am. 113, 1230-1240 (2003).
3. J.-L. Robert, M. Burcher, C. Cohen-Bacrie, and M. Fink, " Time reversal operator decomposition with focused transmission and robustness to speckle noise: Application to microcalcification detection., " J. Acoust. Soc. Am. 119, 3848-3859 (2006).
4. N. Mordant, C. Prada, and M. Fink, " Highly resolved detection and selective focusing in a waveguide using the d.o.r.t method., " J. Acoust. Soc. Am. 105, 2634-2642 (1999).
5. J. F. Lingevitch, H. C. Song, and W. A. Kuperman, " Time reversed reverberation focusing in a waveguide., " J. Acoust. Soc. Am. 111, 2609-2614 (2002).
6. C. F. Gaumond, D. M. Fromm, J. F. Lingevitch, R. Menis, G. F. Edelmann, D. C. Calvo, and E. Kim, " Demonstration at sea of the decomposition-of- the-time-reversal-operator technique., " J. Acoust. Soc. Am. 119, 976-990 (2006).
7. H. Tortel, G. Micolau, and M. Saillard, " Decomposition of the time reversal operator for electromagnetic scattering., " J. Electromagn. Waves Appl. 13, 687-719 (1999).
8. G. Micolau, M. Saillard, and P. Borderies, " Dort method as applied to ultrawideband signals for detection of buried objects., " IEEE Trans. Geosci. Remote Sens. 41, 1813-1820 (2003).
9. S. K. Lehman and A. J. Devaney, " Transmission mode time-reversal super-resolution imaging., " J. Acoust. Soc. Am. 113, 2742-2753 (2003).
10. D. H. Chambers and A. K. Gautesen, " Time reversal for a single spherical scatterer., " J. Acoust. Soc. Am. 109, 2616-2624 (2001).
11. J.-G. Minonzio, C. Prada, D. Chambers, D. Clorennec, and M. Fink, " Characterization of subwavelength elastic cylinders with the decomposition of the time-reversal operator: Theory and experiment., " J. Acoust. Soc. Am. 117, 789-798 (2005).
12. D. H. Chambers and J. G. Berryman, " Analysis of the time-reversal operator for a small spherical scatterer in an electromagnetic field., " IEEE Trans. Antennas Propag. 52, 1729-1738 (2004).
13. D. Chambers, " Analysis of the time reversal operator for scatterers of finite size., " J. Acoust. Soc. Am. 112, 411-419 (2002).
14. H. Zhao, " Analysis of the response matrix for an extended target., " SIAM J. Appl. Math. 64, 725-745 (2004).
15. S. Komilikis, C. Prada, and M. Fink, " Characterization of extended objects with the d.o.r.t. method., " IEEE Ultrasonics Symposium 20, 1401-1404 (1996).
16. C. Prada and M. Fink, " Separation of interfering acoustic scattered signals using the invariants of the time-reversal operator application to lamb waves characterization., " J. Acoust. Soc. Am. 104, 801-807 (1998).
17. G. V. Frisk and H. Uberall, " Creeping waves and lateral waves in acoustic scattering by large elastic cylinders., " J. Acoust. Soc. Am. 59, 46-54 (1976).
18. A. Derem, La diffusion acoustique (CEDOCAR, Paris, 1989), Chap., pp. 198-200.
19. R. D. Doolittle and H. Uberall, " Sound scattering by elastic cylindrical shells., " J. Acoust. Soc. Am. 39, 272-275 (1966).
20. J.-L. Rousselot, La diffusion acoustique (CEDOCAR, Paris, 1989), Chap., p. 351.
21. C. Webb and J. Jones, Handbook of Laser Technology and Applications-Volume 1: Principles (Institute of Physics, Philadelphia, 2004).
22. E. W. Weisstein, " Legendre polynomial., " From MathWorld-A Wolfram Web Resource, http://mathworld.wolfram.com/LegendrePolynomial.html.