球面近场声全息中的阵列传声器分布与球面数值积分

球形传声器阵列是实现封闭空间三维声场重构的测量前端,传声器在球形阵列面上的分布对三维声场重构的精度有重要影响。针对球面近场声全息方法,结合I.H.Sloan,Spherical t-designs,J.Fliege等球面数值积分法,检验传声器数目、传声器几何位置分布、积分权重、波数、基函数扩展项数、声场重构半径等参数对声场重构精度的影响。结果表明:Spherical t-designs球面数值积分法与其它积分法相比,在声场重构误差接近的情形下,允许传声器的数目和位置布置有更多的选择,并且在传声器数目一定时,各点积分权重相等,使得球面近场声全息中球面数值积分计算相对简单。 

Microphone distribution and spherical numerical integration for spherical nearfield acoustic holography

Spherical microphone array is utilized to measure sound pressures for reconstructing three dimensional interior sound fields based on spherical nearfield acoustic holography. How to distribute microphones on the sphere surface and to select spherical numerical integration algorithm, such as I. H. Sloan, Spherical t-designs, J. Fliege and etc., are critical to the reconstruction accuracy of sound fields. The numerical simulations are carried out to examine the impact of parameters, the number of microphones, the positions of microphones, the weight of integral at each discrete point, wave number, the term number of basis function expansion, and the radius of reconstruction surface, to the accuracy of reconstruction. The results of numerical simulations show that Spherical t-designs is able to provide more options of the number and positions of microphones within the same range of reconstruction accuracy, and the simplest algorithm due to equal weight for all integral points.