Comparison of acoustic radiation modes and spherical harmonic functions in the acoustic field reconstructions of spherical sources

Acoustic radiation modes and spherical harmonic functions, which have been both applied in the acoustic field reconstructions of spherical sources, are very similar in the multi-pole radiation pattern and "group" distribution features. Some researchers regard that the acoustic radiation modes of spherical sources as spherical harmonic functions, nevertheless, it has not been theoretically proved yet. In order to analyze the similarities and differences of these two primary functions in acoustic field reconstruction, the inherent relations between them are established in theory, and the effectiveness and reliability in acoustic field reconstruction are compared. The numerical examples results show that the reconstruction results of the two methods are quite same at middle and high excitation frequencies. However, the method based on spherical acoustic radiation modes achieves better reconstruction accuracy at low excitation frequencies, in particular, in a non-free field with interference sources. The conclusion can be made that the acoustic radiation modes has more advantages, which are instructional for selecting acoustic radiation modes or spherical harmonic functions in the acoustic field reconstructions of spherical sources.