An additional physical interpretation in the Luneburg-Kline expansion

The Luneburg-Kline (LK) expansion provides an asymptotic representation of the reflected field from a smooth surface in inverse powers of k. The physical interpretation of the first term in the expansion has long been recognized. The physical significance of the second term is suggested here. Through analysis of the expansion for a parabolic, circular, and elliptic cylinders, further geometric information is seen other than the radius of curvature at the specular point. The other geometric information is the distance between the specular point and the incident shadow boundary.