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Nearfield acoustical holography – a Wigner function approach

Ramapriya, Deepthee Madenoor; Gradoni, Gabriele; Creagh, Stephen C.; Tanner, Gregor; Moers, Elise; Lop�z Arteaga, In�s


Deepthee Madenoor Ramapriya

Gabriele Gradoni

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Professor of Applied Mathematics

Elise Moers

In�s Lop�z Arteaga


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.


Ramapriya, D. M., Gradoni, G., Creagh, S. C., Tanner, G., Moers, E., & Lopéz Arteaga, I. (2020). Nearfield acoustical holography – a Wigner function approach. Journal of Sound and Vibration, 486, Article 115593.

Journal Article Type Article
Acceptance Date Jul 19, 2020
Online Publication Date Jul 20, 2020
Publication Date Nov 10, 2020
Deposit Date Nov 10, 2020
Journal Journal of Sound and Vibration
Print ISSN 0022-460X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 486
Article Number 115593
Keywords Mechanical Engineering; Acoustics and Ultrasonics; Mechanics of Materials; Condensed Matter Physics
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