The main subject of this paper is the aberrations of optical systems in which the various media may have axial distributions of index. The general formulas for the transfer contributions to the third-order aberrations take a particularly simple form for an axial distribution. A numerical illustration of the use of the various formulas is given. In particular, the depth of a given index distribution has little effect on the transfer contributions, whereas the inhomogeneous surface contributions may be quite sensitive to depth.
P. J. SANDS, "Inhomogeneous Lenses, IV. Aberrations of Lenses with Axial Index Distributions," J. Opt. Soc. Am. 61, 1086-1091 (1971)