In the late 1970s, a method was developed to estimate acoustic intensity in one dimension by taking the cross-spectral density of two closely-spaced microphone signals. Since then, multimicrophone probes have been developed to measure three-dimensional intensity as well as energy density. Their usefulness has led to the design of various types of multimicrophone probes, the most common being the four-microphone orthogonal, the four-microphone regular tetrahedron, and the six-microphone designs. These designs generally either consist of microphones suspended in space near each other or mounted on the surface of a sphere. This work analytically compares the relative merits of each probe design in measuring acoustic intensity and investigates the various finite-sum and finite-difference processing methods used with each. The analysis is limited to probes consisting of perfect point sensors in plane wave fields. The comparison is given in terms of average and maximum errors for intensity magnitude and direction as a function of angle of incidence as well as the spread between maximum and minimum errors for intensity magnitude. After existent probe geometries are reviewed, optimization techniques are introduced to predict what the optimal probe geometry would be for any given scenario. The probe is optimized to give the lowest intensity error averaged over angle of incidence of plane waves. This is done for full-space and half-space scenarios.

Recent advances in near-field acoustical holography (NAH) have expanded the theory to interior spaces where multiple sources and/or reflections are present. In 1990, Tamura presented the spatial Fourier transform separation method to measure the reflection coefficient at oblique angles using two measurement planes in the wave number domain. This paper adapts the spatial Fourier transform separation method for application in interior NAH. A practical exploration of important experimental parameters is performed, which include the relative amplitudes of primary and disturbing sources, the measurement plane separation distance, and an acceptable noise floor. This technique is successfully applied in a reverberant environment to reconstruct the velocity of a clamped vibrating plate. NAH methods based on the measurement of pressure and particle velocity have led to the ability to reduce the required measurement locations. Other recent advances in NAH have expanded the theory to interior spaces where multiple sources and/or reflections are present. This paper investigates the use of interpolation techniques to reduce the required measurement locations for interior NAH. Specifically, the benefits of a bi-cubic Hermite surface patch interpolation are discussed and compared to other interpolation routines. Although the required inputs for the Hermite interpolation can be measured using a variety of devices, a scanning six-microphone probe in a tetrahedral configuration is suggested. The six microphones are utilized to simultaneously sample pressure on two parallel planes and estimate the pressure gradients on both of these planes. The two interpolated measurement holograms are used to separate the incoming and outgoing waves using the spatial Fourier-transform method. Analytical simulations of simply supported plates are shown as well as experimental results in a reverberation room to characterize the reduction in measurement locations. Depending on the spatial frequency of the hologram, a measurement location reduction of 20–80% was observed.