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. A 34, 441 (2017)] 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. (C) 2017 Optical Society of America
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