Construction and selection of a directivity wave function improving ill-condition problems in equivalent source method based near-field acoustic holography

Sound-field reconstruction via the equivalent source method presents an ill-conditioned problem. This paper proposes a method in which traditional monopole equivalent source spherical wave functions are replaced with strong directional wave functions such that an ill-conditioned problem can be improved upon when building the integral equations of a near-field acoustic holography model. Using directional wave functions as an integral kernel function can cause the transfer matrix to be main-diagonally dominant. The accuracy of the proposed method for sound-field reconstruction is verified using numerical simulations, and reconstruction stability in the presence of measurement noise is considered. Furthermore, a method for selecting directional wave functions that are appropriate for various model parameters is introduced. The results show that the proposed method can greatly reduce the condition number of the transfer matrix and improve reconstruction stability.