This chapter discusses the asymptotic theory of diffraction. The geometrical theory of diffraction (GTD) was conceived by Keller. Later, he showed that diffraction phenomena can be incorporated into a geometrical strategy and phrased in geometrical terms by introducing diffracted rays. These rays have paths determined by a generalisation of Fermat's principle. The concept of diffracted rays was developed by Keller from the asymptotic evaluation (as the wave number k tends to infinity) of the known exact solution to scattering from simple shapes, referred to as the canonical problems of GTD.

This chapter discusses hybrid diffraction coefficients. A hybrid diffraction coefficient is a combination of the diffraction coefficients corresponding to two types of diffraction phenomena. We consider here the combination of edge diffraction with the launching of creeping waves or the reciprocal situation of a creeping wave diffracted by an edge.

Hybrid methods were introduced in the early 1970s for solving some difficulties encountered with asymptotic methods. A typical situation is the diffraction of an object which is large compared to the wavelength but which has locally in some specific areas a complexity in the geometry (fine details) or in the boundary conditions (thick penetrable material) which fall outside the domain of applicability of asymptotic methods. To this category of targets, we also need to add singularities of the surface for which no explicit expressions for the coefficient of diffraction exist.