Acoustic far-field prediction based on near-field measurements by using several different holography algorithms

Near-field acoustical holography (NAH) is a useful tool for sound field reconstruction and sound source identification. In NAH, a basis model is first selected to represent the physical sound field, and then a near-field measurement is made with a microphone array. Next, the parameters in the selected model can be estimated based on the measurements by using an inverse approach, resulting in the sound field near the source being reconstructed so that the sound source location can be identified. But, in addition to being able to reconstruct the near-field of a source, the far-field can also be predicted with the identified sound source model. A significant amount of work has been performed to study the near-field reconstruction capability of different NAH algorithms, but there has been a limited number of publications in which the far-field prediction accuracy, based on the near-field measurement constructed model, has been considered. In the present experimental work, two multi-transducer loudspeakers were placed side-by-side to create a multi-component sound source, and two sets of measurements were conducted: an intensity probe scanned the sound field generated by the loudspeakers in both the near-field (0.05 m) and far-field (0.48 m) such that the true near- and far-field intensity spatial distributions and total sound power could be identified. Then, based on the near-field pressure measurements, four acoustical holography algorithms, statistically optimized near-field acoustical holography, wideband acoustical holography, l₁-norm minimization, and a hybrid compressive sampling method were used to predict the near- and far-field sound intensity distributions. The near- and far-field prediction results were compared with the direct measurement, and the sound field reconstruction accuracy was studied. It was found that all of the algorithms were able to reconstruct the near-field well when the near-field measurements were used to construct the model. It was found that with the abovementioned models, far-field reconstructions could correctly predict the spatial sound field distribution, but in all of the cases, the total sound power was underestimated.