Vertex radius measurement of an off-axis parabola with a three-ball spherometer

Margaret Z. Dominguez, Jianxin Li, Ping Zhou, James H. Burge

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A spherometer is often used to precisely measure the radius of curvature of a spherical surface. It can also measure the vertex radius of a more complex surface such as an off-axis parabola (OAP). This paper provides a reliable algorithm to find the vertex radius of an OAP by solving a few equations based on the test geometry. This algorithm can also be easily expanded to any conic surface with high-order aspheric coefficients. The algorithm was verified by measuring an 8-inch diameter OAP and comparing the results with its known prescription. Results show good agreement. An example of measuring the vertex radius of a 4-m diameter OAP is also presented. In addition to this, a calculation was done to show that the coma and astigmatism are independent of the clocking of the spherometer on the optic.

Original languageEnglish (US)
Article number124107
JournalOptical Engineering
Issue number12
StatePublished - Dec 1 2016


  • Spherometer
  • off-axis paraboloid
  • vertex radius

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • General Engineering


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