It is shown how the results of a previous paper [J. Opt. Soc. Am. 52, 20 (1962)] may be used to deduce computing formulas for the aberration produced by refraction at either a spherical or aspheric surface. The secondary and higher-order aberrations are seen to fall into two parts, one independent of, and the other dependent on, the aberrations of prior surfaces. The method is illustrated by deriving the computing formulas for the primary and secondary aberrations. The computing formulas are applied to a triplet, and the results are compared with the values of the ray aberration found by ray tracing.
E. F. DENBY, "Monochromatic Aberrations of Symmetrical Optical Systems. II. Computing Formulas," J. Opt. Soc. Am. 52, 25-29 (1962)