物理绕射理论奇异性研究

物理绕射理论是计算尖劈绕射的重要方法，其重要意义是消除了几何绕射理论所带来的奇异值。本文导出了这两种绕射系数的另一种表达式，可以非常明确地说明奇异值消除情况。将绕射系数写成余切函数的形式，奇异点就体现在宗量为0的情形，这种情形恰好就是入射边界或反射边界。物理绕射理论在绝大多数情况下消除了几何绕射理论带来的奇异值。但在一种特殊情形下，仍然存在着奇异，即绕射波沿着劈面且双站角为180°。这种奇异会导致在有些情形下，双站散射计算误差非常大，而在单站情形不会发生奇异。最后，通过二维方柱和三角形柱的散射算例进行了相关验证。

Study on singularity of physical theory of diffraction

Physical theory of diffraction (PTD) is an important method in calculating wedge’s diffraction whose advantage is eliminating the singularity of geometric theory of diffraction (GTD). Another expression of the diffraction factors is introduced that may clearly imply the singularity. The diffraction factor is transformed into an arc tangent function whose singularity is zero and the singularity happens to be in incident bounds and reflection bounds. The PTD eliminates most of the GTD’s singularities, but they still appear under a very special situation. This situation is that scattering wave incidents on the wedge and the bi-static angle is 180°. The singularity may induce a very huge error in bi-static scattering calculation. But in mono-static, there is no sigularity. The examples of 2-dimensional square and triangle’s scattering problems validate the analytical result.