The aim of this contribution is to derive third-order aberration (Seidel) coefficients for a thick lens in air with arbitrary focal length. The explicit analytic dependence of individual aberration coefficients on a lens thickness will be presented. Such formulas make possible to analyze an influence of the lens thickness on lens aberration properties and the replacement of a thick lens optical system by a thin lens model. Equations are described for the re-calculation of aberration coefficients for a different value of focal length and a different value of entrance pupil position. The presented formulas have a fundamental importance for the optical design of optical systems consisting several thick lenses, because these formulas show the influence of the thickness of individual lenses on aberrations of the whole optical system. Furthermore, the thickness of individual lenses can be analytically calculated in order the lens had a required value of specific aberration. The designed optical system then may serve as an initial system for further optimization using optical design software.
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