General scheme for paraxial ray tracing and aberration calculation in inhomogeneous media

A set of general formulae for paraxial ray tracing in inhomogeneous media a re derived, which can be used together with the aberration formulae by Sand s for the first- and third-order analyses of inhomogeneous lenses of all ki nds of gradient function. The choice of an optimum step size for paraxial r ay tracing and aberration integration is discussed, and it is shown that re sults with good accuracy can be obtained with a relatively large step size and very economic computing effort, even for complex gradient functions suc h as the tapered hyperbolic secant.