In non-destructive evaluation (NDE) using ultrasound, a wave is emitted at the outer surface of the part under inspection and propagates through the material. At each discontinuity the incident beam meets, a wave is reflected and the receiver located on the surface of the part thus receives a succession of reflected waves. Thus, the received signal results from the interaction of the wave with the material and gives information on the discontinuities in the medium. The operator's goal is to find out, from the received signal, whether the part has defects and, if so, to determine their characteristics. In concrete terms, a discontinuity shows up in the measurements as an echo having a duration equivalent to the period of the incident wave. However, the wavelength is of the same order as or even longer than the distance between two discontinuities and the presence of two defects close together gives a single common echo. Deconvolution helps with the interpretation of the signals by getting around the lack of resolution of the measurements.We will start by presenting the difficulties involved in interpreting the measurements by means of an example of a weld evaluation using ultrasound. Then, the direct model will be introduced in the form of a convolution: the data is taken to be the result of the convolution between the discontinuities and a convolution kernel formed from the transmitted wave. When the waveform is known, it is possible to infer the discontinuities by applying the approaches already proposed in Chapter 5 concerning Chapter written by Stéphane GAUTIER, Frédéric CHAMPAGNAT and Jérôme IDIER.
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