Some extensions of the exact line integral representation of the physical optics scattered field to multiple interactions between planar surfaces

An exact transformation of the double surface integral representation of the electric physical optics (PO) scattered field by two perfectly conducting flat plates, into a double line integral on the contours of the plates and an integral along a generatrix of the cone having the observation point as the vertex and the contour of the second plate as the basis, is presented. It is shown that the integral along the generatrix can be evaluated asymptotically by integrations by parts. To illustrate the exactness of the transformation, comparisons of numerical results obtained from the double surface and the triple line integral representations are performed. Furthermore, the numerical efficiency of the asymptotic evaluation of the inner integral along a generatrix is checked.