Acoustic imaging in application to reconstruction of rough rigid surface with airborne ultrasound waves

Accurate reconstruction of the surface roughness is of high importance to various areas of science and engineering. One important application of this technology is for remote monitoring of open channel flows through observing its dynamic surface roughness. In this paper a novel airborne acoustic method of roughness reconstruction is proposed and tested with a static rigid rough surface. This method is based on the acoustic holography principle and Kirchhoff approximation which make use of acoustic pressure data collected at multiple receiver points spread along an arch. The Tikhonov regularisation and generalised cross validation technique are used to solve the underdetermined system of equations for the acoustic pressures. The experimental data are collected above a roughness created with a 3D printer. For the given surface, it is shown that the proposed method works well with the various number of receiver positions. In this paper, the tested ratios between the number of surface points at which the surface elevation can be reconstructed and number of receiver positions are 2.5, 5, and 7.5. It is shown that, in a region comparable with the projected size of the main directivity lobe, the method is able to reconstruct the spatial spectrum density of the actual surface elevation with the accuracy of 20%.