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

@article{citeulike:1177344, abstract = {The DORT method (French acronym for decomposition of the time reversal operator) is an active remote sensing technique using an array of antennas for the detection and localization of scatterers. This method is based on the singular value decomposition of the interelement response matrix. In this paper an analytical expression of the singular vectors due to the reflection from a large rigid cylinder is provided. Depending on the array aperture, two asymptotic regimes are described. It is shown that the singular vectors correspond to Hermite-Gaussian modes for large apertures and Legendre polynomials for small ones. Using perturbation theory, the corresponding singular values are deduced. Theoretical predictions are in good agreement with experimental results. \©2006 Acoustical Society of America}, author = {Aubry, Alexandre and de Rosny, Julien and Minonzio, Jean G. and Prada, Claire and Fink, Mathias }, citeulike-article-id = {1177344}, doi = {10.1121/1.2357700}, journal = {The Journal of the Acoustical Society of America}, keywords = {acoustics, inverse}, number = {5}, pages = {2746--2754}, posted-at = {2007-03-20 13:01:24}, priority = {2}, publisher = {ASA}, title = {Gaussian beams and Legendre polynomials as invariants of the time reversal operator for a large rigid cylinder}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=JASMAN000120000005002746000001\&idtype=cvips\&gifs=yes}, volume = {120}, year = {2006} }

TY - JOUR ID - citeulike:1177344 L3 - citeulike-article-id:1177344 TI - Gaussian beams and Legendre polynomials as invariants of the time reversal operator for a large rigid cylinder JF - The Journal of the Acoustical Society of America VL - 120 IS - 5 SP - 2746 EP - 2754 PB - ASA N2 - The DORT method (French acronym for decomposition of the time reversal operator) is an active remote sensing technique using an array of antennas for the detection and localization of scatterers. This method is based on the singular value decomposition of the interelement response matrix. In this paper an analytical expression of the singular vectors due to the reflection from a large rigid cylinder is provided. Depending on the array aperture, two asymptotic regimes are described. It is shown that the singular vectors correspond to Hermite-Gaussian modes for large apertures and Legendre polynomials for small ones. Using perturbation theory, the corresponding singular values are deduced. Theoretical predictions are in good agreement with experimental results. ©2006 Acoustical Society of America KW - acoustics KW - inverse AU - Aubry, Alexandre AU - de Rosny, Julien AU - Minonzio, Jean AU - Prada, Claire AU - Fink, Mathias PY - 2006/// UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JASMAN000120000005002746000001&idtype=cvips&gifs=yes ER -