Evaluation of Time Domain Physical Optics Integral on Curved Surfaces

A scheme to evaluate the physical optics (PO) integral in closed form over the curved triangular patches is presented. The PO integral is interpreted as a Radon transform, as a result the PO integral over the curved triangle surface is reduced to a line integral. This line is determined as the intersection of the plane, which is formed by the propagation direction of the incident wave and the observation direction, and curved triangular surface (integration domain). The line integral in time domain can be evaluated in closed-form. A numerical example that shows the validity and accuracy of the scheme is presented.