Data interpolation method based on the wave superposition algorithm

Abstract

Fast Fourier transform-based near-field acoustic holography requires that the acoustic field should be sampled with a uniform spacing which is less than a half wave length of the highest frequency of interest to avoid spatial aliasing. Therefore, a large number of microphones are demanded for high frequencies. To overcome this difficulty and enhance the reconstruction accuracy, a data interpolation method based on the wave superposition algorithm (WSA) is proposed. At first, WSA is employed to regenerate the acoustic pressures between the measurement points. Then, the accuracy of the regenerated data is improved through an iterative process. In the end, taking the interpolated pressures as input data, the acoustic field can be reconstructed precisely with relatively few measurements. To solve the inherent ill-posed problem, Tikhonov regularization method together with generalized cross validation parameter choice method is utilized in the data interpolation method. Numerical simulation and experimental results demonstrate that this method can enhance the reconstruction accuracy and efficiency.