Wave Guide Imaging through Time Domain Topological Energy

Time Domain Topological Energy (TDTE), uses a measure of the reflected ultrasonic field on an array of transducers placed on the boundary of the imaged medium. Two numerical determinations (direct and adjoint problems) of the acoustical field inside a reference medium are then necessary to obtain the image by computing the topological energy. This technique comes from the field of shape optimisation and mathematical developments for Non Destructive Testing and have shown close links with Time Reversal (TR) concepts. TR mirrors have been employed for various applications in a wide number of situations including wave guides (WG) where very good refocalisation performances have been obtained with a reduced number of transducers instead of an array. Moreover recent works have enlighten that the reverberation properties of a WG allow to re-focalise using TR with only one transducer. For TDTE imaging we choose to model a single transducer placed at one end of a wave guide. The boundaries of the WG create virtual sources that can be understood as a virtual array of transducers. Results obtained numerically for imaging using both TDTE and one transducer in a wave guide with increasing complexity : a hard spherical object and a set of three identical objects placed at the angles of an equilateral triangle are presented and preliminary experimental results are discussed.