Closed-form sag solutions for Cartesian oval surfaces

Chun Che Hsueh, Tamer Elazhary, Masatsugu Nakano, Jose Sasian

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


This paper presents a closed-form solution to the sag of the Cartesian oval and an alternate iterative method for obtaining the sag. The emphasis is in providing a methodology for determining the sag and derivatives of a Cartesian surface for optical design, ray-tracing purposes. We verify our results by comparison of our solutions and by real ray tracing.

Original languageEnglish (US)
Pages (from-to)168-175
Number of pages8
JournalJournal of Optics (India)
Issue number4
StatePublished - Dec 2011


  • Aspheric surfaces
  • Cartesian oval
  • Optical design
  • Ray tracing

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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