A Uniform Diffraction Theory for Wide-Angle Cones

In a recent article (Katsav and Heyman, 2020), we derived an approximate tip-diffraction coefficient for circular wide-angle cones. In the present work, we derive a uniform solution for the field in the geometrical optics (GO) transition zones. The uniform solution has the form of Weber parabolic cylinder function of order -3/2, but far from the transition zones, it reduces to the separate reflection and tip diffraction contributions. The derivation utilizes the approximate spectral integral solution for wide-angle cones derived by Katsav and Heyman (2020), whose form is much simpler than the exact spectral integral solution. The uniform solution is used therefore only inside the transition zone, whereas at large angles it is more accurate to switch to the nonuniform contributions of the reflection and of tip diffraction. The accuracy of the new solution is demonstrated via comparison to the exact conical harmonics solution.