Wave guide imaging through Time Domain Topological Energy

Time Domain Topological Energy (TDTE), uses the reflected ultrasonic field recorded by an array of transducers placed on the boundary of the inspected medium. Two numerical determinations (forward and adjoint problems) of the acoustical field inside a reference medium are necessary to compute an image. Topological Energy is defined as a variation of topological sensitivity or gradient and comes from the field of mathematical optimisation. Recent developments for Non-Destructive Testing have shown the analogy with Time Reversal concepts. Time Reversal mirrors have been employed for various applications in a wide number of situations including wave guides where very good re-focalization performances have been obtained with a reduced number of transducers instead of an array of transducers. Moreover recent works have enlightened that the reverberation properties of a wave guide allow to re-focalize using Time Reversal with only one transducer. For TDTE imaging a single transducer placed at one end of a wave guide has been modelled. The boundaries of the wave guide create virtual sources that can be understood as a virtual array of transducers. Numerical and experimental results are presented using TDTE and a single transducer in a wave guide for targets and conditions of increasing complexity.