Nearfield acoustical holography – a Wigner function approach

Abstract

We propose to use Wigner transformation methods as a tool for propagating measured acoustic signals from and towards a source region. We demonstrate the usefulness of the approach both for source reconstruction purposes and as a stable numerical simulation tool with build-in filtering mechanisms. The starting point is a statistical description of the sound field in terms of spatial correlation functions. Using the concept of Wigner transformation – a half Fourier transform method, the correlation function can be associated with a phase space distribution, thus introducing direction or momentum information. A corresponding free-field propagator for Wigner function distributions is derived and the ray-limit of this propagator is discussed. Acoustic data are acquired in an experiment using an ‘acoustical camera’; the sound pressure emanating from a vibrating rectangular plate is measured on a 32 × 32 microphone array in coincidence, making it possible to get correlated data with relatively high resolution. Measurements and simulations are compared at different heights above the source plane. It is demonstrated that the Wigner function approach provides a stable tool to propagate correlation data. It is furthermore suitable for nearfield holography where the sound field is propagated back to the plate surface. The directional components encoded in the Wigner function can be used to read off the distance between the source and measurement plane on sub-wavelength scales.