Super resolution, time reversal focusing using path extending properties of scatterers

Abstract

Time reversal is a process where a sound is recorded at a specific location, temporally reversed, and then played back to focus at the same location as the original recording. This paper will focus on the use of scatterers placed within a wavelength (the assumed near field) of time reversal focusing to achieve super resolution. A one-dimensional pipe system is used with extensions that simulate the increased path length due to diffraction around an object. This longer path length, if unaccounted for, leads to a decrease in the effective wave speed. As the effective wave speed decreases, the spatial extent of the focusing decreases, creating super resolution. Although previous work refers to the scattering property of the medium as key to achieving super resolution, this paper shows that the path extending properties of scatterers only show super resolution when the distance between measurements does not take into account the longer path length traveled around scatterers. Consequently, it supports the understanding that resonances within the medium are more likely to yield super resolution focusing than using passive scattering.