This paper presents an objective method for estimating the performance of 3D microphone arrays, which is also applicable to 2D arrays. The method incorporates the physical characteristics and relative positions of the microphones, merging these elements through a weighted summation to derive the arrays' directional patterns. These patterns are represented as a "Modified Steering Vector." Additionally, leveraging the spatial properties of spherical harmonics, we transform the array's directional pattern into the spherical harmonic domain. This transformation enables a quantitative analysis of the physical properties of each component, providing a comprehensive understanding of the array's performance. Overall, the proposed method offers a deeply insightful and versatile framework for evaluating the performance of both 2D and 3D microphone arrays by fully exploiting their inherent physical characteristics.
