Spherical wave expansion coefficients for radiation from a planar velocity source

A general theory for obtaining spherical wave function expansion coefficients for a sound beam transmitted by a planar velocity source is presented. By neglecting evanescent wave components and thus making the proposed method only approximate in the near field, it is shown that these coefficients can be obtained for any expansion point using just the normal velocity condition in the source plane. Additionally, simplifications are presented for axisymmetric sources. Results are compared with direct numerical evaluation of the Rayleigh integral for source conditions corresponding to a circular and rectangular piston. The present theory can be used in calculations of acoustic scattering and radiation force for spherical objects, or in spherical acoustical holography applications.