Primary aberration coefficients for axial gradient-index lenses

As for homogeneous lenses, for axial gradients the analysis of the Seidel and chromatic aberration coefficients can be very useful in lens design. However, at present few commercial optical design programs list the Seidel aberrations of GRIN lenses and none of them lists the chromatic aberrations. In order to facilitate the computer implementation of the chromatic aberrations of axial GRIN lenses a new mathematical derivation for the axial and lateral color coefficients is presented. Also, new qualitative insight into the properties of axial GRIN lenses is obtained by introducing the thin-lens approximation in the aberration expressions. Within the domain of validity of this approximation, the primary aberrations of an axial GRIN lens are equivalent to those of a pair of homogeneous aspherical lenses in contact, having a common plane surface and having refractive indices and Abbe numbers equal to the corresponding axial GRIN values at the two end surfaces.