A computing scheme involving only 19 entries per surface is developed for the calculation <i>ab initio</i> of the coefficient of tertiary spherical aberration (and incidentally also the primary and secondary coefficients), and the contributions thereto by the individual (spherical) refracting surfaces of a centered system. A detailed example is provided.
H. A. BUCHDAHL, "Optical Aberration Coefficients. I. The Coefficient of Tertiary Spherical Aberration," J. Opt. Soc. Am. 46, 941-941 (1956)