Hybrid integration technique for efficient and accurate computation of diffraction integrals

Numerical evaluation of diffraction integrals is often time consuming because the integrand is a rapidly varying function. Therefore much effort has been expended in developing asymptotic techniques. However, these techniques are invalid in many circumstances, for example, in the vicinity of caustics and cusps of geometrical or diffracted rays. When asymptotic theories fail, efficient computation can be obtained by using a hybrid integration technique, which combines numerical integration with asymptotic methods. The accuracy, applicability, and computational savings of this hybrid technique are examined.