Calculation of diffraction in the presence of aberrations by numerical methods based on critical points and semi-periodic zones

摘要

The numerical calculation of diffraction integrals in systems with aberrations is addressed from the point of view of a new geometrical interpretation of the diffraction phenomena. This interpretation is based on the division of the integration domain in semiperiodic zones that isolate the integrand oscillations. Moreover, the critical points of the aperture allow to identify the zones with a net contribution to the diffracted field. with the help of this interpretation it is possible to define methods for calculating the diffraction of a spherical wave incident on an aperture. We study the problems that arise when these methods have to be applied to waves in aberrated systems and we propose a solution based on the analysis of the behavior of the optical path of the wave incident on the exit pupil of the system.