ABSTRACT
The diffraction formulae of Rayleigh-Sommerfeld and Kirchhoff may all be regarded as mathematical refinements of Huygens' principle (Huygens 1690), according to which the field at some observation point is given as a sum of an infinite number of secondary waves, one from each point in the aperture. The evaluation of this sum often represents a big problem, because the integrands of the double integrals usually vary rapidly over the integration domain. Numerical evaluations of diffraction integrals therefore are time-consuming. This chapter provides a brief review of asymptotic diffraction theories or ray theories, with special emphasis on explaining the basic physical ideas behind them. For the case in which the incident field is a plane or spherical wave, it was first shown by Maggi (1888) and later by Rubinowicz. In the case of a general incident wave, Miyamoto and Wolf (1962b) used the method of stationary phase to show that most of the secondary waves originating at the boundary interfere destructively.
