Fringe wave calculation at a finite distance from a perfectly conducting wedge

The physical theory of diffraction (method of the fringe waves) is an exceptionally fruitful theory, which has not lost its relevance up to now. The fringe wave from the edge of a perfectly conducting wedge makes it possible to clarify the solution obtained by the method of physical optics in those cases where the electrical size of the object does not make it possible to use direct numerical methods. For radar problems, when the distance between the radar and the object is large enough, the scattered field in the observation point has the form of a plane wave, so the angle diagrams of the fringe wave do not depend on the distance. However, in the general case, such dependence may exist, and this issue needs additional research. The second problem is that the source may be located at a finite distance from the edge, in which case we should assume that the incident wave is not a plane wave but a cylindrical one. Therefore, it is necessary to investigate fringe waves in the line-source excitation.

It was shown that the use of uniform asymptotic formulas for the plane wave incident on a half-plane leads to a difference from P.Ya. Ufimtsev's results in the region of the grazing angles. When the wedge is excited by a cylindrical wave (line-source), the calculation results may also deviate from the well-known angle diagrams obtained by the physical theory of diffraction. The calculation results are in complete agreement with P.Ya. Ufimtsev's theory when the line-source and the observation point are moved away from the edge at infinity.

The obtained results allow expanding the applicability of the physical theory of diffraction and providing a methodological basis for solving a more complex problem for a fringe wave when impedance wedge is excited with line-source.