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 background of the patch holography procedure that has previously been introduced to mitigate the finite measurement aperture effect by allowing the extension of the sound field beyond the measurement aperture based on the use of an iterative algorithm; it is also shown that the latter iterative algorithm can be used regardless of the spatial distribution of measured data. Numerical simulations were performed by using a synthetic sound field created by a point-driven, simply supported plate to demonstrate the latter point: a multi-patch holography procedure is described that allows a sound field to be reconstructed from the hologram pressure measured over multiple, unconnected patches, and it is also shown that a related approach allows spatial resolution enhancement by interpolation between measured points, thus helping to improve the reconstruction accuracy, particularly at high frequencies.
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