The Gaussian beam mode analysis of classical phase aberrations in diffraction-limitedoptical systems

Abstract

Gaussian beam mode analysis (GBMA) offers a more intuitive physical insightinto how light beams evolve as they propagate than the conventional Fresneldiffraction integral approach. In this paper we illustrate that GBMA is acomputationally efficient, alternative technique for tracing the evolution ofa diffracting coherent beam. In previous papers we demonstrated thestraightforward application of GBMA to the computation of the classicaldiffraction patterns associated with a range of standard apertures. In this paperwe show how the GBMA technique can be expanded to investigate the effects ofaberrations in the presence of diffraction by introducing the appropriatephase error term into the propagating quasi-optical beam. We compareour technique to the standard diffraction integral calculation for coma,astigmatism and spherical aberration, taking—for comparison—examplesfrom the classic text ‘Principles of Optics’ by Born and Wolf. We showthe advantages of GBMA for allowing the defocusing of an aberratedimage to be evaluated quickly, which is particularly important and usefulfor probing the consequences of astigmatism and spherical aberration.