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.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





Zachary Collins, Fourier, NAH, interior, acoustics, near-field acoustical holography, interpolation, particle velocity, wave separation, Tamura, six-microphone probe