Effective Fringe Equivalent Currents Expressions

Fringe equivalent currents expressions derived by Michaeli are finite for all aspects of illumination and observation except for the Ufimtsev singularity. However, they may yield inaccurate results when the direction of the incident ray is near the edge under consideration. Alternative expressions of fringe equivalent currents are derived in this communication to overcome the drawback. They are obtained by asymptotic endpoint evaluation of the fringe currents radiation integral over a proper coordinate between the normal to the edge and the grazing diffracted ray and further modification for the elimination of false singularities. Numerical results are presented to demonstrate the validity of the present expressions.