Reconstruction of source distributions from sound pressures measured over discontinuous regions: multipatch...

In the present work, a method of alternating orthogonal projections is described in the context of near-field acoustical holography; it allows missing (or "not measured") data to be recovered, thus relieving the strictness of measurement requirements related to the use of the discrete Fourier transform. The method described here provides the detailed foundation for the patch holography procedure that has previously been introduced to mitigate finite measurement aperture effects by allowing the sound field to be iteratively extended beyond the measurement aperture. It is also shown that the latter iterative algorithm can be used regardless of the spatial distribution of measured data: i.e., patches can be discontinuous. Numerical simulations performed by using a synthetic sound field created by a point-driven, simply supported plate were used to demonstrate the latter point. In particular, a multipatch holography procedure is described that allows a source distribution to be reconstructed from the hologram pressure measured over multiple, unconnected patches. It is finally shown that a related approach allows spatial resolution enhancement by interpolation between measured points.