  The optical aberrations of a system can be described in terms of the wave
aberrations, defined as the departure from the ideal spherical wavefront; or
the ray aberrations, which are in turn the deviations from the paraxial ray
intersection measured in the image plane. The classical connection between the
two descriptions is an approximation, the error of which has, so far, not been
quantified analytically. We derive exact analytical equations for computing the
wavefront surface, the aberrated ray directions, and the transverse ray
aberrations in terms of the wave aberrations (OPD) and the reference sphere. We
introduce precise conditions for a function to be an OPD function, show that
every such function has an associated wavefront, and study the error arising
from the classical approximation. We establish strict conditions for the error
to be small. We illustrate our results with numerical simulations. Our results
show that large numerical apertures and high-frequency OPD functions yield
larger approximation errors.
