Multi-view videogrammetry for the estimate of plate sound radiation

This paper explores the possibility of estimating the acoustic pressure field resulting from the vibrations of thin structures using photogrammetric techniques. In particular, the performance of measurement systems using two or more cameras to estimate the displacement of 3D markers placed on the surface of a plate are analyzed by simulation. The projection of the markers on the image plane of each camera is calculated assuming a perfectly calibrated system, in which the errors in the 3D reconstruction of the marker positions are substantially determined by the intrinsic pixellation intrinsic to the measurement process. The acoustic pressure in space is finally calculated, starting from the position of the markers, by means of the Rayleigh integral. The accuracy of the estimate is evaluated by varying the geometry of the cameras setup, their resolution and their number. The results presented show that the estimation of the acoustic radiation is substantially more accurate than the accuracy with which the vibration is estimated. The effect is due to the smoothing operation intrinsically linked to the Rayleigh integration procedure. This study demonstrates the effectiveness of optical systems with multiple, relatively low-cost low-resolution cameras for the measurement of the acoustic pressure field generated by flexural vibrations of distributed structures.