In the course of the design of an optical system a knowledge of higher order aberration coefficients and of the contributions thereto by the individual surfaces is of great value. The present paper provides a computing scheme for the full set of tertiary (and of course primary and secondary) monochromatic aberration coefficients of symmetrical optical systems composed of spherical surfaces. This particular scheme is intended for use with ordinary desk calculating machines, and comprises only 192 entries of the usual kind per surface. The method of construction of the scheme is discussed, and a complete numerical example provided. The checks used to ensure the correctness of the scheme at the same time test the correctness of certain long sets of equations contained in the author’s monograph on optical aberration coefficients; and one misprint in them was thus discovered. This is corrected here. A new nomenclature for higher order aberrations is proposed.
H. A. BUCHDAHL, "Optical Aberration Coefficients. III. The Computation of the Tertiary Coefficients," J. Opt. Soc. Am. 48, 747-756 (1958)