Sampling Rules for an Inhomogeneous Plane-Wave Representation of Scattered Fields

Inhomogeneous plane waves (IPWs) based on a linear contour deformation provide an accurate and concise field representation for scattering problems in which source and observation domains are visible within a limited angular sector. Given an error level, we derive closed-form expressions for the truncation limit, the sampling step, and the contour slope that minimize the number of plane waves. A relation is drawn between the required number of plane waves and the degrees of freedom of the field, defined as the minimum number of orthonormal basis functions that represents scattered fields. The sampling rules are then applied to an efficient evaluation of the physical optics radiation integral.