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

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