Simple approach to the generalized Minkwitz theorem.

The Minkwitz theorem plays an important role in the design of progressive addition lenses. Recently, this theorem has been generalized by Esser et al. [J. Opt. Soc. Am. A34, 441 (2017)10.1364/JOSAA.34.000441JOAOD60740-3232] to non-umbilic lines under the assumption of a symmetric surface. We present a simplified derivation and generalize their findings to arbitrary but sufficiently smooth surfaces.