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Applied Optics

Applied Optics


  • Vol. 25, Iss. 19 — Oct. 1, 1986
  • pp: 3585–3588

Conic that best fits an off-axis conic section

Octavio Cardona-Nunez, Alejandro Cornejo-Rodriguez, Rufino Diaz-Uribe, Alberto Cordero-Davila, and Jesus Pedraza-Contreras  »View Author Affiliations

Applied Optics, Vol. 25, Issue 19, pp. 3585-3588 (1986)

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To help in the fabrication of off-axis conic sections, we present a method to approximate this off-axis section by an on-axis conic centered on the portion desired. This method is based on the method of continuum least squares to obtain the vertex’s curvature and conic constant of the fitted conic on-axis, given the curvature at the vertex and the conic constant of the parent conic from where we want the section and the size of that section. Simple analytic expressions for the curvature and conic constant are derived in terms of the parameters of the off-axis section.

© 1986 Optical Society of America

Original Manuscript: May 19, 1986
Published: October 1, 1986

Octavio Cardona-Nunez, Alejandro Cornejo-Rodriguez, Rufino Diaz-Uribe, Alberto Cordero-Davila, and Jesus Pedraza-Contreras, "Conic that best fits an off-axis conic section," Appl. Opt. 25, 3585-3588 (1986)

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  1. G. LeMaitre, “Compensation des Aberrations par Elasticite,” Nouv. Rev. Opt. 5, 361 (1974). [CrossRef]
  2. J. Lubliner, J. E. Nelson, “Stressed Mirror Polishing. 1: A Technique for Producing Nonaxisymmetric Mirrors,” Appl. Opt. 19, 2332 (1980). [CrossRef] [PubMed]
  3. A. S. Leonard, “The New Science of Tilted-Mirror Optics and Its Application to High Performance Reflecting Telescopes,” presented at Western Amateur Astronomers and Association of Lunar and Planetary Observers, San Diego (1969), p. 31.
  4. O. N. Stravroudis, The Optics of Rays, Wavefronts and Caustics (Academic, New York, 1976), pp. 88 and 91.

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