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.