In this work an expression for the solution of the Helmholtz equation for wedge spaces is derived. Such propagation spaces represent scenarios for many acoustical problems where a free field assumption is not eligible. The proposed sound field model is derived from the general solution of the wave equation in cylindrical coordinates, using sets of orthonormal basis functions. The latter are modified to satisfy several boundary conditions representing the reflective behaviour of wedge-shaped propagation spaces. This formulation is then used in the context of nearfield acoustical holography (NAH) and to obtain the expression of the Neumann Green function. The model and its suitability for NAH is demonstrated through both numerical simulations and measured data, where the latter was acquired for the specific case of a loudspeaker on a hemi-cylindrical rigid baffle.

Microphone arrays as a means of sound field acquisition have been the topic of extensive research for more than eight decades now. A number of designs have been suggested, each trying to overcome difficulties that are inherent to either the decomposition of the sound field, the transducers in use or the presence of the array itself. This work presents a theoretical analysis of circular microphone arrays that do not measure the sound pressure but the component of its gradient that is tangential to a given boundary. Its performance is compared to that of a conventional pressure sensor array as a benchmark. The focus of the analysis and subsequent assessment lies on spatial aliasing and performance in the presence of noise.

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Microphone arrays have already been successfully applied to record sound fields. They are typically composed of pressure sensors and different designs have been suggested, each trying to overcome practical difficulties, such as transducer noise, spatial aliasing and non-uniqueness of the inverse solution. Typical designs are of spherical (3D) or circular form (2D) and use pressure sensors. The array corpus is usually either solid or as acoustically transparent as possible. In this paper, the theoretical model of a circular microphone array, observing the tangential component of the pressure gradient on its boundary is presented.