Imaging of elastic wave guides interconnected by a junction

A method for imaging a structure composed of at least one wave guide connected to a junction, the structure supporting elastic wave guided propagation modes, the structure having at least one defect, the method comprising the following steps:

• providing a plurality of pairs of non-colocalized elastic wave sensors comprising transmitting sensors and receiving sensors,
• measuring with the plurality of pairs of non-colocalized elastic wave sensors, for at least one operating frequency, a plurality of signals propagating in the structure, the measured signals being arranged in a measurement matrix having dimensions equal to a number of transmitting sensors by a number of receiving sensors,
• determining with a processing unit a plurality of propagation modes guided by the structure,
• correcting with the processing unit the measured signals based on ultrasound signals measured or simulated for the same structure in the absence of any defect,
• converting with the processing unit the measurement matrix into a wave field scattering matrix U,
• determining with the processing unit, at each point of a sampling grid, a test vector F defining the structure without any defect, the components of the test vector F being the projections of a Green tensor from the defect-free domain onto the transverse functions of the guided propagation modes,
• applying with the processing unit a numerical inversion method to determine a vector H of modal components such that U.H=F at each point of a sampling grid,
• determining with the processing unit an image of the structure based on the vector H, and
• displaying the image on a screen and/or interface in response to the processing unit.