Minimum and absolute minimum spherical aberration of a simple, thin lens

TLDR: In this article, an equation is derived for minimizing the aberration itself, instead of the function Ls, and on the basis of the equation the object image distances can be found for which a given lens will exhibit an absolute minimum spherical aberration.

Abstract: Traditional treatments of third‐order spherical aberration of a thin lens express the results in terms of a function Ls, involving a lens shape factor q and an object‐image position factor p. The function Ls is defined in terms of the difference of the reciprocal paraxial and zonal image distances instead of the difference in distances, which is actually the longitudinal spherical aberration. The treatments show that a lens will have minimum spherical aberration for a shape q determined by minimizing Ls relative to q for a given p. In the present work it is shown that the same lens will actually exhibit smaller spherical aberration for values of p<0 determined by minimizing Ls relative to p. An equation is derived for minimizing the aberration itself, instead of the function Ls, and on the basis of the equation the object‐image distances can be found for which a given lens will exhibit an absolute minimum spherical aberration. The results of the analyses are in good agreement with the results of mathemati...