Simultaneous reconstruction of the thicknesses of a layered medium: The inverse problem
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The objective of this work is to measure the acoustical properties of individual layers, particularly the individual layer thicknesses, in a multi-layered medium. The layered medium in this study was a laminated plate consisting of three metallic layers. The theoretical model for the transmission of a longitudinal wave through the layered medium was obtained by using the well-known T-matrix approach. A multi-parameter inversion scheme was developed. Experiments were conducted on several commercially available three-layered metallic specimens using transducers of different center-frequencies. Sensitivity analysis was performed and errors for the measurements were estimated from the 3-D error surface plot. Good agreement between the ultrasonic measurement and direct microscopic measurement of the thicknesses was observed for all the specimens tested.