Although classical imaging is limited by the Rayleigh criterion, it has been demonstrated that subwavelength imaging of two point-like scatterers can be achieved with probing sensors arrays, even if the scatterers are located in the far field of the sensors. However, the role of noise is crucial to determine the resolution limit. This paper proposes a quantitative study of the influence of noise on the subwavelength resolution obtained with the DORT-MUSIC method. The DORT method, French acronym for decomposition of the time reversal operator, consists in studying the invariants of the time reversal operator. The method is combined here with the estimator MUSIC (MUltiple SIgnal Classification) to detect and image two close metallic wires. The microwaves measurements are performed between 2.6 GHz and 4 GHz. Two wires of λ/100 diameters separated by λ/6 are imaged and separated experimentally. To interpret this result in terms of noise level, the analytical expression of the eigenvectors of the time reversal operator perturbed by the noise is established. We then deduce the noise level above which the subwavelength resolution fails. Numerical simulations and experimental results validate the theoretical developments.
Julien de Rosny,
"Influence of Noise on Subwavelength Imaging of Two Close Scatterers Using Time Reversal Method: Theory and Experiments," Progress In Electromagnetics Research,
Vol. 98, 333-358, 2009. doi:10.2528/PIER09071004
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