Abstract
<jats:p>The article discusses the limitations of scalar or vector wave expansion of the electromagnetic field. It is shown the values of the radiation pattern can be taken as the amplitudes of scalar plane waves propagating in the corresponding directions. The weight function that selects a single linear combination of two plane waves propagating towards each other is proposed. Due to this, the accuracy of the scalar plane wave expansion into a single spectrum in the entire space was significantly increased. In addition, a unit sphere discretization into triangular polygons, followed by the diffraction integrals calculation for each polygon was proposed. This solution made it possible to significantly increase the distance at which the wave field can be decomposed into a finite sum of scalar plane waves. The proposed scalar plane wave expansion allows calculation the wave field close to its sources. The conducted assessments showed methodological errors outside the minimum sphere enclosing the sources are equivalent to stray signal at a level less than −40 dB.</jats:p>