Superresolution and Duality for Time-Reversal of Waves in Self-Similar Media
arXiv:physics/0502124 · doi:10.1016/j.physleta.2005.05.030
Abstract
We analyze the time reversal of waves in a turbulent medium using the parabolic Markovian model. We prove that the time reversal resolution can be a nonlinear function of the wavelength and independent of the aperture. We establish a duality relation between the turbulence-induced wave spread and the time-reversal resolution which can be viewed as an uncertainty inequality for random media. The inequality becomes an equality when the wave structure function is Gaussian.