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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 2 — Feb. 1, 2012
  • pp: 174–178

Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays

Psang Dain Lin and Chung-Yu Tsai  »View Author Affiliations

JOSA A, Vol. 29, Issue 2, pp. 174-178 (2012)

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Snell’s law describes the relationship between the incidence angle and reflection (or refraction) angle of a light ray impinging on the interface between two different isotropic media. In this paper, Snell’s law is used to derive the unit normal vectors of an aspherical surface given a knowledge of the unit directional vectors of the incoming and outgoing rays. The proposed method has important applications in the design and fabrication of aspherical surfaces since the surface normal vectors determine not only the optical performance of the surface but also the cutting tool angles required to machine the surfaces.

© 2012 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design
(080.3620) Geometric optics : Lens system design
(080.1753) Geometric optics : Computation methods
(080.4225) Geometric optics : Nonspherical lens design
(080.4228) Geometric optics : Nonspherical mirror surfaces

ToC Category:
Geometric Optics

Original Manuscript: October 4, 2011
Revised Manuscript: November 9, 2011
Manuscript Accepted: November 9, 2011
Published: January 17, 2012

Psang Dain Lin and Chung-Yu Tsai, "Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays," J. Opt. Soc. Am. A 29, 174-178 (2012)

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