Visibility of a spherical disk illuminated by a plane wave under the grazing incident

The electromagnetic wave diffraction by a PEC axially symmetric screen has been considered. In [H. Chou et al., 2001; G. Morris, 1980] the problem was solved using Geometrical and Physical Optics methods. In the present paper the exact Maxwell equations with fields, which satisfy Sommerfeld radiation condition, Meixner edge condition and PEC boundary condition on the rotation surface are solved using the rigorous theory of singular and hypersingular integral equations. In [G. Morris, 1980], the authors reduced the above-mentioned problem to a set of integrodifferential one-dimensional equations and solved it numerically using piecewise constant presentation of unknown functions. However, this method converges only for the E-polarized axially symmetric problem. PEC spherical disk was considered in [S.S. Vinogradov, 1983] by the method of analytical regularization. This method has a controlled accuracy, but using the method presented in [S.S. Vinogradov, 1983] only the problem with a plane wave propagating along the axis of the spherical disk can be solved. In contrast, the method presented here has a guaranteed convergence for an arbitrary primary field.