Computation of the physical optics integral on NURBS surfaces using a radon transform interpretation

Abstract

Physical optics (PO) requires the calculation of a surface integral on a structure, which can be called as the PO integral. The surface of most structures can be accurately represented by nonuniform rational B-spline (NURBS) surfaces. In this letter, the PO integral over NURBS surfaces is reduced to an exact line integral by using a radon transform (RT) interpretation. The integration line is shown to be the time-dependent intersection line of the NURBS surface of interest with a plane determined by the illumination and observation directions. Hence, the accuracy of evaluating the PO integral is limited only by the geometrical evaluations involving the NURBS surfaces. The accuracy of the derived closed form expression is demonstrated through numerical examples.