If the glasses constituting a symmetric optical system are inhomogeneous, any chromatic paraxial-aberration coefficient can be expressed as a sum of the usual surface contributions, together with a sum of integrals over each inhomogeneous medium. The explicit form of the various contributions to the chromatic paraxialaberration coefficients of the first and second chromatic degree are written down. Given the dependence of the refractive index on both wavelength and position, these formulas can be used to compute the chromatic paraxial-aberration coefficients. The effectiveness of the inhomogeneities as additional degrees of freedom for the control of chromatic aberrations is discussed. Some recent work on the dispersion of glasses is reported. This work supports the use of Buchdahl’s dispersion formula and color coordinate ω in the context of the chromatic aberrations of systems operating in the visible part of the spectrum.
P. J. SANDS, "Inhomogeneous Lenses, II. Chromatic Paraxial Aberrations," J. Opt. Soc. Am. 61, 777-783 (1971)