Paraxial Propagation of Astigmatic Wavefronts in Optical Systems by an Augmented Stepalong Method for Vergences

PURPOSE: The propagation of astigmatic wavefronts through astigmatic optical systems is reconsidered in the wavefront perspective. METHODS: The stepalong method for vergences, described by 2x2 matrices, is applied and augmented to produce off-axis information like the magnification. This so-called augmented stepalong method (ASAM) is derived by applying the paraxial propagation of astigmatic wavefronts to tilted wavefronts as well. RESULTS: The features of the ASAM are discussed for a single surface, a thick lens, and a general system. CONCLUSIONS: The ASAM provides all necessary information to describe a centered astigmatic optical system in paraxial approximation.