Basic theory and properties of statistically optimized near-field acoustical holography

To avoid the requirement set by standard near-field acoustical holography (NAH) to measure an area that fully covers the source, a set of so-called patch NAH methods has been introduced. One such method is the statistically optimized NAH (SONAH). In this method, the acoustic quantities on a mapping surface near the measurement surface are calculated by using a transfer matrix defined in such a way that all propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy. The present paper gives an overview of the basic theory of SONAH, including a description of phenomena such as spatial aliasing and wave-number domain leakage. A revised and generalized mathematical formulation is given, covering the calculation of all three components of particle velocity and the use of up to six virtual source planes. A set of formulas for the inherent estimation error level of the method is derived and used to visualize the regions of validity of the SONAH predictions for some typical microphone array geometries. The sensitivity of the inherent error level distribution to changes in the parameters of the SONAH algorithm is also investigated.