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Near-field acoustical holography incorporating compressive sampling: Effect of measurement distance and array density

To identify sound source locations and strength by using near-field acoustical 
holography (NAH), many microphones are generally required in order to span 
the source region and to ensure a sufficiently high spatial sampling rate. It is often the case that hundreds of microphones are needed, so such measurements are 
costly, which has limited the application of NAH in industrial settings. Recently, 
however, it has been shown that it is possible to accurately identify concentrated 
sound sources with a limited number of microphones based on compressive sampling theory. Here, the theory of the four NAH methods that were studied in the 
present work, that is, statistically optimized near-field acoustical holography 
(SONAH), wideband acoustical holography (WBH), l1-norm minimization, and a 
hybrid compressive sampling method, is briefly reviewed. Note that the latter three 
procedures incorporate elements of compressive sampling. Then, a simulation with 
one monopole as the sound source was conducted to illustrate some basic characteristics of these algorithms. In the experimental portion of the work, a multi-element 
loudspeaker was used as the sound source. A near-field intensity scan was conducted 
to measure both the true intensity spatial distribution and the sound power generated 
by the loudspeaker to provide a basis against which the values obtained from the holography reconstructions could be compared. The sound field was reconstructed by 
using both near- and far-field measurements, and the number of microphone measurements used to reconstruct the sound field was systematically decreased by increasing the spacing between microphones. Both in the simulation and experiment, 
the sound field was reconstructed by using the four NAH methods mentioned above. 
Then, the reconstruction results were compared with the measured intensity results in 
terms of spatial localization and sound power, and the benefits of the compressive 
sampling approach are illustrated.