The boundary integral equation (BIE) on interior walls with surface impedance conditions is implemented to the iterative physical optics method and how to treat the singularities involved in the BIE of an impedance cavity is described. Singular integrals over a rectangular region can be represented by simple elementary functions.

Expressions are derived for estimating the scattered and diffracted field in the presence of the polygonal cylinder using high frequency technique which is closely related with equivalent current or equivalent moment method proposed formerly. As the first step, we verified the method by applying it to various kinds of polygonal cylinders. The numerical results for radiation patterns are compared with those obtained by other methods when they are available. The agreement between them is fairly good and difference between them is not recognised in the figures except in a small part of region where observation point lies near a shadow boundary of the polygonal cylinder. The discrepancy is few decibels. Next we study a possibility of estimating the diffracted field of smooth convex cylinder by approximating it with corresponding polygonal cylinder. As an illustration we consider radiation of electric and magnetic line source in the presence of conducting circular cylinder since the exact solution of the problem is readily obtained. The approximation of smooth object with corresponding edged object is found to be useful from the standpoint of diffraction. The method is also applied to estimate the diffracted field by curved wedge and curved half plane.

The radar cross section (RCS) of a dielectric-coated cylindrical cavity was measured and the measurements were compared with those calculated according to the iterative physical optics (IPO). The IPO analysis used the equivalent-impedance boundary condition (EIBC) based on transmission-line theory which takes into account the thickness of the coating. It was consequently found that this condition is much more effective than the ordinary-impedance boundary condition based on the intrinsic impedance of the material.

A correction of the physical optics approximation by accounting for the presence of specific currents concentrated near shadow boundaries on the surface of a convex non-metallic scatterer is analysed by considering a canonical problem of diffraction of a plane electromagnetic wave incident normally to the axis of an infinite circular cylinder with impedance boundary conditions. The analysis focuses on the development of Fock-type asymptotic representations for magnetic field tangent components on the surface of the scatterer. The Fock-type representation of the surface field is uniformly valid within the penumbra region, providing a continuous transition from the geometrical optics formulas on the lit portion of the surface to the creeping waves approximation in the deep shadow region. A new numerical procedure for evaluating Fock-type integrals is proposed that extracts rapidly varying factors and approximates the rest, slowly varying coefficients via interpolation. This allows us to obtain accurate and simple representations for the shadow boundary currents that can be directly inserted into the radiation integral and effectively integrated. We show that accounting for the shadow boundary currents considerably improves the traditional PO analysis of the high-frequency electromagnetic fields scattered from smooth and convex non-metallic obstacles, particularly near the forward scattering direction.

Electromagnetic field diffracted by conducting circular disk and circular hole in the conducting plate is formulated by the method of Kobayashi potential. The field is expressed by linear combination of functions which satisfy the required boundary conditions except on the disk or hole. Thus the functions may be regarded as eigen functions of the configuration. By imposing the remaining boundary conditions, we can derive the matrix equations for the expansion coefficients. It may be verified readily that each eigen function satisfies edge conditions for induced current on the disk and for aperture field distribution on the hole. It may also be verified that the solutions for the disk and the hole satisfy Babinet's principle. Matrix elements of the equations for the expansion coefficients are given by two kinds of infinite integrals and the series solutions for these integrals are derived. The validity of these expressions are verified numerically by comparing with the results obtained from direct numerical integrations.

The Kobayashi potential in electromagnetic theory is reviewed. As an illustration we consider two problems, diffraction of plane wave by disk and rectangular plate of perfect conductor. Some numerical results are compared with approximated and experimental results when they are available to verify the validity of the present method. We think the present method can be used as reference solutions of the related problems.