This paper develops the theory of aberrations of concentric optical systems, supposed nontelescopic. In Part One the monochromatic-aberration coefficients of orders three, five, and seven, and some paraxial and nonparaxial chromatic-aberration coefficients are obtained explicitly on the basis of known relations from the algebraic theory of general systems. Part Two extends the algebraic theory of concentric systems to all orders, the displacement being exhibited in closed form involving a single unspecified function, i.e., the spherical-aberration function. The Hamiltonian theory of concentric systems is briefly considered in Part Three.
H. A. BUCHDAHL, "Optical Aberration Coefficients. X. Theory of Concentric Optical Systems," J. Opt. Soc. Am. 52, 1361-1364 (1962)