Fast topological imaging.

Mathematical optimization methods based on the topological sensitivity analysis have been used to develop innovative ultrasonic imaging methods. With a single illumination of the medium, they have proved experimentally to yield a lateral resolution comparable to classical multiple-illumination techniques. As these methods are based on the numerical simulations of two wave fields, they require extensive computation. A time-domain finite-difference scheme is usually used for that purpose. This paper presents the development of an experimental imaging method based on the topological sensitivity. The numerical cost is reduced by replacing the numerical simulations by simple mathematical operations between the radiation patterns of the array's transducers and the frequency-domain signals to be emitted. These radiation patterns are preliminary computed once and for all. They were obtained with a finite element model for the anisotropic elastodynamic case and with semi-analytical integrations for the acoustic case. Experimental results are presented for a composite material sample and for a prefractal network immersed in water. A lateral resolution below 2.5 times the wavelength is obtained with a single plane wave illumination. The method is also applied with multiple illuminations, so that objects hidden in complex media can be investigated.