A concise, purely algebraic theory of the monochromatic primary aberrations of the symmetrical optical system is developed by means of a method depending on the consideration of quantities which reduce to optical invariants in the paraxial limit. The derivation of summation theorems is rendered superfluous. At every stage the order of the errors committed in the various approximations involved is considered in detail, with a corresponding gain in rigor. The equations for the final aberrations are derived in a well-known form. They contain aberration coefficients closely resembling the usual Seidel sums, and reducing to the latter when all the refracting surfaces are spherical. The increase in the labor involved in computing these more general sums is very small.
H. A. BUCHDAHL, "Algebraic Theory of the Primary Aberrations of the Symmetrical Optical System," J. Opt. Soc. Am. 38, 14-18 (1948)