Regularised reconstruction of sound fields with a spherical microphone array

Spherical near field acoustic holography with microphones mounted on a rigid spherical surface is used to reconstruct the incident sound field. However, reconstruction outside the sphere is an ill-posed inverse problem, and since this is very sensitive to the measurement noise, straightforward implementation might lead to disastrous reconstructions. A large number of regularisation tools based on singular value decomposition are available, and it has been found that the acoustic holography problem for certain geometries can be formulated in such a way that similarities to singular value decomposition become apparent. Hence, a number of regularisation methods, including truncated singular value decomposition, standard Tikhonov, constrained Tikhonov, iterative Tikhonov, Landweber and Rutishauser, have been adapted for spherical near field acoustic holography. The accuracy of the methods is examined by means of simulations and measurements, which leads to practical recommendations on the use of regularisation techniques regarding space and frequency.