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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition by Tim Mellow, Leo Beranek

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13.19. Near-field acoustical holography [8]

The forward problem

In Section 13.3 we stated that an infinite plane counts as a closed surface over which a boundary surface integral may be evaluated because it isolates the sources on one side of the plane from the observation field on the other. You will also recall from Section 13.15 that the far-field pressure distribution is the Fourier transform of the velocity distribution over an infinite plane. To calculate the near-field pressure we also have to take the inverse Fourier transform, and this technique is known as near-field acoustical holography. If we take the Fourier Green's function of Eq. (13.33) and insert it into the dipole part of the Kirchhoff–Helmholtz boundary integral of ...

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