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.