Experimental surface shape reconstruction using microphone arrays

The sound field scattered by a smooth rough surface, and recorded by multiple microphones, can often be modelled by means of an underdetermined system of equations, obtained from boundary integral equations resolved at the surface with Kirchhoff approximation. The same underdetermined system can be inverted, yielding an estimate of the surface shape. Regularisation techniques are applied to the inverse problem. In this work, the procedure is validated experimentally on a set of acoustically rigid surfaces. In contrast with previous tests, where a single microphone was used to scan a rough surface along an arch, in this study an array of up to 34 microphones arranged on a plane parallel to the surface has been used. Furthermore, multiple frequencies of excitation in the range 10-25 kHz have been tested simultaneously using a broadband source. Uncertainties involved in the measurements are discussed. In particular, the uncertainty associated with differences in the response between microphones has been addressed by means of a calibration performed in situ over a flat rigid surface. The plane array configuration is demonstrated to be an equally effective but potentially more versatile alternative to the curved array solution. The effects of the choice of frequency on the resolution and robustness of the reconstruction are highlighted.