ALGEBRAIC CORRECTIONS FOR PARAXIAL WAVE-FIELDS

Asymptotic analysis of the angular spectrum solution for diffraction i s used to establish the validity of a standard, formal series for nonp araxial wave propagation. The lowest term corresponds to the field in the Fresnel approximation, and this derivation clarifies some of the r emarkable aspects of Fresnel validity for both small and large propaga tion distances. This asymptotic approach is extended to derive simple, generic algebraic corrections to the field estimates found by using t he paraxial model, i.e., the Fresnel approximation. Contour maps of th e field errors associated with the diffraction of collimated beams-bot h uniform and Gaussian-in two and three dimensions demonstrate the eff ectiveness of these corrections. (C) 1997 Optical Society of America.