Reconstruction of the gradient field in the cross-section of an acoustic wave and its usefulness in processing acoustic wave fields

Abstract

This paper proposes a method of reconstructing the gradient field in a cross-section of the acoustic wave using the laser beam deflection tomography, then verifing that the simultaneous acquisitions of the relative acoustic pressure distribution and the gradient field can make the direct employment of Kirchhoff’s integral theorem feasible. Specifically, a position-sensitive detector (PSD) is used to sense the deflection of a laser beam impinging on a propagating acoustic wave. The deflection of the laser beam can be divided into two parts; one is in the plane that laser beams go through, and the other is perpendicular to the plane. Combining the tomographic results using the two parts of the deflection, the gradient field of the propagating acoustic wave in a cross-section is obtained, which is an extended version of beam deflection tomography. Based on the gradient of a wavefield along with the relative sound pressure distribution, Kirchhoff’s integral theorem can be directly employed to calculate and analyze the wavefield further, which was hardly achieved in the past due to the lack of dense gradient sensing regimes. To verify the usefulness, two experiments are conducted, whose results indicate that the densely and precisely acquired gradient field of an acoustic wave is useful in solving the problem of port and starboard ambiguity, and the problem of accurate near-field prediction can also be well addressed, which in a deeper sense benefit from the direct employment of Kirchhoff’s integral theorem in practical applications.