Generalized Huygens-Fresnel integral for a single small aberration

Abstract

The generalized Huygens-Fresnel (GHF) integral is modified to take into account the effects of a single small arbitrary aberration. This is accomplished by considering the ray transfer matrix (RTM) of an optical element with aberrations as a perturbation of the RTM in the absence of aberrations. The elements of the perturbed RTM is then used to write the kernel of the GHF integral. Effects of the aberration on a gaussian beam are discussed using the complex beam parameter in the presence of aberrations.