Properties of the transformation from the spherical wave expansion to the plane wave expansion

The transformation between the spherical wave expansion (SWE) and the plane wave expansion (PWE) is investigated with respect to a range of its fundamental properties. First, the transformation of individual spherical waves is studied in order to understand how these contribute to the different regions of the plane wave spectrum. Second, the number of spherical waves necessary to accurately determine the PWE over different regions of the spectral domain is investigated. Third, numerical aspects of the transformation are addressed.