Relationship between the critical points and the semiperiodic zones in scalar diffraction

Abstract

Two different concepts arise in the context of scalar diffraction theory: the critical points of the stationary phase approximation for the calculation of highly oscillatory integrals (such as the diffraction integrals) and the semiperiodic zone construction (due to Fresnel) for the application of the Huygens principle. The present work aims at showing the relationship between both concepts when a diffracting aperture is present. The main result is that the position of the critical points indicates the most relevant semiperiodic zones for the calculation of the diffracted field. Consequently, simple numerical algorithms for the computation of diffraction integrals will be devised.