Spatial resolution of time-reversal mirrors in two-dimensional and three-dimensional free space environments

Ifanila Rakotoarisoa (1) , David Marx (1) , Christian Prax (1) , Vincent Valeau (1)

1 PPrime [Poitiers] - Institut Pprime [UPR 3346]

Time-reversal can be used to locate unknown acoustics sources in a medium at rest or in a flow. This method is based on the time-reversal invariance of the wave propagation equation. A series of time-reversal simulations has been performed with a "mirror" in two-dimensional and three-dimensional free space environments. The waves propagation is simulated by solving the linearized Euler's equations. The results permit to characterize the time-reversal method in terms of spatial resolution and localisation error by analyzing the focal spot width for each simulation. In this paper, mathematical expressions of the time-reversed pressure and approached formulas for the resolution are derived following the diffraction theory and the phase conjugation in two and three-dimensional cases. Numerical and theoretical results are then compared. The focal spot width is then fully determined by two ratios involving three parameters: the array-source distance, the array length and the wavelength.

Mots clés: Acoustics; Time-reversal; diffraction; localisation

Domaines: Acoustique [physics.class-ph]

Ifanila Rakotoarisoa, David Marx, Christian Prax, Vincent Valeau. Spatial resolution of time-reversal mirrors in two-dimensional and three-dimensional free space environments. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00811055⟩