2002/06/06 by George Papanicolaou, Leonid Ryzhik, Papanicolaou, George +4
Engineering · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Geophysical Methods and Applications #Microwave Imaging and Scattering Analysis #Ultrasonics and Acoustic Wave Propagation #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0206095
arxiv created 2002/06/06 · openalex publication_date 2002/06/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When a signal is emitted from a source, recorded by an array of transducers, time reversed and re-emitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency, remote sensing regime, and show that, because of multiple scattering, in an inhomogeneous or random medium it can improve beyond the diffraction limit. We also show that the back-propagated signal from a spatially localized narrow-band source is self-averaging, or statistically stable, and relate this to the self-averaging properties of functionals of the Wigner distribution in phase space. Time reversal from spatially distributed sources is self-averaging only for broad-band signals. The array of transducers operates in a remote-sensing regime so we analyze time reversal with the parabolic or paraxial wave equation.