Numerical consideration and some improvement of corner diffraction formulas applicable to spherical wave incidence

Abstract Diffraction by a corner is one of the canonical problems remaining unsolved. However, several practical formulas have been proposed; any one of which must be able to be incorporated in the geometrical theory of diffraction (GTD). Of these, the corner diffraction formulas that can be applied to the spherical wave incidence are Burnside‐Pathak's formula (BP formula) and Zhang's formula (Z formula). In this paper, the BP formula and the Z formula are numerically compared by means of a hypothetical model consisting of a quarter infinite plane and an infinitesimal dipole. It is found that the BP formula and the Z formula become similar as long as they are not applied near the shadow boundary. The BP formula requires the edge parameters in the numerical process despite dealing with the corner diffraction. On the other hand, the Z formula needs only the parameters related to the corner. However, this formula experiences small discontinuity when the shadow boundary is traversed. In this paper, an empirical modification function is introduced into the Z formula so that a new corner diffraction formula (MZ formula) is proposed so that the diffracted field is uniform and continuous across the boundaries.