Abstract

This paper presents a clear and rigorous derivation of Feder’s well-known equations for the third-order aberrations. The derivation starts with Born and Wolf’s version of a Hamilton's angle characteristic for a single spherical surface. We then derive the addition theorem of aberrations and write expressions for the third-order ray aberrations of n-surface systems. Finally, we write the aberration expressions in terms of axial and chief rays and derive Feder’s numerically efficient equations for the third-order aberrations.

© 1988 Optical Society of America