Wideband holography based spherical equivalent source method with rigid spherical arrays

Spherical equivalent source method (S-ESM) with rigid spherical arrays is able to achieve good sound field reconstruction and acoustic source identification in three-dimensional free-field spaces. However, the S-ESM solved by the standard Tikhonov regularization is restricted to the low-frequency reconstruction and source identification at small measurement distances. To make S-ESM achieve good reconstruction and source identification at high frequencies and large hologram distances, this study proposes a sparsity-promoting approach denoted as wideband holography based S-ESM (WBH-based S-ESM), which applies a steepest descent method to iteratively solve S-ESM. Firstly, the framework of WBH-based S-ESM is established. Subsequently, to examine its validity, the performance of reconstruction and source identification is compared with Tikhonov regularization. Finally, a focus is concerned with the adaptability to large hologram distances. Several meaningful results have emerged from simulations and experiments: (1) WBH-based S-ESM can make good sound field reconstruction and acoustic source identification at medium-high frequencies. It extends the upper frequency limit of S-ESM. (2) The maximum hologram distance of WBH-based S-ESM at high frequencies is greater than that of Tikhonov regularization. It enlarges the measurement distance of S-ESM. This study will demonstrate the potential of WBH-based S-ESM as a useful tool for reconstruction and source identification.