Chromatic paraxial aberration coefficients for radial gradient-index lenses

A simple derivation of analytic expressions for the chromatic paraxial aberration coefficients of radial gradient-index lenses is presented. By decomposing the transverse chromatic aberration vector of an arbitrary paraxial ray in contributions from refraction at the surfaces and from transfer through the inhomogeneous media of the system, remarkably short formulas for the contributions of transfer through the gradient medium to the axial and lateral color coefficients are obtained. In the thin-lens approximation these expressions lead to well-known results for the total chromatic aberrations of a radial gradient-index lens.