Characterization of thin layers in multi-layered structures: On the problem of finding starting values for numerical solutions to inverse problems

Several model-based techniques have been proposed for characterizing thin layers within multi-layered materials. One problem with these methods is that the models are non-linear with respect to the parameters. Hence, iterative numerical methods must be used estimating the model parameters, i.e. for solving the inverse problem based on measurements. For material structures where the propagation times through the individual layers are shorter than the duration of the transmitted ultrasound pulse, the received waveform will consist of several overlapping echoes. For the parameter estimation to work, good initial guesses of the times of flight are required, which are difficult to obtain due to the severe overlap of the echoes. In this paper we propose a filtering scheme, that compresses the transmitted pulse into a shorter pulse, thus enabling the echoes from within the material structure to be detected. The method is evaluated using simulations on a three-layered material for varying signal-to-noise conditions.