Reconstructing transient acoustic radiation from an arbitrary object with a uniform surface velocity distribution

This paper presents the general formulations for reconstructing the transient acoustic field generated by an arbitrary object with a uniformly distributed surface velocity in free space. These formulations are derived from the Kirchhoff-Helmholtz integral theory that correlates the transient acoustic pressure at any field point to those on the source surface. For a class of acoustic radiation problems involving an arbitrarily oscillating object with a uniformly distributed surface velocity, for example, a loudspeaker membrane, the normal surface velocity is frequency dependent but is spatially invariant. Accordingly, the surface acoustic pressure is expressible as the product of the surface velocity and the quantity that can be solved explicitly by using the Kirchhoff-Helmholtz integral equation. This surface acoustic pressure can be correlated to the field acoustic pressure using the Kirchhoff-Helmholtz integral formulation. Consequently, it is possible to use nearfield acoustic holography to reconstruct acoustic quantities in entire three-dimensional space based on a single set of acoustic pressure measurements taken in the near field of the target object. Examples of applying these formulations to reconstructing the transient acoustic pressure fields produced by various arbitrary objects are demonstrated.