Optimization of spherical numerical integration methods in reconstruction of sound field with spherical microphone array

Abstract

Choosing an effective spherical numerical integration method is one of the key problems in reconstruction of incident sound field by using spherical microphone array based on spherical near-field acoustic holography (SNAH). Many different spherical numerical integration methods are reported, such as I.H.Sloan, Spherical-t design, J.Fliege, etc., each method applies different distributions of discrete positions and integral weights in the design of spherical microphone array. In the paper, the accuracies of sound pressure reconstruction results based on SNAH with different spherical numerical integration methods are examined and compared. It is found that spherical-t integration method can provide more options of discrete points, simple algorithmic due to equal weight of each point, and the same or higher precision of sound pressure reconstruction. Meanwhile, the expansion terms of reconstructed sound pressure has to be truncated at an optimal number in order to minimize the impact of spherical numerical integration error, the approach to choosing the optimal truncated term number with respect of the number of microphones in spherical numerical integration is discussed in details.