Shadow boundary incremental length diffraction coefficients for perfectly conducting smooth, convex surfaces


  • Arthur D. Yaghjian,

  • Robert A. Shore,

  • Margaret B. Woodworth


General expressions are obtained for incremental length diffraction coefficients (ILDCs) that can be integrated along the shadow boundaries of perfectly conducting surfaces to correct for the fields radiated by the “shadow boundary current” missing from the physical optics (PO) current approximation. As an initial step in obtaining these shadow boundary ILDCs, uniform high-frequency approximations are derived for the scattered and PO far fields of perfectly conducting circular cylinders illuminated by normally and obliquely incident plane waves. Subtracting the approximate PO far fields from the approximate scattered far fields and separating the resulting fields into contributions from the top and bottom of the cylinder leads to a uniform high-frequency approximation for the fields radiated by the shadow boundary current at a single shadow boundary of the cylinder. The shadow boundary ILDCs are then determined by substituting these high-frequency approximations for the shadow boundary fields into the general formulas derived in previous papers for obtaining three-dimensional ILDCs from the two-dimensional far fields of cylindrical scatterers. Comparisons with the exact eigenfunction solution for plane wave scattering by a sphere show that the integration of the ILDC fields around the shadow boundary of the sphere significantly enhances the accuracy of the PO far fields, especially for large bistatic scattering angles. Finally, the shadow boundary ILDCs are modified to increase their accuracy when they are applied to surfaces with more rapidly varying radii of curvature.